From 187ab586cb03c2f44811003d88faeb3760eaec25 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?R=C3=A9mi=20Th=C3=A9riault?= <13123390+rempsyc@users.noreply.github.com> Date: Thu, 5 Oct 2023 10:54:04 -0400 Subject: [PATCH] JOSE paper (#586) Co-authored-by: Dominique Makowski Co-authored-by: Daniel --- DESCRIPTION | 5 +- NEWS.md | 4 +- inst/WORDLIST | 24 +- papers/JOSE/apa.csl | 1917 +++++++++++++++++ papers/JOSE/arxiv.sty | 255 +++ papers/JOSE/cover_letter.Rmd | 29 + papers/JOSE/cover_letter.pdf | Bin 0 -> 56483 bytes papers/JOSE/paper.Rmd | 296 +++ .../mybibfile.bib => JOSE/paper.bib} | 19 +- papers/JOSE/paper.log | 1133 ++++++++++ papers/JOSE/paper.md | 325 +++ papers/JOSE/paper.pdf | Bin 0 -> 593364 bytes .../paper_files/figure-latex/model_fig-1.pdf | Bin 0 -> 8485 bytes .../paper.Rmd => JOSE/paper_longform.Rmd} | 118 +- papers/JOSE/table1.jpg | Bin 0 -> 393255 bytes papers/JOSS/{paper.bib => paper_temp.bib} | 0 papers/JOSS/{paper.md => paper_temp.md} | 0 papers/Mathematics/cover_letter.Rmd 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.../figure-latex/unnamed-chunk-5-2.pdf | Bin 6695 -> 0 bytes vignettes/check_outliers.Rmd | 300 +++ vignettes/paper.bib | 161 ++ 38 files changed, 4529 insertions(+), 3797 deletions(-) create mode 100644 papers/JOSE/apa.csl create mode 100644 papers/JOSE/arxiv.sty create mode 100644 papers/JOSE/cover_letter.Rmd create mode 100644 papers/JOSE/cover_letter.pdf create mode 100644 papers/JOSE/paper.Rmd rename papers/{Mathematics/mybibfile.bib => JOSE/paper.bib} (90%) create mode 100644 papers/JOSE/paper.log create mode 100644 papers/JOSE/paper.md create mode 100644 papers/JOSE/paper.pdf create mode 100644 papers/JOSE/paper_files/figure-latex/model_fig-1.pdf rename papers/{Mathematics/paper.Rmd => JOSE/paper_longform.Rmd} (85%) create mode 100644 papers/JOSE/table1.jpg rename papers/JOSS/{paper.bib => paper_temp.bib} (100%) rename papers/JOSS/{paper.md => paper_temp.md} (100%) delete mode 100644 papers/Mathematics/cover_letter.Rmd delete mode 100644 papers/Mathematics/journalnames.tex delete mode 100644 papers/Mathematics/logo-mdpi.pdf delete mode 100644 papers/Mathematics/logo-orcid.pdf delete mode 100644 papers/Mathematics/logo-updates.pdf delete mode 100644 papers/Mathematics/mdpi.bst delete mode 100644 papers/Mathematics/mdpi.cls delete mode 100644 papers/Mathematics/paper.pdf delete mode 100644 papers/Mathematics/paper.tex delete mode 100644 papers/Mathematics/paper_files/figure-latex/model-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/model2-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/multimethod-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/multivariate-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/scatter-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/univariate-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/unnamed-chunk-3-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/unnamed-chunk-4-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/unnamed-chunk-5-1.pdf delete mode 100644 papers/Mathematics/paper_files/figure-latex/unnamed-chunk-5-2.pdf create mode 100644 vignettes/check_outliers.Rmd create mode 100644 vignettes/paper.bib diff --git a/DESCRIPTION b/DESCRIPTION index 933df479a..d72634892 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,7 +1,7 @@ Type: Package Package: performance Title: Assessment of Regression Models Performance -Version: 0.10.5.6 +Version: 0.10.6 Authors@R: c(person(given = "Daniel", family = "Lüdecke", @@ -93,7 +93,9 @@ Suggests: dbscan, estimatr, fixest, + flextable, forecast, + ftExtra, gamm4, ggplot2, glmmTMB, @@ -128,6 +130,7 @@ Suggests: psych, qqplotr (>= 0.0.6), randomForest, + rempsyc, rmarkdown, rstanarm, rstantools, diff --git a/NEWS.md b/NEWS.md index 06eee8f47..bc7687113 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,6 +1,6 @@ -# performance (development version) +# performance 0.10.6 -## General +## General * Support for `nestedLogit` models. diff --git a/inst/WORDLIST b/inst/WORDLIST index adf602827..fbef7c991 100644 --- a/inst/WORDLIST +++ b/inst/WORDLIST @@ -9,6 +9,7 @@ Ankerst Archimbaud Arel Asq +BCI BFBayesFactor BMJ Baayen @@ -75,6 +76,7 @@ Gazen Gelman Gnanadesikan Guilford +HDI HJ Hastie Herron @@ -110,10 +112,10 @@ Killeen Kliegl Kristensen Kullback -Lakens LOF LOGLOSS LOOIC +Lakens Laniado Leibler Lemeshow @@ -123,6 +125,7 @@ Leys Lillo Liu Lomax +MADs MSA Maddala Magee @@ -148,6 +151,7 @@ Nakagawa's Nordhausen Normed ORCID +OSF Olkin PNFI Pek @@ -193,7 +197,6 @@ Tibshirani Tily Tjur Tjur's -Trochim Tsai Tweedie VIF @@ -207,9 +210,9 @@ Visualisation Vuong Vuong's WAIC -WMK Weisberg Windmeijer +Winsorization Witten Xu YL @@ -237,6 +240,7 @@ brmsfit cauchy clusterable concurvity +datawizard dbscan der detrend @@ -252,23 +256,21 @@ fpsyg gam geoms ggplot -github gjo glm glmmTMB glmrob grey heteroskedasticity -homoskedasticity homoscedasticity +homoskedasticity https intra intraclass -io -ize joss kmeans lavaan +lm lme lmrob lmtest @@ -285,18 +287,22 @@ models’ multicollinearity multimodel multiresponse +multivariable nd nonnest overfitted patilindrajeets poisson preprint +priori pscl quared quartile quartiles rOpenSci +recoding rempsyc +reproducibility rescaling rma rmarkdown @@ -308,6 +314,7 @@ se smicd sphericity strengejacke +suboptimal subscale subscales theoreritcal @@ -317,5 +324,8 @@ und underfitted underfitting visualisation +winsorization +winsorize +winsorized xy youtube diff --git a/papers/JOSE/apa.csl b/papers/JOSE/apa.csl new file mode 100644 index 000000000..946c7fcd2 --- /dev/null +++ b/papers/JOSE/apa.csl @@ -0,0 +1,1917 @@ + + \ No newline at end of file diff --git a/papers/JOSE/arxiv.sty b/papers/JOSE/arxiv.sty new file mode 100644 index 000000000..f32d6d899 --- /dev/null +++ b/papers/JOSE/arxiv.sty @@ -0,0 +1,255 @@ +\NeedsTeXFormat{LaTeX2e} + +\ProcessOptions\relax + +% fonts +\renewcommand{\rmdefault}{ptm} +\renewcommand{\sfdefault}{phv} + +% set page geometry +\usepackage[verbose=true,letterpaper]{geometry} +\AtBeginDocument{ + \newgeometry{ + textheight=9in, + textwidth=6.5in, + top=1in, + headheight=14pt, + headsep=25pt, + footskip=30pt + } +} + +\widowpenalty=10000 +\clubpenalty=10000 +\flushbottom +\sloppy + +\usepackage{fancyhdr} +\fancyhf{} +\pagestyle{fancy} +\renewcommand{\headrulewidth}{0pt} +\fancyheadoffset{0pt} +\rhead{\scshape A preprint - \today} +\cfoot{\thepage} + + +%Handling Keywords +\def\keywordname{{\bfseries \emph Keywords}}% +\def\keywords#1{\par\addvspace\medskipamount{\rightskip=0pt plus1cm +\def\and{\ifhmode\unskip\nobreak\fi\ $\cdot$ +}\noindent\keywordname\enspace\ignorespaces#1\par}} + +% font sizes with reduced leading +\renewcommand{\normalsize}{% + \@setfontsize\normalsize\@xpt\@xipt + \abovedisplayskip 7\p@ \@plus 2\p@ \@minus 5\p@ + \abovedisplayshortskip \z@ \@plus 3\p@ + \belowdisplayskip \abovedisplayskip + \belowdisplayshortskip 4\p@ \@plus 3\p@ \@minus 3\p@ +} +\normalsize +\renewcommand{\small}{% + \@setfontsize\small\@ixpt\@xpt + \abovedisplayskip 6\p@ \@plus 1.5\p@ \@minus 4\p@ + \abovedisplayshortskip \z@ \@plus 2\p@ + \belowdisplayskip \abovedisplayskip + \belowdisplayshortskip 3\p@ \@plus 2\p@ \@minus 2\p@ +} +\renewcommand{\footnotesize}{\@setfontsize\footnotesize\@ixpt\@xpt} +\renewcommand{\scriptsize}{\@setfontsize\scriptsize\@viipt\@viiipt} +\renewcommand{\tiny}{\@setfontsize\tiny\@vipt\@viipt} +\renewcommand{\large}{\@setfontsize\large\@xiipt{14}} +\renewcommand{\Large}{\@setfontsize\Large\@xivpt{16}} +\renewcommand{\LARGE}{\@setfontsize\LARGE\@xviipt{20}} +\renewcommand{\huge}{\@setfontsize\huge\@xxpt{23}} +\renewcommand{\Huge}{\@setfontsize\Huge\@xxvpt{28}} + +% sections with less space +\providecommand{\section}{} +\renewcommand{\section}{% + \@startsection{section}{1}{\z@}% + {-2.0ex \@plus -0.5ex \@minus -0.2ex}% + { 1.5ex \@plus 0.3ex \@minus 0.2ex}% + {\large\bf\raggedright}% +} +\providecommand{\subsection}{} +\renewcommand{\subsection}{% + \@startsection{subsection}{2}{\z@}% + {-1.8ex \@plus -0.5ex \@minus -0.2ex}% + { 0.8ex \@plus 0.2ex}% + {\normalsize\bf\raggedright}% +} +\providecommand{\subsubsection}{} +\renewcommand{\subsubsection}{% + \@startsection{subsubsection}{3}{\z@}% + {-1.5ex \@plus -0.5ex \@minus -0.2ex}% + { 0.5ex \@plus 0.2ex}% + {\normalsize\bf\raggedright}% +} +\providecommand{\paragraph}{} +\renewcommand{\paragraph}{% + \@startsection{paragraph}{4}{\z@}% + {1.5ex \@plus 0.5ex \@minus 0.2ex}% + {-1em}% + {\normalsize\bf}% +} +\providecommand{\subparagraph}{} +\renewcommand{\subparagraph}{% + \@startsection{subparagraph}{5}{\z@}% + {1.5ex \@plus 0.5ex \@minus 0.2ex}% + {-1em}% + {\normalsize\bf}% +} +\providecommand{\subsubsubsection}{} +\renewcommand{\subsubsubsection}{% + \vskip5pt{\noindent\normalsize\rm\raggedright}% +} + +% float placement +\renewcommand{\topfraction }{0.85} +\renewcommand{\bottomfraction }{0.4} +\renewcommand{\textfraction }{0.1} +\renewcommand{\floatpagefraction}{0.7} + +\newlength{\@abovecaptionskip}\setlength{\@abovecaptionskip}{7\p@} +\newlength{\@belowcaptionskip}\setlength{\@belowcaptionskip}{\z@} + +\setlength{\abovecaptionskip}{\@abovecaptionskip} +\setlength{\belowcaptionskip}{\@belowcaptionskip} + +% swap above/belowcaptionskip lengths for tables +\renewenvironment{table} + {\setlength{\abovecaptionskip}{\@belowcaptionskip}% + \setlength{\belowcaptionskip}{\@abovecaptionskip}% + \@float{table}} + {\end@float} + +% footnote formatting +\setlength{\footnotesep }{6.65\p@} +\setlength{\skip\footins}{9\p@ \@plus 4\p@ \@minus 2\p@} +\renewcommand{\footnoterule}{\kern-3\p@ \hrule width 12pc \kern 2.6\p@} +\setcounter{footnote}{0} + +% paragraph formatting +\setlength{\parindent}{\z@} +\setlength{\parskip }{5.5\p@} + +% list formatting +\setlength{\topsep }{4\p@ \@plus 1\p@ \@minus 2\p@} +\setlength{\partopsep }{1\p@ \@plus 0.5\p@ \@minus 0.5\p@} +\setlength{\itemsep }{2\p@ \@plus 1\p@ \@minus 0.5\p@} +\setlength{\parsep }{2\p@ \@plus 1\p@ \@minus 0.5\p@} +\setlength{\leftmargin }{3pc} +\setlength{\leftmargini }{\leftmargin} +\setlength{\leftmarginii }{2em} +\setlength{\leftmarginiii}{1.5em} +\setlength{\leftmarginiv }{1.0em} +\setlength{\leftmarginv }{0.5em} +\def\@listi {\leftmargin\leftmargini} +\def\@listii {\leftmargin\leftmarginii + \labelwidth\leftmarginii + \advance\labelwidth-\labelsep + \topsep 2\p@ \@plus 1\p@ \@minus 0.5\p@ + \parsep 1\p@ \@plus 0.5\p@ \@minus 0.5\p@ + \itemsep \parsep} +\def\@listiii{\leftmargin\leftmarginiii + \labelwidth\leftmarginiii + \advance\labelwidth-\labelsep + \topsep 1\p@ \@plus 0.5\p@ \@minus 0.5\p@ + \parsep \z@ + \partopsep 0.5\p@ \@plus 0\p@ \@minus 0.5\p@ + \itemsep \topsep} +\def\@listiv {\leftmargin\leftmarginiv + \labelwidth\leftmarginiv + \advance\labelwidth-\labelsep} +\def\@listv {\leftmargin\leftmarginv + \labelwidth\leftmarginv + \advance\labelwidth-\labelsep} +\def\@listvi {\leftmargin\leftmarginvi + \labelwidth\leftmarginvi + \advance\labelwidth-\labelsep} + +% create title +\providecommand{\maketitle}{} +\renewcommand{\maketitle}{% + \par + \begingroup + \renewcommand{\thefootnote}{\fnsymbol{footnote}} + % for perfect author name centering + \renewcommand{\@makefnmark}{\hbox to \z@{$^{\@thefnmark}$\hss}} + % The footnote-mark was overlapping the footnote-text, + % added the following to fix this problem (MK) + \long\def\@makefntext##1{% + \parindent 1em\noindent + \hbox to 1.8em{\hss $\m@th ^{\@thefnmark}$}##1 + } + \thispagestyle{empty} + \@maketitle + \@thanks + %\@notice + \endgroup + \let\maketitle\relax + \let\thanks\relax +} + +% rules for title box at top of first page +\newcommand{\@toptitlebar}{ + \hrule height 2\p@ + \vskip 0.25in + \vskip -\parskip% +} +\newcommand{\@bottomtitlebar}{ + \vskip 0.29in + \vskip -\parskip + \hrule height 2\p@ + \vskip 0.09in% +} + +% create title (includes both anonymized and non-anonymized versions) +\providecommand{\@maketitle}{} +\renewcommand{\@maketitle}{% + \vbox{% + \hsize\textwidth + \linewidth\hsize + \vskip 0.1in + \@toptitlebar + \centering + {\LARGE\sc \@title\par} + \@bottomtitlebar + \textsc{A Preprint}\\ + \vskip 0.1in + \def\And{% + \end{tabular}\hfil\linebreak[0]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \def\AND{% + \end{tabular}\hfil\linebreak[4]\hfil% + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\ignorespaces% + } + \begin{tabular}[t]{c}\bf\rule{\z@}{24\p@}\@author\end{tabular}% + \vskip 0.4in \@minus 0.1in \center{\today} \vskip 0.2in + } +} + +% add conference notice to bottom of first page +\newcommand{\ftype@noticebox}{8} +\newcommand{\@notice}{% + % give a bit of extra room back to authors on first page + \enlargethispage{2\baselineskip}% + \@float{noticebox}[b]% + \footnotesize\@noticestring% + \end@float% +} + +% abstract styling +\renewenvironment{abstract} +{ + \centerline + {\large \bfseries \scshape Abstract} + \begin{quote} +} +{ + \end{quote} +} + +\endinput diff --git a/papers/JOSE/cover_letter.Rmd b/papers/JOSE/cover_letter.Rmd new file mode 100644 index 000000000..4251c050a --- /dev/null +++ b/papers/JOSE/cover_letter.Rmd @@ -0,0 +1,29 @@ +--- +output: pdf_document +--- + +Dear Dr. Vazire, + +We are pleased to submit this paper to *Collabra: Psychology*. + +The paper, titled "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*", provides an overview of current recommendations and best practices regarding the diagnosis and treatment of outliers, a common issue faced by researchers---and a potential source of scientific malpractice. + +It explains the key approaches, highlights recommendations, and shows how users can adopt them in their R analysis with a single function. The manuscript covers univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting method, among other things. + +Beyond acting like a concise review of outlier treatment procedures and practical tutorial, we also introduce a new outlier-detection method that relies on a consensus-based approach. In this sense, the paper fits well with the "Methodology and Research Practice in Psychology" section of the journal, as it essentially communicates to psychologists how to easily follow some of the best practices in the detection of statistical outlier using currently available open source and free software. This makes the manuscript relevant to data science, behavioural science, and good research and statistical practices more generally. + +As Associated Editor, we would like to suggest Jeffrey Girard, as he is familiar with the *easystats* and R ecosystems, as well as good statistical practices. Additionally, we would like to request a streamlined review, as the manuscript has been rejected within the previous 365 days from the journal *Mathematics*. Accordingly, we provide in this submission a detailed letter that includes prior reviews, the decision letter, as well as how we addressed the reviewers' comments. We have in this regard integrated most of the changes suggested by the reviewers. Note that the previous editors and reviewers have not given their permission for their comments to be openly available at *Collabra: Psychology*. However, although an open review was requested, the reviewers did not sign their reviews. + +Our current submission is original and has been neither published elsewhere nor is currently under consideration for publication elsewhere. All authors have contributed substantially to the software and manuscript. All authors gave final approval to the manuscript and accept to be accountable. We have no conflicts of interest to disclose. We have also read the Transparency and Openness policy of the Editorial Policies of *Collabra: Psychology*. + +Thank you for considering our submission. + +On the behalf of all authors, + +Rémi Thériault + +Department of Psychology, + +Université du Québec à Montréal, + +Montréal, Québec, Canada \ No newline at end of file diff --git a/papers/JOSE/cover_letter.pdf b/papers/JOSE/cover_letter.pdf new file mode 100644 index 0000000000000000000000000000000000000000..15650f828a5911b0fdaa1526bfab944c863573a8 GIT binary patch literal 56483 zcma&M19T=`(=Hs_m`tq6#I|kQ6Wg{Yb~3ST+qNgRZA^@lnauOO&v)McU+eT*UH9(l zs@ip3Ro&U$X(AZ`Axc^*Mku1mnZ5-mT09y&D_v744h}qOc|2-iD+Mb&Y5_cTx_7-C z9<`8(y(S(P7nFge{%)0Cz80cB) z8$i7~+u7S1=vY8GFZrvA$F4NOwx3rVq-K{V%YHfHC1tK?TRc&6IdzcS;!gz@-l}a> z633Rk%Dp}YM##iDO+WPGL<02%fpEX?jBpIptbKY2JlHyqgy(+VwGyo+@1a9`INLNK z?vv`5{Y+$gCv*Oa+B$8zuud$B)QZXHF5>5P7Rn&=M(@|Y{Pwgtzv_WvC|lJMX`u4e zH{W9oO*GRa8{>X+#?-(;l3GuC>Exy{(k}=7(7`;+z{Fu`J(OUwhXYW_?{u%^w4V;r 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zgeBE~@GE2YpRx{0vKbcXp1bTC>ra)a5wLS!m22v1rW?~Pw1jwKwFeEWj`dU?o9hcq zY1xsJF=+m7YO+L4LHS-mSiz)??X>mn8-5ZhqEY+zt~A~9i^2suG#b#bLg89YmHLI_ zGOaRy_(3ZbQl9NxsUVoyQy#+#q~}ol=Hc86jvXWdc7-ZnUhDxp!K;Qj*Zyv7XRF7-81k4N$G> zx&eC(_t+P)p;Tg5Sp4>Gn{rWCCBfA4MhA@o$tR?;2?b|_jfNiG-qt^JfM}8An*MM$ zRKw%rJ>+LCpA9gr6E8B#PA525UQU{*QSw)?oM;n-cClBkeJDo5E&78SGb$8=EA0Nz5QD;N#qWcyN-t&{5vjGRmfB2_Ag3FRB}jeJu|S8^U74u*knnI; z>f4oxm%C!X#tBACk}+)12;o~dW!n94_6#Qj9o%=t^OjE~ageQa(UTNYvs3gWZs=i! ziiKY#+rlp*pu(y9Z2bpHg;U{03qO+G4)rpl9qQtH{3?em{6hS9sB5Q6Bq0kVlDZNk zlG2JfA~T@7PRozfspZFC@=MYac)8OD<#MNIAj(%>UEI!ZyMLu3k3Er!(3hVj$7y}5 z@;!KV&Mdk_LLd8em-6ih&KkptqN5yRkKGaUF6StjLLmgVq&l#inGh1S5W1+R z5R$942Y~Yf&D@>J^#Fi?Rl^T*OaL8=4iSGz3i|&?Qr@HsMD+vC1-}Misj)f9>5=T= zH!AtfAFHp1)Vz9Z^_A%>l9>s9FH*+lRIzua=Ww=fzG-An!|sBI`7nI*txt9M#KM7u znG{d)LEi&iZ}VrP1JyrHRm>#jIX=>0Uu~RSBP=?p@BP-d@E=VV=Qa)li=8L_Vg;jlSq&+t%D0dk@_EMe34qjx94zVg@HbTOF0uY2@VnYP>-H zAguXYH7&8OXIEO`>b^DP!OF~2rmc3_UyJ%{Mjm@NTxZ=sl-4rrr}yc}%;dYKZ_`MP zz3@+aQne0kvS<;xyGu6r{HENQ1mUXrw+tYwQ1hjbAr&~5p|JLVW!-U2Hc-b+(4)U^P*t_?X-aHcX;edx|WDwvP zE0iUqTsHBjdzscnMo<>~)Hu2wgi_ zX5lJBDeHGJOw)Jlp7MHPF8?E$(8&CE#pTMx!z(O@wz|ZhWv<0%T!*f#+Y>!AbclD8 zXlvxPC-j-EPl7$a=G~e;crr7sZc1*pJZ&yAV8hb_`q~#)9cB4DbkLQ%(>h#zVt#L} zv>tq5FLLkU1!Oj5ExD;)lHFSRK1Uv&bq4v-NtxX3uv-J;(9Jio4gP#pu>&93xo%(O zXC?4kOefcQ-N*FmZWt_6N=?dSCujS z8R!bNIx8ogybN@*O$+ryj(w7<Xp1kaC^wgmdY5zkbmkHqA z+-~%^^@#M&yBv1gU5-d+2FGBc!s!F(W=Vob@ZLeh6I*T6%cY($W+7(SUuB+!2?~9mQSmq8=_xUfUj+)zCn7I=>2NVGsDi^yUu< zGRb{wKM+{BIg?`K$#SE*bJuG`r?_j9SyWI&E~N2qqZbr+@r&aaGiVN;WZ>7Lw4bVP zMmY%49UQ@nDiVf4z)%=aPiuOzoM{XtWw;rYOyKD3=D~ZAt0s26e%w$lYJNzMESiW0XMR~677J4MQy&TiuJ+||C>-&pIir!_JK*v-1R9I^aa;uO4EphS zXgreeiemK_Y)V9u|ut{Fqa4BJe-QVYr3P@^P`)rN?72 z?15zx16Wx>a8v3D3itfN571~VX#SoBH=&-pBMp3sn!lsrdODExZiJ2|9*fh$Xc37d xZG). + +## Multivariate Outliers + +Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. + +However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. + +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. + +In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r multivariate} +outliers <- check_outliers(data, method = "mcd") +outliers +``` + +Here, we detected 9 multivariate outliers (i.e,. when looking at all variables of our dataset together). + +Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). + +## Model-Based Outliers + +Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). + +In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +Currently, most lm models are supported (with the exception of `glmmTMB`, `lmrob`, and `glmrob` models), as long as they are supported by the underlying functions `stats::cooks.distance()` (or `loo::pareto_k_values()`) and `insight::get_data()` (for a full list of the 225 models currently supported by the `insight` package, see https://easystats.github.io/insight/#list-of-supported-models-by-class). Also note that although `check_outliers()` supports the pipe operators (`|>` or `%>%`), it does not support `tidymodels` at this time. We show a demo below. + +```{r model} +model <- lm(disp ~ mpg * disp, data = data) +outliers <- check_outliers(model, method = "cook") +outliers +``` + +Using the model-based outlier detection method, we identified a single outlier. + +Table 1 below summarizes which methods to use in which cases, and with what threshold. The recommended thresholds are the default thresholds. + +```{r table1_prep, echo=FALSE} +df <- data.frame( + `Statistical Test` = c( + "Supported regression model", + "Structural Equation Modeling (or other unsupported model)", + "Simple test with few variables (*t* test, correlation, etc.)"), + `Diagnosis Method` = c( + "**Model-based**: Cook (or Pareto for Bayesian models)", + "**Multivariate**: Minimum Covariance Determinant (MCD)", + "**Univariate**: robust *z* scores (MAD)"), + `Recommended Threshold` = c( + "_qf(0.5, ncol(x), nrow(x) - ncol(x))_ (or 0.7 for Pareto)", + "_qchisq(p = 1 - 0.001, df = ncol(x))_", + "_qnorm(p = 1 - 0.001 / 2)_, ~ 3.29"), + `Function Usage` = c( + '_check_outliers(model, method = "cook")_', + '_check_outliers(data, method = "mcd")_', + '_check_outliers(data, method = "zscore_robust")_'), + check.names = FALSE +) +``` + +### Table 1 + +_Summary of Statistical Outlier Detection Methods Recommendations_ + +```{r table1_print, echo=FALSE, message=FALSE, eval=FALSE} +x <- flextable::flextable(df, cwidth = 1.25) +x <- flextable::theme_apa(x) +x <- flextable::font(x, fontname = "Latin Modern Roman", part = "all") +x <- flextable::fontsize(x, size = 10, part = "all") +ftExtra::colformat_md(x) + +``` + +![](table1.jpg) + +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package (Figure 1). + +```{r model_fig, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} +plot(outliers) +``` + +## Cook's Distance vs. MCD + +@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. + +Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. + +## Composite Outlier Score + +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. + +```{r multimethod, fig.cap = "Visual depiction of outliers using several different statistical outlier detection methods."} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) +which(outliers) +``` + +Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: + +```{r} +attributes(outliers)$outlier_var$zscore_robust +``` + +An example sentence for reporting the usage of the composite method could be: + +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. + +# Handling Outliers + +The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. + +## Error, Interesting, and Random Outliers + +@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. + +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. + +We should also keep in mind that there might be error outliers that are not detected by statistical tools, but should nonetheless be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded. We could call these observations *undetected* error outliers, in the sense that although they do not statistically stand out, they do not belong to the theoretical or empirical distribution of interest (e.g., teenagers). In this way, we should not blindly rely on statistical outlier detection methods; doing our due diligence to investigate undetected error outliers relative to our specific research question is also essential for valid inferences. + +## Winsorization + +_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. + +The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. + +## The Importance of Transparency + +Finally, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. + +# References \ No newline at end of file diff --git a/papers/Mathematics/mybibfile.bib b/papers/JOSE/paper.bib similarity index 90% rename from papers/Mathematics/mybibfile.bib rename to papers/JOSE/paper.bib index 463fd9e2b..56c8ae7e1 100644 --- a/papers/Mathematics/mybibfile.bib +++ b/papers/JOSE/paper.bib @@ -41,18 +41,17 @@ @article{simmons2011false URL = {https://doi.org/10.1177/0956797611417632}, } -@Article{easystatspackage, - title = {easystats: Framework for Easy Statistical Modeling, Visualization, and Reporting}, - author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Brenton M. Wiernik and Etienne Bacher and Rémi Thériault and Dominique Makowski}, - journal = {CRAN}, - year = {2022}, - note = {R package}, - url = {https://easystats.github.io/easystats/}, - } +@software{easystatspackage, + title = {{easystats}: Streamline Model Interpretation, Visualization, and Reporting}, + author = {Daniel Lüdecke and Dominique Makowski and Mattan S. Ben-Shachar and Indrajeet Patil and Brenton M. Wiernik and Etienne Bacher and Rémi Thériault}, + date = {2023-02-04T22:06:06Z}, + origdate = {2019-01-28T10:39:29Z}, + url = {https://easystats.github.io/easystats/} +} @Article{ludecke2021performance, author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Philip Waggoner and Dominique Makowski}, - title = {{performance}: An R package for assessment, comparison and testing of statistical models}, + title = {{performance}: An {R} package for assessment, comparison and testing of statistical models}, volume = {6}, number = {60}, journal = {Journal of Open Source Software}, @@ -146,7 +145,7 @@ @article{ratcliff1993methods } @book{mcelreath2020statistical, - title={Statistical rethinking: A Bayesian course with examples in R and Stan}, + title={Statistical rethinking: A Bayesian course with examples in {R} and Stan}, author={McElreath, Richard}, year={2020}, publisher={CRC press} diff --git a/papers/JOSE/paper.log b/papers/JOSE/paper.log new file mode 100644 index 000000000..e31fca364 --- /dev/null +++ b/papers/JOSE/paper.log @@ -0,0 +1,1133 @@ +This is XeTeX, Version 3.141592653-2.6-0.999995 (TeX Live 2023) (preloaded format=xelatex 2023.10.4) 4 OCT 2023 18:48 +entering extended mode + restricted \write18 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An introduction to identifying statistical outliers in R with *easystats*" +tags: + - R + - univariate outliers + - multivariate outliers + - robust detection methods + - easystats +authors: + - name: Rémi Thériault + orcid: 0000-0003-4315-6788 + affiliation: 1 + - name: Mattan S. Ben-Shachar + orcid: 0000-0002-4287-4801 + affiliation: 2 + - name: Indrajeet Patil + orcid: 0000-0003-1995-6531 + affiliation: 3 + - name: Daniel Lüdecke + orcid: 0000-0002-8895-3206 + affiliation: 4 + - name: Brenton M. Wiernik + orcid: 0000-0001-9560-6336 + affiliation: 5 + - name: Dominique Makowski + orcid: 0000-0001-5375-9967 + affiliation: 6 +affiliations: + - index: 1 + name: Department of Psychology, Université du Québec à Montréal, Montréal, Québec, Canada + - index: 2 + name: Independent Researcher, Ramat Gan, Israel + - index: 3 + name: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany + - index: 4 + name: Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, Germany + - index: 5 + name: Independent Researcher, Tampa, FL, USA + - index: 6 + name: School of Psychology, University of Sussex, Brighton, UK +correspondence: theriault.remi@courrier.uqam.ca. +type: article +status: submit +date: 7 June 2023 +bibliography: paper.bib +simplesummary: | + The *{performance}* package from the *easystats* ecosystem makes it easy to + diagnose outliers in R and according to current best practices thanks to the + `check_outiers()` function. +keywords: | + univariate outliers; multivariate outliers; robust detection methods; R; easystats +acknowledgement: | + *{performance}* is part of the collaborative + [*easystats*](https://github.com/easystats/easystats) ecosystem + [@easystatspackage]. Thus, we thank all + [members of easystats](https://github.com/orgs/easystats/people), + contributors, and users alike. +authorcontributions: | + R.T. drafted the paper; all authors contributed to both the writing of the + paper and the conception of the software. +funding: | + This research received no external funding. +conflictsofinterest: | + The authors declare no conflict of interest. +abbreviations: + - short: SOD + long: Statistical outlier detection + - short: SEM + long: Structural equation modelling + - short: SD + long: Standard deviation + - short: MAD + long: Median absolute deviation + - short: IQR + long: Interquartile range + - short: HDI + long: Highest density interval + - short: BCI + long: Bias corrected and accelerated interval + - short: MCD + long: Minimum covariance determinant + - short: ICS + long: invariant coordinate selection + - short: OSF + long: Open Science Framework +output: + rticles::joss_article: + journal: "JOSE" +csl: apa.csl +--- + + + +# Summary + +Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. Here, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude by reviewing the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. + +# Statement of Need + +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it can be hard to assess and the boundaries of "abnormal", difficult to define---they may belong to a different distribution (originating from a different generative process) or simply be extreme cases, statistically rare but not impossible. + +Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. + +One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. Installation instructions can be found on [GitHub](https://github.com/easystats/performance) or its [website](https://easystats.github.io/performance/), and its list of dependencies on [CRAN](https://cran.r-project.org/package=performance). + +The instructional materials that follow are aimed at an audience of researchers who want to follow good practices, and are appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. + +# Identifying Outliers + +Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and those methods also assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. + +Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. + +One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. Identifying observations the regression model does not fit well can help find information relevant to our specific research context. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). + +When no method is readily available to detect model-based outliers, such as for structural equation modelling (SEM), looking for multivariate outliers may be of relevance. For simple tests (_t_ tests or correlations) that compare values of the same variable, it can be appropriate to check for univariate outliers. However, univariate methods can give false positives since _t_ tests and correlations, ultimately, are also models/multivariable statistics. They are in this sense more limited, but we show them nonetheless for educational purposes. + +Importantly, whatever approach researchers choose remains a subjective decision, which usage (and rationale) must be transparently documented and reproducible [@leys2019outliers]. Researchers should commit (ideally in a preregistration) to an outlier treatment method before collecting the data. They should report in the paper their decisions and details of their methods, as well as any deviation from their original plan. These transparency practices can help reduce false positives due to excessive researchers' degrees of freedom (i.e., choice flexibility throughout the analysis). In the following section, we will go through each of the mentioned methods and provide examples on how to implement them with R. + +## Univariate Outliers + +Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. + +Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument. + +Below we provide example code using the `mtcars` dataset, which was extracted from the 1974 *Motor Trend* US magazine. The dataset contains fuel consumption and 10 characteristics of automobile design and performance for 32 different car models (see `?mtcars` for details). We chose this dataset because it is accessible from base R and familiar to many R users. We might want to conduct specific statistical analyses on this data set, say, _t_ tests or structural equation modelling, but first, we want to check for outliers that may influence those test results. + +Because the automobile names are stored as column names in `mtcars`, we first have to convert them to an ID column to benefit from the `check_outliers()` ID argument. Furthermore, we only really need a couple columns for this demonstration, so we choose the first four (`mpg` = Miles/(US) gallon; `cyl` = Number of cylinders; `disp` = Displacement; `hp` = Gross horsepower). Finally, because there are no outliers in this dataset, we add two artificial outliers before running our function. + + +```r +library(performance) + +# Create some artificial outliers and an ID column +data <- rbind(mtcars[1:4], 42, 55) +data <- cbind(car = row.names(data), data) + +outliers <- check_outliers(data, method = "zscore_robust", ID = "car") +outliers +``` + +``` +#> 2 outliers detected: cases 33, 34. +#> - Based on the following method and threshold: zscore_robust (3.291). +#> - For variables: mpg, cyl, disp, hp. +#> +#> ----------------------------------------------------------------------------- +#> +#> The following observations were considered outliers for two or more +#> variables by at least one of the selected methods: +#> +#> Row car n_Zscore_robust +#> 1 33 33 2 +#> 2 34 34 2 +#> +#> ----------------------------------------------------------------------------- +#> Outliers per variable (zscore_robust): +#> +#> $mpg +#> Row car Distance_Zscore_robust +#> 33 33 33 3.709699 +#> 34 34 34 5.848328 +#> +#> $cyl +#> Row car Distance_Zscore_robust +#> 33 33 33 12.14083 +#> 34 34 34 16.52502 +``` + +What we see is that `check_outliers()` with the robust _z_ score method detected two outliers: cases 33 and 34, which were the observations we added ourselves. They were flagged for two variables specifically: `mpg` (Miles/(US) gallon) and `cyl` (Number of cylinders), and the output provides their exact _z_ score for those variables. + +We describe how to deal with those cases in more details later in the paper, but should we want to exclude these detected outliers from the main dataset, we can extract row numbers using `which()` on the output object, which can then be used for indexing: + + +```r +which(outliers) +``` + +``` +#> [1] 33 34 +``` + +```r +data_clean <- data[-which(outliers), ] +``` + +Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). + +## Multivariate Outliers + +Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. + +However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. + +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. + +In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + + +```r +outliers <- check_outliers(data, method = "mcd") +outliers +``` + +``` +#> 9 outliers detected: cases 7, 15, 16, 17, 24, 29, 31, 33, 34. +#> - Based on the following method and threshold: mcd (20). +#> - For variables: mpg, cyl, disp, hp. +``` + +Here, we detected 9 multivariate outliers (i.e,. when looking at all variables of our dataset together). + +Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). + +## Model-Based Outliers + +Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). + +In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +Currently, most lm models are supported (with the exception of `glmmTMB`, `lmrob`, and `glmrob` models), as long as they are supported by the underlying functions `stats::cooks.distance()` (or `loo::pareto_k_values()`) and `insight::get_data()` (for a full list of the 225 models currently supported by the `insight` package, see https://easystats.github.io/insight/#list-of-supported-models-by-class). Also note that although `check_outliers()` supports the pipe operators (`|>` or `%>%`), it does not support `tidymodels` at this time. We show a demo below. + + +```r +model <- lm(disp ~ mpg * disp, data = data) +outliers <- check_outliers(model, method = "cook") +outliers +``` + +``` +#> 1 outlier detected: case 34. +#> - Based on the following method and threshold: cook (0.708). +#> - For variable: (Whole model). +``` + +Using the model-based outlier detection method, we identified a single outlier. + +Table 1 below summarizes which methods to use in which cases, and with what threshold. The recommended thresholds are the default thresholds. + + + +### Table 1 + +_Summary of Statistical Outlier Detection Methods Recommendations_ + + + +![](table1.jpg) + +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package (Figure 1). + + +```r +plot(outliers) +``` + +\begin{figure} +\includegraphics[width=1\linewidth]{paper_files/figure-latex/model_fig-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model.}\label{fig:model_fig} +\end{figure} + +## Cook's Distance vs. MCD + +@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. + +Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. + +## Composite Outlier Score + +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. + + +```r +outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) +which(outliers) +``` + +``` +#> [1] 33 34 +``` + +Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: + + +```r +attributes(outliers)$outlier_var$zscore_robust +``` + +``` +#> $mpg +#> Row Distance_Zscore_robust +#> 33 33 3.709699 +#> 34 34 5.848328 +``` + +An example sentence for reporting the usage of the composite method could be: + +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. + +# Handling Outliers + +The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. + +## Error, Interesting, and Random Outliers + +@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. + +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. + +We should also keep in mind that there might be error outliers that are not detected by statistical tools, but should nonetheless be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded. We could call these observations *undetected* error outliers, in the sense that although they do not statistically stand out, they do not belong to the theoretical or empirical distribution of interest (e.g., teenagers). In this way, we should not blindly rely on statistical outlier detection methods; doing our due diligence to investigate undetected error outliers relative to our specific research question is also essential for valid inferences. + +## Winsorization + +_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. + +The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. + +## The Importance of Transparency + +Finally, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. + +# References diff --git a/papers/JOSE/paper.pdf b/papers/JOSE/paper.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9e6812e5e0cb56d3150c59aa302ad3a60bc8456f GIT binary patch literal 593364 zcmbSyRY03f(C$YmQnW>jOQBeCOV9$vihF?o#fwXDrxYm^cL>lHcbDMq1b5fq7FCp`qKP?xngNZekhzO^qr=vON7Znq0 zb5j>i4ObJFf6wxE#+K%sI#y;b-)OnHxVSjw%&jcHxzO?g0Gv_|whqo3j>e|uoS)3y ztW3>iosB&?C9Pb*s^-p84t9aTCU?iRYcL44GT?tIf{clNE zJA34}f235M&CRS#T^yWgdBnsxWvpyn%$+%9Y>i#a|93%7MRR*gmv30yKpq~Tm>3q= z#o6504$EWVCizX6c1CYo*E0-)gMmKf+(F)BTjU(F~EplCM!zQGPu3%<`q? z1;Y+~EnudlMr>T*9fFVTw&YK!nbiYI&DjNPlPXDGRP$;#EfRL zK4kAD>MSOVe*F0H#SiEUD1%bDtu4x!#K-T_p7Y^_y(;xfORuz0Ul7m^pBPx2-FDEF zqr~IAARro4$buL@E;rI#|F=s^8`$pSWH;f^krNc~@&)3r7O%QNMNuBjM+}rR=&-k~ 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The following packages are loaded in our class file: fontenc, calc, indentfirst, fancyhdr, graphicx, lastpage, ifthen, lineno, float, amsmath, setspace, enumitem, mathpazo, booktabs, titlesec, etoolbox, amsthm, hyphenat, natbib, hyperref, footmisc, geometry, caption, url, mdframed, tabto, soul, multirow, microtype, tikz - -%================================================================= -%% Please use the following mathematics environments: Theorem, Lemma, Corollary, Proposition, Characterization, Property, Problem, Example, ExamplesandDefinitions, Hypothesis, Remark, Definition -%% For proofs, please use the proof environment (the amsthm package is loaded by the MDPI class). - -%================================================================= -% Full title of the paper (Capitalized) -\Title{Check your outliers! An introduction to identifying statistical -outliers in R with \emph{easystats}} - -% Authors, for the paper (add full first names) -\Author{Rémi -Thériault$^{1,*}$\href{https://orcid.org/0000-0003-4315-6788}{\orcidicon}, Mattan -S. -Ben-Shachar$^{2}$\href{https://orcid.org/0000-0002-4287-4801}{\orcidicon}, Indrajeet -Patil$^{3}$\href{https://orcid.org/0000-0003-1995-6531}{\orcidicon}, Daniel -Lüdecke$^{4}$\href{https://orcid.org/0000-0002-8895-3206}{\orcidicon}, Brenton -M. -Wiernik$^{5}$\href{https://orcid.org/0000-0001-9560-6336}{\orcidicon}, Dominique -Makowski$^{6}$\href{https://orcid.org/0000-0001-5375-9967}{\orcidicon}} - -% Authors, for metadata in PDF -\AuthorNames{Rémi Thériault, Mattan S. Ben-Shachar, Indrajeet -Patil, Daniel Lüdecke, Brenton M. Wiernik, Dominique Makowski} - -% Affiliations / Addresses (Add [1] after \address if there is only one affiliation.) -\address{% -$^{1}$ \quad Department of Psychology, Université du Québec à Montréal, -Montréal, Québec, Canada; \\ -$^{2}$ \quad Independent Researcher; \\ -$^{3}$ \quad Center for Humans and Machines, Max Planck Institute for -Human Development, Berlin, Germany; \\ -$^{4}$ \quad Institute of Medical Sociology, University Medical Center -Hamburg-Eppendorf, Germany; \\ -$^{5}$ \quad Independent Researcher, Tampa, FL, USA; \\ -$^{6}$ \quad School of Psychology, University of Sussex, Brighton, -UK; \\ -} -% Contact information of the corresponding author -\corres{Correspondence: \href{mailto:theriault.remi@courrier.uqam.ca}{\nolinkurl{theriault.remi@courrier.uqam.ca}}.} - -% Current address and/or shared authorship - - - - - - - - -% The commands \thirdnote{} till \eighthnote{} are available for further notes - -% Simple summary -\simplesumm{The \emph{\{performance\}} package from the \emph{easystats} -ecosystem makes it easy to diagnose outliers in R and according to -current best practices thanks to the \texttt{check\_outiers()} -function.} - -% Abstract (Do not insert blank lines, i.e. \\) -\abstract{Beyond the challenge of keeping up-to-date with current best -practices regarding the diagnosis and treatment of outliers, an -additional difficulty arises concerning the mathematical implementation -of the recommended methods. In this paper, we provide an overview of -current recommandations and best practices and demonstrate how they can -easily and conveniently be implemented in the R statistical computing -software, using the \emph{\{performance\}} package of the -\emph{easystats} ecosystem. We cover univariate, multivariate, and -model-based statistical outlier detection methods, their recommended -threshold, standard output, and plotting methods. We conclude with -recommendations on the handling of outliers: the different theoretical -types of outliers, whether to exclude or winsorize them, and the -importance of transparency.} - -% Keywords -\keyword{univariate outliers; multivariate outliers; robust detection -methods; R; easystats} - -% The fields PACS, MSC, and JEL may be left empty or commented out if not applicable -%\PACS{J0101} -%\MSC{} -%\JEL{} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Only for the journal Diversity -%\LSID{\url{http://}} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Only for the journal Applied Sciences: -%\featuredapplication{Authors are encouraged to provide a concise description of the specific application or a potential application of the work. This section is not mandatory.} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Only for the journal Data: -%\dataset{DOI number or link to the deposited data set in cases where the data set is published or set to be published separately. If the data set is submitted and will be published as a supplement to this paper in the journal Data, this field will be filled by the editors of the journal. In this case, please make sure to submit the data set as a supplement when entering your manuscript into our manuscript editorial system.} - -%\datasetlicense{license under which the data set is made available (CC0, CC-BY, CC-BY-SA, CC-BY-NC, etc.)} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Only for the journal Toxins -%\keycontribution{The breakthroughs or highlights of the manuscript. Authors can write one or two sentences to describe the most important part of the paper.} - -%\setcounter{secnumdepth}{4} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% Pandoc syntax highlighting -\usepackage{color} -\usepackage{fancyvrb} -\newcommand{\VerbBar}{|} -\newcommand{\VERB}{\Verb[commandchars=\\\{\}]} -\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}} -% Add ',fontsize=\small' for more characters per line -\usepackage{framed} -\definecolor{shadecolor}{RGB}{248,248,248} -\newenvironment{Shaded}{\begin{snugshade}}{\end{snugshade}} -\newcommand{\AlertTok}[1]{\textcolor[rgb]{0.94,0.16,0.16}{#1}} -\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.77,0.63,0.00}{#1}} -\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\BuiltInTok}[1]{#1} -\newcommand{\CharTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} -\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} -\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{#1}} -\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\ErrorTok}[1]{\textcolor[rgb]{0.64,0.00,0.00}{\textbf{#1}}} -\newcommand{\ExtensionTok}[1]{#1} -\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.00,0.00,0.81}{#1}} -\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\ImportTok}[1]{#1} -\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} -\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.13,0.29,0.53}{\textbf{#1}}} -\newcommand{\NormalTok}[1]{#1} -\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.81,0.36,0.00}{\textbf{#1}}} -\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{#1}} -\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textit{#1}}} -\newcommand{\RegionMarkerTok}[1]{#1} -\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\StringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.00,0.00,0.00}{#1}} -\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.31,0.60,0.02}{#1}} -\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.56,0.35,0.01}{\textbf{\textit{#1}}}} - -% tightlist command for lists without linebreak -\providecommand{\tightlist}{% - \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}} - -% From pandoc table feature -\usepackage{longtable,booktabs,array} -\usepackage{calc} % for calculating minipage widths -% Correct order of tables after \paragraph or \subparagraph -\usepackage{etoolbox} -\makeatletter -\patchcmd\longtable{\par}{\if@noskipsec\mbox{}\fi\par}{}{} -\makeatother -% Allow footnotes in longtable head/foot -\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}} -\makesavenoteenv{longtable} - - - -\begin{document} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\hypertarget{introduction}{% -\section{Introduction}\label{introduction}} - -Real-life data often contain observations that can be considered -\emph{abnormal} when compared to the main population. The cause of -it---be it because they belong to a different distribution (originating -from a different generative process) or simply being extreme cases, -statistically rare but not impossible---can be hard to assess, and the -boundaries of ``abnormal'' are hard to define. - -Nonetheless, the improper handling of these outliers can substantially -affect statistical model estimations, biasing effect estimations and -weakening the models' predictive performance. It is thus essential to -address this problem in a thoughtful manner. Yet, despite the existence -of established recommendations and guidelines, many researchers still do -not treat outliers in a consistent manner, or do so using inappropriate -strategies \citep{simmons2011false, leys2013outliers}. - -One possible reason is that researchers are not aware of the existing -recommendations, or do not know how to implement them using their -analysis software. In this paper, we show how to follow current best -practices for automatic and reproducible statistical outlier detection -(SOD) using R and the \emph{\{performance\}} package -\citep{ludecke2021performance}, which is part of the \emph{easystats} -ecosystem of packages that build an R framework for easy statistical -modeling, visualization, and reporting \citep{easystatspackage}. - -\hypertarget{identifying-outliers}{% -\section{Identifying Outliers}\label{identifying-outliers}} - -Although many researchers attempt to identify outliers with measures -based on the mean (e.g., \emph{z} scores), those methods are problematic -because the mean and standard deviation themselves are not robust to the -influence of outliers and they assume normally distributed data (i.e., a -Gaussian distribution). Therefore, current guidelines recommend using -robust methods to identify outliers, such as those relying on the median -as opposed to the mean -\citep{leys2019outliers, leys2013outliers, leys2018outliers}. - -Nonetheless, which exact outlier method to use depends on many factors. -In some cases, eye-gauging odd observations can be an appropriate -solution, though many researchers will favour algorithmic solutions to -detect potential outliers, for example, based on a continuous value -expressing the observation stands out from the others. - -One of the factors to consider when selecting an algorithmic outlier -detection method is the statistical test of interest. When using a -regression model, relevant information can be found by identifying -observations that do not fit well with the model. This approach, known -as model-based outliers detection (as outliers are extracted after the -statistical model has been fit), can be contrasted with -distribution-based outliers detection, which is based on the distance -between an observation and the ``center'' of its population. Various -quantification strategies of this distance exist for the latter, both -univariate (involving only one variable at a time) or multivariate -(involving multiple variables). - -When no method is readily available to detect model-based outliers, such -as for structural equation modelling (SEM), looking for multivariate -outliers may be of relevance. For simple tests (\emph{t} tests or -correlations) that compare values of the same variable, it can be -appropriate to check for univariate outliers. However, univariate -methods can give false positives since \emph{t} tests and correlations, -ultimately, are also models/multivariable statistics. They are in this -sense more limited, but we show them nonetheless for educational -purposes. - -Importantly, whatever approach researchers choose remains a subjective -decision, which usage (and rationale) must be transparently documented -and reproducible \citep{leys2019outliers}. Researchers should commit -(ideally in a preregistration) to an outlier treatment method before -collecting the data. They should report in the paper their decisions and -details of their methods, as well as any deviation from their original -plan. These transparency practices can help reduce false positives due -to excessive researchers' degrees of freedom (i.e., choice flexibility -throughout the analysis). In the following section, we will go through -each of the mentioned methods and provide examples on how to implement -them with R. - -\hypertarget{univariate-outliers}{% -\subsection{Univariate Outliers}\label{univariate-outliers}} - -Researchers frequently attempt to identify outliers using measures of -deviation from the center of a variable's distribution. One of the most -popular such procedure is the \emph{z} score transformation, which -computes the distance in standard deviation (SD) from the mean. However, -as mentioned earlier, this popular method is not robust. Therefore, for -univariate outliers, it is recommended to use the median along with the -Median Absolute Deviation (MAD), which are more robust than the -interquartile range or the mean and its standard deviation -\citep{leys2019outliers, leys2013outliers}. - -Researchers can identify outliers based on robust (i.e., MAD-based) -\emph{z} scores using the \texttt{check\_outliers()} function of the -\emph{\{performance\}} package, by specifying -\texttt{method\ =\ "zscore\_robust"}.\footnote{Note that - \texttt{check\_outliers()} only checks numeric variables.} Although -\citet{leys2013outliers} suggest a default threshold of 2.5 and -\citet{leys2019outliers} a threshold of 3, \emph{\{performance\}} uses -by default a less conservative threshold of -\textasciitilde3.29.\footnote{3.29 is an approximation of the two-tailed - critical value for \emph{p} \textless{} .001, obtained through - \texttt{qnorm(p\ =\ 1\ -\ 0.001\ /\ 2)}. We chose this threshold for - consistency with the thresholds of all our other methods.} That is, -data points will be flagged as outliers if they go beyond +/- -\textasciitilde3.29 MAD. Users can adjust this threshold using the -\texttt{threshold} argument, as demonstrated below. - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{library}\NormalTok{(performance)} - -\CommentTok{\# Create some artificial outliers and an ID column} -\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{rbind}\NormalTok{(mtcars[}\DecValTok{1}\SpecialCharTok{:}\DecValTok{4}\NormalTok{], }\DecValTok{42}\NormalTok{, }\DecValTok{55}\NormalTok{)} -\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{cbind}\NormalTok{(}\AttributeTok{car =} \FunctionTok{row.names}\NormalTok{(data), data)} - -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"zscore\_robust"}\NormalTok{, }\AttributeTok{ID =} \StringTok{"car"}\NormalTok{)} -\NormalTok{outliers} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> 2 outliers detected: cases 33, 34. -#> - Based on the following method and threshold: zscore_robust (3.09). -#> - For variables: mpg, cyl, disp, hp. -#> -#> ----------------------------------------------------------------------------- -#> -#> The following observations were considered outliers for two or more -#> variables by at least one of the selected methods: -#> -#> Row car n_Zscore_robust -#> 1 33 33 2 -#> 2 34 34 2 -#> -#> ----------------------------------------------------------------------------- -#> Outliers per variable (zscore_robust): -#> -#> $mpg -#> Row car Distance_Zscore_robust -#> 33 33 33 3.709699 -#> 34 34 34 5.848328 -#> -#> $cyl -#> Row car Distance_Zscore_robust -#> 33 33 33 12.14083 -#> 34 34 34 16.52502 -\end{verbatim} - -The row numbers of the detected outliers can be obtained by using -\texttt{which()} on the output object, which can be used for exclusions -for example: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 33 34 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data\_clean }\OtherTok{\textless{}{-}}\NormalTok{ data[}\SpecialCharTok{{-}}\FunctionTok{which}\NormalTok{(outliers), ]} -\end{Highlighting} -\end{Shaded} - -All \texttt{check\_outliers()} output objects possess a \texttt{plot()} -method, meaning it is also possible to visualize the outliers: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{library}\NormalTok{(see)} - -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/univariate-1} \caption{Visual depiction of outliers using the robust z-score method.}\label{fig:univariate} -\end{figure} - -Other univariate methods are available, such as using the interquartile -range (IQR), or based on different intervals, such as the Highest -Density Interval (HDI) or the Bias Corrected and Accelerated Interval -(BCI). These methods are documented and described in the function's -\href{https://easystats.github.io/performance/reference/check_outliers.html}{help -page}. - -\hypertarget{multivariate-outliers}{% -\subsection{Multivariate Outliers}\label{multivariate-outliers}} - -Univariate outliers can be useful when the focus is on a particular -variable, for instance the reaction time, as extreme values might be -indicative of inattention or non-task-related behavior\footnote{ Note - that they might not be the optimal way of treating reaction time - outliers \citep{ratcliff1993methods, van1995statistical}}. - -However, in many scenarios, variables of a data set are not independent, -and an abnormal observation will impact multiple dimensions. For -instance, a participant giving random answers to a questionnaire. In -this case, computing the \emph{z} score for each of the questions might -not lead to satisfactory results. Instead, one might want to look at -these variables together. - -One common approach for this is to compute multivariate distance metrics -such as the Mahalanobis distance. Although the Mahalanobis distance is -very popular, just like the regular \emph{z} scores method, it is not -robust and is heavily influenced by the outliers themselves. Therefore, -for multivariate outliers, it is recommended to use the Minimum -Covariance Determinant, a robust version of the Mahalanobis distance -\citep[MCD,][]{leys2018outliers, leys2019outliers}. - -In \emph{\{performance\}}'s \texttt{check\_outliers()}, one can use this -approach with \texttt{method\ =\ "mcd"}.\footnote{Our default threshold - for the MCD method is defined by - \texttt{stats::qchisq(p\ =\ 1\ -\ 0.001,\ df\ =\ ncol(x))}, which - again is an approximation of the critical value for \emph{p} - \textless{} .001 consistent with the thresholds of our other methods.} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"mcd"}\NormalTok{)} -\NormalTok{outliers} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> 9 outliers detected: cases 7, 15, 16, 17, 24, 29, 31, 33, 34. -#> - Based on the following method and threshold: mcd (20). -#> - For variables: mpg, cyl, disp, hp. -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/multivariate-1} \caption{Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance.}\label{fig:multivariate} -\end{figure} - -Other multivariate methods are available, such as another type of robust -Mahalanobis distance that in this case relies on an orthogonalized -Gnanadesikan-Kettenring pairwise estimator -\citep{gnanadesikan1972robust}. These methods are documented and -described in the function's -\href{https://easystats.github.io/performance/reference/check_outliers.html}{help -page}. - -\hypertarget{model-based-outliers}{% -\subsection{Model-Based Outliers}\label{model-based-outliers}} - -Working with regression models creates the possibility of using -model-based SOD methods. These methods rely on the concept of -\emph{leverage}, that is, how much influence a given observation can -have on the model estimates. If few observations have a relatively -strong leverage/influence on the model, one can suspect that the model's -estimates are biased by these observations, in which case flagging them -as outliers could prove helpful (see next section, ``Handling -Outliers''). - -In \{performance\}, two such model-based SOD methods are currently -available: Cook's distance, for regular regression models, and Pareto, -for Bayesian models. As such, \texttt{check\_outliers()} can be applied -directly on regression model objects, by simply specifying -\texttt{method\ =\ "cook"} (or \texttt{method\ =\ "pareto"} for Bayesian -models).\footnote{Our default threshold for the Cook method is defined - by \texttt{stats::qf(0.5,\ ncol(x),\ nrow(x)\ -\ ncol(x))}, which - again is an approximation of the critical value for \emph{p} - \textless{} .001 consistent with the thresholds of our other methods.} - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{model }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(disp }\SpecialCharTok{\textasciitilde{}}\NormalTok{ mpg }\SpecialCharTok{*}\NormalTok{ disp, }\AttributeTok{data =}\NormalTok{ data)} -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \StringTok{"cook"}\NormalTok{)} -\NormalTok{outliers} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> 1 outlier detected: case 34. -#> - Based on the following method and threshold: cook (0.708). -#> - For variable: (Whole model). -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model-1} \caption{Visual depiction of outliers based on Cook's distance (leverage and standardized residuals).}\label{fig:model} -\end{figure} - -Table 1 below summarizes which methods to use in which cases, and with -what threshold. - -\begin{longtable}[]{@{} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3506}} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3161}} - >{\raggedright\arraybackslash}p{(\columnwidth - 4\tabcolsep) * \real{0.3333}}@{}} -\caption{Summary of Statistical Outlier Detection Methods -Recommendations.}\tabularnewline -\toprule() -\begin{minipage}[b]{\linewidth}\raggedright -Statistical Test -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Diagnosis Method -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Recommended Threshold -\end{minipage} \\ -\midrule() -\endfirsthead -\toprule() -\begin{minipage}[b]{\linewidth}\raggedright -Statistical Test -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Diagnosis Method -\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright -Recommended Threshold -\end{minipage} \\ -\midrule() -\endhead -Supported regression model & \textbf{Model-based}: Cook (or Pareto for -Bayesian models) & \texttt{qf(0.5,\ ncol(x),\ nrow(x)\ -\ ncol(x))} (or -0.7 for Pareto) \\ -Structural Equation Modeling (or other unsupported model) & -\textbf{Multivariate}: Minimum Covariance Determinant (MCD) & -\texttt{qchisq(p\ =\ 1\ -\ 0.001,\ df\ =\ ncol(x))} \\ -Simple test with few variables (\emph{t} test, correlation, etc.) & -\textbf{Univariate}: robust \emph{z} scores (MAD) & -\texttt{qnorm(p\ =\ 1\ -\ 0.001\ /\ 2)}, \textasciitilde{} 3.29 \\ -\bottomrule() -\end{longtable} - -\hypertarget{cooks-distance-vs.-mcd}{% -\subsubsection{Cook's Distance vs.~MCD}\label{cooks-distance-vs.-mcd}} - -\citet{leys2018outliers} report a preference for the MCD method over -Cook's distance. This is because Cook's distance removes one observation -at a time and checks its corresponding influence on the model each time -\citep{cook1977detection}, and flags any observation that has a large -influence. In the view of these authors, when there are several -outliers, the process of removing a single outlier at a time is -problematic as the model remains ``contaminated'' or influenced by other -possible outliers in the model, rendering this method suboptimal in the -presence of multiple outliers. - -However, distribution-based approaches are not a silver bullet either, -and there are cases where the usage of methods agnostic to theoretical -and statistical models of interest might be problematic. For example, a -very tall person would be expected to also be much heavier than average, -but that would still fit with the expected association between height -and weight (i.e., it would be in line with a model such as -\texttt{weight\ \textasciitilde{}\ height}). In contrast, using -multivariate outlier detection methods there may flag this person as -being an outlier---being unusual on two variables, height and -weight---even though the pattern fits perfectly with our predictions. - -In the example below, we plot the raw data and see two possible -outliers. The first one falls along the regression line, and is -therefore ``in line'' with our hypothesis. The second one clearly -diverges from the regression line, and therefore we can conclude that -this outlier may have a disproportionate influence on our model. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data }\OtherTok{\textless{}{-}}\NormalTok{ women[}\FunctionTok{rep}\NormalTok{(}\FunctionTok{seq\_len}\NormalTok{(}\FunctionTok{nrow}\NormalTok{(women)), }\AttributeTok{each =} \DecValTok{100}\NormalTok{), ]} -\NormalTok{data }\OtherTok{\textless{}{-}} \FunctionTok{rbind}\NormalTok{(data, }\FunctionTok{c}\NormalTok{(}\DecValTok{100}\NormalTok{, }\DecValTok{258}\NormalTok{), }\FunctionTok{c}\NormalTok{(}\DecValTok{100}\NormalTok{, }\DecValTok{200}\NormalTok{))} -\NormalTok{model }\OtherTok{\textless{}{-}} \FunctionTok{lm}\NormalTok{(weight }\SpecialCharTok{\textasciitilde{}}\NormalTok{ height, data)} -\NormalTok{rempsyc}\SpecialCharTok{::}\FunctionTok{nice\_scatter}\NormalTok{(data, }\StringTok{"height"}\NormalTok{, }\StringTok{"weight"}\NormalTok{)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/scatter-1} \caption{Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right).}\label{fig:scatter} -\end{figure} - -Using either the \emph{z}-score or MCD methods, our model-consistent -observation will be incorrectly flagged as an outlier or influential -observation. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \FunctionTok{c}\NormalTok{(}\StringTok{"zscore\_robust"}\NormalTok{, }\StringTok{"mcd"}\NormalTok{))} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1501 1502 -\end{verbatim} - -In contrast, the model-based detection method displays the desired -behaviour: it correctly flags the person who is very tall but very -light, without flagging the person who is both tall and heavy. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \StringTok{"cook"}\NormalTok{)} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1502 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{plot}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{figure} -\includegraphics[width=1\linewidth]{paper_files/figure-latex/model2-1} \caption{The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation).}\label{fig:model2} -\end{figure} - -Finally, unusual observations happen naturally: extreme observations are -expected even when taken from a normal distribution. While statistical -models can integrate this ``expectation'', multivariate outlier methods -might be too conservative, flagging too many observations despite -belonging to the right generative process. For these reasons, we believe -that model-based methods are still preferable to the MCD when using -supported regression models. Additionally, if the presence of multiple -outliers is a significant concern, regression methods that are more -robust to outliers should be considered---like \emph{t} regression or -quantile regression---as they render their precise identification less -critical \citep{mcelreath2020statistical}. - -\hypertarget{multiple-methods}{% -\subsection{Multiple Methods}\label{multiple-methods}} - -An alternative approach that is possible is to combine several methods, -based on the assumption that different methods provide different angles -of looking at the problem. By applying a variety of methods, one can -hope to ``triangulate'' the true outliers (those consistently flagged by -multiple methods) and thus attempt to minimize false positives. - -In practice, this approach computes a composite outlier score, formed of -the average of the binary (0 or 1) classification results of each -method. It represents the probability that each observation is -classified as an outlier by at least one method. The default decision -rule classifies rows with composite outlier scores superior or equal to -0.5 as outlier observations (i.e., that were classified as outliers by -at least half of the methods). In \emph{\{performance\}}'s -\texttt{check\_outliers()}, one can use this approach by including all -desired methods in the corresponding argument. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{outliers }\OtherTok{\textless{}{-}} \FunctionTok{check\_outliers}\NormalTok{(model, }\AttributeTok{method =} \FunctionTok{c}\NormalTok{(}\StringTok{"zscore\_robust"}\NormalTok{, }\StringTok{"mcd"}\NormalTok{, }\StringTok{"cook"}\NormalTok{))} -\FunctionTok{which}\NormalTok{(outliers)} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> [1] 1501 1502 -\end{verbatim} - -Outliers (counts or per variables) for individual methods can then be -obtained through attributes. For example: - -\begin{Shaded} -\begin{Highlighting}[] -\FunctionTok{attributes}\NormalTok{(outliers)}\SpecialCharTok{$}\NormalTok{outlier\_var}\SpecialCharTok{$}\NormalTok{zscore\_robust} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> $weight -#> Row Distance_Zscore_robust -#> 1501 1501 6.913530 -#> 1502 1502 3.653492 -#> -#> $height -#> Row Distance_Zscore_robust -#> 1501 1501 5.901794 -#> 1502 1502 5.901794 -\end{verbatim} - -An example sentence for reporting the usage of the composite method -could be: - -\begin{quote} -Based on a composite outlier score (see the `check\_outliers()' function -in the `performance' R package, \citep{ludecke2021performance}) obtained -via the joint application of multiple outliers detection algorithms ((a) -median absolute deviation (MAD)-based robust \emph{z} scores, -\citep{leys2013outliers}; (b) Mahalanobis minimum covariance determinant -(MCD), \citep{leys2019outliers}; and (c) Cook's distance, -\citep{cook1977detection}), we excluded two participants that were -classified as outliers by at least half of the methods used. -\end{quote} - -\hypertarget{handling-outliers}{% -\section{Handling Outliers}\label{handling-outliers}} - -The above section demonstrated how to identify outliers using the -\texttt{check\_outliers()} function in the \emph{\{performance\}} -package. But what should we do with these outliers once identified? -Although it is common to automatically discard any observation that has -been marked as ``an outlier'' as if it might infect the rest of the data -with its statistical ailment, we believe that the use of SOD methods is -but one step in the get-to-know-your-data pipeline; a researcher or -analyst's \emph{domain knowledge} must be involved in the decision of -how to deal with observations marked as outliers by means of SOD. -Indeed, automatic tools can help detect outliers, but they are nowhere -near perfect. Although they can be useful to flag suspect data, they can -have misses and false alarms, and they cannot replace human eyes and -proper vigilance from the researcher. If you do end up manually -inspecting your data for outliers, it can be helpful to think of -outliers as belonging to different types of outliers, or categories, -which can help decide what to do with a given outlier. - -\hypertarget{error-interesting-and-random-outliers}{% -\subsection{Error, Interesting, and Random -Outliers}\label{error-interesting-and-random-outliers}} - -\citet{leys2019outliers} distinguish between error outliers, interesting -outliers, and random outliers. \emph{Error outliers} are likely due to -human error and should be corrected before data analysis or outright -removed since they are invalid observations. \emph{Interesting outliers} -are not due to technical error and may be of theoretical interest; it -might thus be relevant to investigate them further even though they -should be removed from the current analysis of interest. \emph{Random -outliers} are assumed to be due to chance alone and to belong to the -correct distribution and, therefore, should be retained. - -It is recommended to \emph{keep} observations which are expected to be -part of the distribution of interest, even if they are outliers -\citep{leys2019outliers}. However, if it is suspected that the outliers -belong to an alternative distribution, then those observations could -have a large impact on the results and call into question their -robustness, especially if significance is conditional on their -inclusion. - -On the other hand, there are also outliers that cannot be detected by -statistical tools, but should be found and removed. For example, if we -are studying the effects of X on Y among teenagers and we have one -observation from a 20-year-old, this observation might not be a -\emph{statistical outlier}, but it is an outlier in the \emph{context} -of our research, and should be discarded to allow for valid inferences. - -\hypertarget{winsorization}{% -\subsection{Winsorization}\label{winsorization}} - -\emph{Removing} outliers can in this case be a valid strategy, and -ideally one would report results with and without outliers to see the -extent of their impact on results. This approach however can reduce -statistical power. Therefore, some propose a \emph{recoding} approach, -namely, winsorization: bringing outliers back within acceptable limits -\citep[e.g., 3 MADs,][]{tukey1963less}. However, if possible, it is -recommended to collect enough data so that even after removing outliers, -there is still sufficient statistical power without having to resort to -winsorization \citep{leys2019outliers}. - -The \emph{easystats} ecosystem makes it easy to incorporate this step -into your workflow through the \texttt{winsorize()} function of -\emph{\{datawizard\}}, a lightweight R package to facilitate data -wrangling and statistical transformations \citep{patil2022datawizard}. -This procedure will bring back univariate outliers within the limits of -`acceptable' values, based either on the percentile, the \emph{z} score, -or its robust alternative based on the MAD. - -\begin{Shaded} -\begin{Highlighting}[] -\NormalTok{data[}\DecValTok{1501}\SpecialCharTok{:}\DecValTok{1502}\NormalTok{, ] }\CommentTok{\# See outliers rows} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> height weight -#> 1501 100 258 -#> 1502 100 200 -\end{verbatim} - -\begin{Shaded} -\begin{Highlighting}[] -\CommentTok{\# Winsorizing using the MAD} -\FunctionTok{library}\NormalTok{(datawizard)} -\NormalTok{winsorized\_data }\OtherTok{\textless{}{-}} \FunctionTok{winsorize}\NormalTok{(data, }\AttributeTok{method =} \StringTok{"zscore"}\NormalTok{, }\AttributeTok{robust =} \ConstantTok{TRUE}\NormalTok{, }\AttributeTok{threshold =} \DecValTok{3}\NormalTok{)} - -\CommentTok{\# Values \textgreater{} +/{-} MAD have been winsorized} -\NormalTok{winsorized\_data[}\DecValTok{1501}\SpecialCharTok{:}\DecValTok{1502}\NormalTok{, ]} -\end{Highlighting} -\end{Shaded} - -\begin{verbatim} -#> height weight -#> 1501 82.7912 188.3736 -#> 1502 82.7912 188.3736 -\end{verbatim} - -\hypertarget{the-importance-of-transparency}{% -\subsection{The Importance of -Transparency}\label{the-importance-of-transparency}} - -Once again, it is a critical part of a sound outlier treatment that -regardless of which SOD method used, it should be reported in a -reproducible manner. Ideally, the handling of outliers should be -specified \emph{a priori} with as much detail as possible, and -preregistered, to limit researchers' degrees of freedom and therefore -risks of false positives \citep{leys2019outliers}. This is especially -true given that interesting outliers and random outliers are often times -hard to distinguish in practice. Thus, researchers should always -prioritize transparency and report all of the following information: (a) -how many outliers were identified; (b) according to which method and -criteria, (c) using which function of which R package (if applicable), -and (d) how they were handled (excluded or winsorized, if the latter, -using what threshold). If at all possible, (e) the corresponding code -script along with the data should be shared on a public repository like -the Open Science Framework (OSF), so that the exclusion criteria can be -reproduced precisely. - -\hypertarget{conclusion}{% -\section{Conclusion}\label{conclusion}} - -In this paper, we have showed how to investigate outliers using the -\texttt{check\_outliers()} function of the \emph{\{performance\}} -package while following current good practices. However, best practice -for outlier treatment does not stop at using appropriate statistical -algorithms, but entails respecting existing recommendations, such as -preregistration, reproducibility, consistency, transparency, and -justification. Ideally, one would additionally also report the package, -function, and threshold used (linking to the full code when possible). -We hope that this paper and the accompanying \texttt{check\_outlier()} -function of \emph{easystats} will help researchers engage in good -research practices while providing a smooth outlier detection -experience. - -% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% %% optional -% \supplementary{The following are available online at www.mdpi.com/link, Figure S1: title, Table S1: title, Video S1: title.} -% -% % Only for the journal Methods and Protocols: -% % If you wish to submit a video article, please do so with any other supplementary material. -% % \supplementary{The following are available at www.mdpi.com/link: Figure S1: title, Table S1: title, Video S1: title. A supporting video article is available at doi: link.} - -\vspace{6pt} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\acknowledgments{\emph{\{performance\}} is part of the collaborative -\href{https://github.com/easystats/easystats}{\emph{easystats}} -ecosystem \citep{easystatspackage}. Thus, we thank all -\href{https://github.com/orgs/easystats/people}{members of easystats}, -contributors, and users alike.} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\authorcontributions{R.T. drafted the paper; all authors contributed to -both the writing of the paper and the conception of the software.} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\conflictsofinterest{The authors declare no conflict of interest.} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% optional -\abbreviations{The following abbreviations are used in this manuscript:\\ - -\noindent -\begin{tabular}{@{}ll} -SOD & Statistical outlier detection \\ -SEM & Structural equation modelling \\ -SD & Standard deviation \\ -MAD & Median absolute deviation \\ -IQR & Interquartile range \\ -HDI & Highest density interval \\ -BCI & Bias corrected and accelerated interval \\ -MCD & Minimum covariance determinant \\ -ICS & invariant coordinate selection \\ -OSF & Open Science Framework \\ -\end{tabular}} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% Citations and References in Supplementary files are permitted provided that they also appear in the reference list here. - -%===================================== -% References, variant A: internal bibliography -%===================================== -%\reftitle{References} -%\begin{thebibliography}{999} -% Reference 1 -%\bibitem[Author1(year)]{ref-journal} -%Author1, T. The title of the cited article. {\em Journal Abbreviation} {\bf 2008}, {\em 10}, 142--149. -% Reference 2 -%\bibitem[Author2(year)]{ref-book} -%Author2, L. The title of the cited contribution. In {\em The Book Title}; Editor1, F., Editor2, A., Eds.; Publishing House: City, Country, 2007; pp. 32--58. -%\end{thebibliography} - -% The following MDPI journals use author-date citation: Arts, Econometrics, Economies, Genealogy, Humanities, IJFS, JRFM, Laws, Religions, Risks, Social Sciences. For those journals, please follow the formatting guidelines on http://www.mdpi.com/authors/references -% To cite two works by the same author: \citeauthor{ref-journal-1a} (\citeyear{ref-journal-1a}, \citeyear{ref-journal-1b}). This produces: Whittaker (1967, 1975) -% To cite two works by the same author with specific pages: \citeauthor{ref-journal-3a} (\citeyear{ref-journal-3a}, p. 328; \citeyear{ref-journal-3b}, p.475). This produces: Wong (1999, p. 328; 2000, p. 475) - -%===================================== -% References, variant B: external bibliography -%===================================== -\reftitle{References} -\externalbibliography{yes} -\bibliography{mybibfile.bib} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% optional - -%% for journal Sci -%\reviewreports{\\ -%Reviewer 1 comments and authors’ response\\ -%Reviewer 2 comments and authors’ response\\ -%Reviewer 3 comments and authors’ response -%} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - -\end{document} diff --git a/papers/Mathematics/paper_files/figure-latex/model-1.pdf b/papers/Mathematics/paper_files/figure-latex/model-1.pdf deleted file mode 100644 index 981b683182c03b614ea89b61e359f74ecda8f020..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 7824 zcmZ{JcRZY1*S1IyBm~i-4IxM{jNW_iqed6TL=2;hZuAx{38MEJ9KCm?@B6o|Yq9AlC~@=g2oSLaEd_lI8Vy33xf1aKcmePy 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zfVUgWo=gx37AC`H{__Hgiiik_0PTT)*&tZ8fxCc+ziePpY^wjXVLxnOb;5tyz+h|_ z{>ugt``3O#LV{Rv^q+o$5Zw9y+a~cZn}~$OzjBBQO8l!nQLqG7QvK(Cq7b2f$3n!h z-z + \usepackage[utf8]{inputenc} + %\VignetteIndexEntry{Checking outliers with *performance*} + %\VignetteEngine{knitr::rmarkdown} +editor_options: + chunk_output_type: console +--- + +```{r , include=FALSE} +library(knitr) +library(performance) +options(knitr.kable.NA = "") +knitr::opts_chunk$set( + comment = ">", + message = FALSE, + warning = FALSE, + out.width = "100%", + dpi = 450 +) +options(digits = 2) + +pkgs <- c( + "see", "performance", "datawizard", "rempsyc", + "ggplot2", "flextable", "ftExtra" +) +successfully_loaded <- vapply(pkgs, requireNamespace, FUN.VALUE = logical(1L), quietly = TRUE) +can_evaluate <- all(successfully_loaded) + +if (can_evaluate) { + knitr::opts_chunk$set(eval = TRUE) + vapply(pkgs, require, FUN.VALUE = logical(1L), quietly = TRUE, character.only = TRUE) +} else { + knitr::opts_chunk$set(eval = FALSE) +} +``` + + +# Reuse of this Material + +> Note: This vignette is an extended write-up of the [JOSE paper](https://jose.theoj.org/papers/42749638170253bb2854649fb52bf4ca). This educational module can be freely reused for teaching purposes as long as the original JOSE paper and this vignette are cited or acknowledged. The raw code file, which can be adapted to other rmarkdown formats for teaching purposes, can be accessed [here](https://github.com/easystats/performance/blob/HEAD/vignettes/check_outliers.Rmd). To contribute to and improve this content directly, please submit a Pull Request at the *{performance}* package GitHub repository by following our usual contributing guidelines: https://easystats.github.io/performance/CONTRIBUTING.html. To report issues or problems, with this module, or seek support, please open an issue: https://github.com/easystats/performance/issues. + +# Summary + +Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. In this vignette, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and model-based statistical outlier detection methods, their recommended threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of transparency. + +# Statement of Need + +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. + +Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. + +One possible reason is that researchers are not aware of the existing recommendations, or do not know how to implement them using their analysis software. In this paper, we show how to follow current best practices for automatic and reproducible statistical outlier detection (SOD) using R and the *{performance}* package [@ludecke2021performance], which is part of the *easystats* ecosystem of packages that build an R framework for easy statistical modeling, visualization, and reporting [@easystatspackage]. Installation instructions can be found on [GitHub](https://github.com/easystats/performance) or its [website](https://easystats.github.io/performance/), and its list of dependencies on [CRAN](https://cran.r-project.org/package=performance). + +The instructional materials that follow are aimed at an audience of researchers who want to follow good practices, and are appropriate for advanced undergraduate students, graduate students, professors, or professionals having to deal with the nuances of outlier treatment. + +# Identifying Outliers + +Although many researchers attempt to identify outliers with measures based on the mean (e.g., _z_ scores), those methods are problematic because the mean and standard deviation themselves are not robust to the influence of outliers and those methods also assume normally distributed data (i.e., a Gaussian distribution). Therefore, current guidelines recommend using robust methods to identify outliers, such as those relying on the median as opposed to the mean [@leys2019outliers; @leys2013outliers; @leys2018outliers]. + +Nonetheless, which exact outlier method to use depends on many factors. In some cases, eye-gauging odd observations can be an appropriate solution, though many researchers will favour algorithmic solutions to detect potential outliers, for example, based on a continuous value expressing the observation stands out from the others. + +One of the factors to consider when selecting an algorithmic outlier detection method is the statistical test of interest. When using a regression model, relevant information can be found by identifying observations that do not fit well with the model. This approach, known as model-based outliers detection (as outliers are extracted after the statistical model has been fit), can be contrasted with distribution-based outliers detection, which is based on the distance between an observation and the "center" of its population. Various quantification strategies of this distance exist for the latter, both univariate (involving only one variable at a time) or multivariate (involving multiple variables). + +When no method is readily available to detect model-based outliers, such as for structural equation modelling (SEM), looking for multivariate outliers may be of relevance. For simple tests (_t_ tests or correlations) that compare values of the same variable, it can be appropriate to check for univariate outliers. However, univariate methods can give false positives since _t_ tests and correlations, ultimately, are also models/multivariable statistics. They are in this sense more limited, but we show them nonetheless for educational purposes. + +Importantly, whatever approach researchers choose remains a subjective decision, which usage (and rationale) must be transparently documented and reproducible [@leys2019outliers]. Researchers should commit (ideally in a preregistration) to an outlier treatment method before collecting the data. They should report in the paper their decisions and details of their methods, as well as any deviation from their original plan. These transparency practices can help reduce false positives due to excessive researchers' degrees of freedom (i.e., choice flexibility throughout the analysis). In the following section, we will go through each of the mentioned methods and provide examples on how to implement them with R. + +## Univariate Outliers + +Researchers frequently attempt to identify outliers using measures of deviation from the center of a variable's distribution. One of the most popular such procedure is the _z_ score transformation, which computes the distance in standard deviation (SD) from the mean. However, as mentioned earlier, this popular method is not robust. Therefore, for univariate outliers, it is recommended to use the median along with the Median Absolute Deviation (MAD), which are more robust than the interquartile range or the mean and its standard deviation [@leys2019outliers; @leys2013outliers]. + +Researchers can identify outliers based on robust (i.e., MAD-based) _z_ scores using the `check_outliers()` function of the *{performance}* package, by specifying `method = "zscore_robust"`.^[Note that `check_outliers()` only checks numeric variables.] Although @leys2013outliers suggest a default threshold of 2.5 and @leys2019outliers a threshold of 3, *{performance}* uses by default a less conservative threshold of ~3.29.^[3.29 is an approximation of the two-tailed critical value for _p_ < .001, obtained through `qnorm(p = 1 - 0.001 / 2)`. We chose this threshold for consistency with the thresholds of all our other methods.] That is, data points will be flagged as outliers if they go beyond +/- ~3.29 MAD. Users can adjust this threshold using the `threshold` argument. + +Below we provide example code using the `mtcars` dataset, which was extracted from the 1974 *Motor Trend* US magazine. The dataset contains fuel consumption and 10 characteristics of automobile design and performance for 32 different car models (see `?mtcars` for details). We chose this dataset because it is accessible from base R and familiar to many R users. We might want to conduct specific statistical analyses on this data set, say, _t_ tests or structural equation modelling, but first, we want to check for outliers that may influence those test results. + +Because the automobile names are stored as column names in `mtcars`, we first have to convert them to an ID column to benefit from the `check_outliers()` ID argument. Furthermore, we only really need a couple columns for this demonstration, so we choose the first four (`mpg` = Miles/(US) gallon; `cyl` = Number of cylinders; `disp` = Displacement; `hp` = Gross horsepower). Finally, because there are no outliers in this dataset, we add two artificial outliers before running our function. + +```{r z_score} +library(performance) + +# Create some artificial outliers and an ID column +data <- rbind(mtcars[1:4], 42, 55) +data <- cbind(car = row.names(data), data) + +outliers <- check_outliers(data, method = "zscore_robust", ID = "car") +outliers +``` + +What we see is that `check_outliers()` with the robust _z_ score method detected two outliers: cases 33 and 34, which were the observations we added ourselves. They were flagged for two variables specifically: `mpg` (Miles/(US) gallon) and `cyl` (Number of cylinders), and the output provides their exact _z_ score for those variables. + +We describe how to deal with those cases in more details later in the paper, but should we want to exclude these detected outliers from the main dataset, we can extract row numbers using `which()` on the output object, which can then be used for indexing: + +```{r} +which(outliers) + +data_clean <- data[-which(outliers), ] +``` + +All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers using the generic `plot()` function on the resulting outlier object after loading the {see} package. + +```{r univariate, eval=FALSE} +library(see) +plot(outliers) +``` + +```{r univariate_implicit, fig.cap = "Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.", echo=FALSE} +library(see) +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 + )) +``` + +Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). + +## Multivariate Outliers + +Univariate outliers can be useful when the focus is on a particular variable, for instance the reaction time, as extreme values might be indicative of inattention or non-task-related behavior^[ Note that they might not be the optimal way of treating reaction time outliers [@ratcliff1993methods; @van1995statistical]]. + +However, in many scenarios, variables of a data set are not independent, and an abnormal observation will impact multiple dimensions. For instance, a participant giving random answers to a questionnaire. In this case, computing the _z_ score for each of the questions might not lead to satisfactory results. Instead, one might want to look at these variables together. + +One common approach for this is to compute multivariate distance metrics such as the Mahalanobis distance. Although the Mahalanobis distance is very popular, just like the regular _z_ scores method, it is not robust and is heavily influenced by the outliers themselves. Therefore, for multivariate outliers, it is recommended to use the Minimum Covariance Determinant, a robust version of the Mahalanobis distance [MCD, @leys2018outliers; @leys2019outliers]. + +In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +```{r multivariate} +outliers <- check_outliers(data, method = "mcd") +outliers +``` + +Here, we detected 9 multivariate outliers (i.e,. when looking at all variables of our dataset together). + +```{r multivariate_plot, eval=FALSE} +plot(outliers) +``` + +```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 + )) +``` + +Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). + +## Model-Based Outliers + +Working with regression models creates the possibility of using model-based SOD methods. These methods rely on the concept of *leverage*, that is, how much influence a given observation can have on the model estimates. If few observations have a relatively strong leverage/influence on the model, one can suspect that the model's estimates are biased by these observations, in which case flagging them as outliers could prove helpful (see next section, "Handling Outliers"). + +In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] + +Currently, most lm models are supported (with the exception of `glmmTMB`, `lmrob`, and `glmrob` models), as long as they are supported by the underlying functions `stats::cooks.distance()` (or `loo::pareto_k_values()`) and `insight::get_data()` (for a full list of the 225 models currently supported by the `insight` package, see https://easystats.github.io/insight/#list-of-supported-models-by-class). Also note that although `check_outliers()` supports the pipe operators (`|>` or `%>%`), it does not support `tidymodels` at this time. We show a demo below. + +```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} +model <- lm(disp ~ mpg * hp, data = data) +outliers <- check_outliers(model, method = "cook") +outliers + +plot(outliers) +``` + +Using the model-based outlier detection method, we identified two outliers. + +Table 1 below summarizes which methods to use in which cases, and with what threshold. The recommended thresholds are the default thresholds. + +```{r table1_prep, echo=FALSE} +df <- data.frame( + `Statistical Test` = c( + "Supported regression model", + "Structural Equation Modeling (or other unsupported model)", + "Simple test with few variables (*t* test, correlation, etc.)" + ), + `Diagnosis Method` = c( + "**Model-based**: Cook (or Pareto for Bayesian models)", + "**Multivariate**: Minimum Covariance Determinant (MCD)", + "**Univariate**: robust *z* scores (MAD)" + ), + `Recommended Threshold` = c( + "_qf(0.5, ncol(x), nrow(x) - ncol(x))_ (or 0.7 for Pareto)", + "_qchisq(p = 1 - 0.001, df = ncol(x))_", + "_qnorm(p = 1 - 0.001 / 2)_, ~ 3.29" + ), + `Function Usage` = c( + '_check_outliers(model, method = "cook")_', + '_check_outliers(data, method = "mcd")_', + '_check_outliers(data, method = "zscore_robust")_' + ), + check.names = FALSE +) +``` + +### Table 1 + +_Summary of Statistical Outlier Detection Methods Recommendations_ + +```{r table1_print, echo=FALSE, message=FALSE} +x <- flextable::flextable(df, cwidth = 2.25) +x <- flextable::theme_apa(x) +x <- flextable::font(x, fontname = "Latin Modern Roman", part = "all") +# x <- flextable::fontsize(x, size = 10, part = "all") +ftExtra::colformat_md(x) +``` + +## Cook's Distance vs. MCD + +@leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. + +However, distribution-based approaches are not a silver bullet either, and there are cases where the usage of methods agnostic to theoretical and statistical models of interest might be problematic. For example, a very tall person would be expected to also be much heavier than average, but that would still fit with the expected association between height and weight (i.e., it would be in line with a model such as `weight ~ height`). In contrast, using multivariate outlier detection methods there may flag this person as being an outlier---being unusual on two variables, height and weight---even though the pattern fits perfectly with our predictions. + +In the example below, we plot the raw data and see two possible outliers. The first one falls along the regression line, and is therefore "in line" with our hypothesis. The second one clearly diverges from the regression line, and therefore we can conclude that this outlier may have a disproportionate influence on our model. + +```{r scatter, fig.cap = "Scatter plot of height and weight, with two extreme observations: one model-consistent (top-right) and the other, model-inconsistent (i.e., an outlier; bottom-right)."} +data <- women[rep(seq_len(nrow(women)), each = 100), ] +data <- rbind(data, c(100, 258), c(100, 200)) +model <- lm(weight ~ height, data) +rempsyc::nice_scatter(data, "height", "weight") +``` + +Using either the *z*-score or MCD methods, our model-consistent observation will be incorrectly flagged as an outlier or influential observation. + +```{r} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd")) +which(outliers) +``` + +In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. + +```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model."} +outliers <- check_outliers(model, method = "cook") +which(outliers) +plot(outliers) +``` + +Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. + +## Composite Outlier Score + +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. + +In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. + +```{r multimethod, fig.cap = "Visual depiction of outliers using several different statistical outlier detection methods."} +outliers <- check_outliers(model, method = c("zscore_robust", "mcd", "cook")) +which(outliers) +``` + +Outliers (counts or per variables) for individual methods can then be obtained through attributes. For example: + +```{r} +attributes(outliers)$outlier_var$zscore_robust +``` + +An example sentence for reporting the usage of the composite method could be: + +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. + +# Handling Outliers + +The above section demonstrated how to identify outliers using the `check_outliers()` function in the *{performance}* package. But what should we do with these outliers once identified? Although it is common to automatically discard any observation that has been marked as "an outlier" as if it might infect the rest of the data with its statistical ailment, we believe that the use of SOD methods is but one step in the get-to-know-your-data pipeline; a researcher or analyst's _domain knowledge_ must be involved in the decision of how to deal with observations marked as outliers by means of SOD. Indeed, automatic tools can help detect outliers, but they are nowhere near perfect. Although they can be useful to flag suspect data, they can have misses and false alarms, and they cannot replace human eyes and proper vigilance from the researcher. If you do end up manually inspecting your data for outliers, it can be helpful to think of outliers as belonging to different types of outliers, or categories, which can help decide what to do with a given outlier. + +## Error, Interesting, and Random Outliers + +@leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. + +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. + +We should also keep in mind that there might be error outliers that are not detected by statistical tools, but should nonetheless be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded. We could call these observations *undetected* error outliers, in the sense that although they do not statistically stand out, they do not belong to the theoretical or empirical distribution of interest (e.g., teenagers). In this way, we should not blindly rely on statistical outlier detection methods; doing our due diligence to investigate undetected error outliers relative to our specific research question is also essential for valid inferences. + +## Winsorization + +_Removing_ outliers can in this case be a valid strategy, and ideally one would report results with and without outliers to see the extent of their impact on results. This approach however can reduce statistical power. Therefore, some propose a _recoding_ approach, namely, winsorization: bringing outliers back within acceptable limits [e.g., 3 MADs, @tukey1963less]. However, if possible, it is recommended to collect enough data so that even after removing outliers, there is still sufficient statistical power without having to resort to winsorization [@leys2019outliers]. + +The _easystats_ ecosystem makes it easy to incorporate this step into your workflow through the `winsorize()` function of *{datawizard}*, a lightweight R package to facilitate data wrangling and statistical transformations [@patil2022datawizard]. This procedure will bring back univariate outliers within the limits of 'acceptable' values, based either on the percentile, the _z_ score, or its robust alternative based on the MAD. + +```{r winsorization} +data[1501:1502, ] # See outliers rows +# Winsorizing using the MAD +library(datawizard) +winsorized_data <- winsorize(data, method = "zscore", robust = TRUE, threshold = 3) +# Values > +/- MAD have been winsorized +winsorized_data[1501:1502, ] +``` + +## The Importance of Transparency + +Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. + +# Conclusion + +In this vignette, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. + +# References diff --git a/vignettes/paper.bib b/vignettes/paper.bib new file mode 100644 index 000000000..56c8ae7e1 --- /dev/null +++ b/vignettes/paper.bib @@ -0,0 +1,161 @@ +@article{leys2019outliers, + title = {How to Classify, Detect, and Manage Univariate and Multivariate Outliers, With Emphasis on Pre-Registration},author = {Leys, Christophe and Delacre, Marie and Mora, Youri L. and Lakens, Daniël and Ley, Christophe}, + journal = {International Review of Social Psychology}, + year = {2019}, + doi = {10.5334/irsp.289} +} + +@article{leys2013outliers, + title = {Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median}, + author = {Christophe Leys and Christophe Ley and Olivier Klein and Philippe Bernard and Laurent Licata}, + journal = {Journal of Experimental Social Psychology}, + volume = {49}, + number = {4}, + pages = {764-766}, + year = {2013}, + doi = {10.1016/j.jesp.2013.03.013}, + url = {https://doi.org/10.1016/j.jesp.2013.03.013} +} + +@article{leys2018outliers, + title = {Detecting multivariate outliers: Use a robust variant of the Mahalanobis distance}, + journal = {Journal of Experimental Social Psychology}, + volume = {74}, + pages = {150-156}, + year = {2018}, + issn = {0022-1031}, + doi = {10.1016/j.jesp.2017.09.011}, + url = {https://www.sciencedirect.com/science/article/pii/S0022103117302123}, + author = {Christophe Leys and Olivier Klein and Yves Dominicy and Christophe Ley}, +} + +@article{simmons2011false, + author = {Joseph P. Simmons and Leif D. Nelson and Uri Simonsohn}, + title ={False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant}, + journal = {Psychological Science}, + volume = {22}, + number = {11}, + pages = {1359-1366}, + year = {2011}, + doi = {10.1177/0956797611417632}, + URL = {https://doi.org/10.1177/0956797611417632}, +} + +@software{easystatspackage, + title = {{easystats}: Streamline Model Interpretation, Visualization, and Reporting}, + author = {Daniel Lüdecke and Dominique Makowski and Mattan S. Ben-Shachar and Indrajeet Patil and Brenton M. Wiernik and Etienne Bacher and Rémi Thériault}, + date = {2023-02-04T22:06:06Z}, + origdate = {2019-01-28T10:39:29Z}, + url = {https://easystats.github.io/easystats/} +} + +@Article{ludecke2021performance, + author = {Daniel Lüdecke and Mattan S. Ben-Shachar and Indrajeet Patil and Philip Waggoner and Dominique Makowski}, + title = {{performance}: An {R} package for assessment, comparison and testing of statistical models}, + volume = {6}, + number = {60}, + journal = {Journal of Open Source Software}, + year = {2021}, + pages = {3139}, + doi = {10.21105/joss.03139}, + url = {https://doi.org/10.21105/joss.03139} + } + +@Article{patil2022datawizard, + title = {{datawizard}: An {R} package for easy data preparation and statistical transformations}, + author = {Indrajeet Patil and Dominique Makowski and Mattan S. Ben-Shachar and Brenton M. Wiernik and Etienne Bacher and Daniel Lüdecke}, + journal = {Journal of Open Source Software}, + year = {2022}, + volume = {7}, + number = {78}, + pages = {4684}, + doi = {10.21105/joss.04684}, + } + +@article{cook1977detection, + author = {R. Dennis Cook}, + title = {Detection of Influential Observation in Linear Regression}, + journal = {Technometrics}, + volume = {19}, + number = {1}, + pages = {15-18}, + year = {1977}, + publisher = {Taylor & Francis}, + doi = {10.1080/00401706.1977.10489493} +} + +@book{iglewicz1993outliers, + title = {How to detect and handle outliers (Vol. 16)}, + publisher = {Asq Press}, + author = {Iglewicz, B. and Hoaglin, D. C}, + year = {1993} +} + +@article{gnanadesikan1972robust, + title = {Robust estimates, residuals, and outlier detection with multiresponse data}, + author = {Gnanadesikan, R. and Kettenring, J. R}, + journal = {Biometrics}, + pages = {81-124}, + year = {1972} +} + +@article{hubert2018mcd, + author = {Hubert, Mia and Debruyne, Michiel and Rousseeuw, Peter J.}, + title = {Minimum covariance determinant and extensions}, + journal = {Wiley Interdisciplinary Reviews: Computational Statistics}, + volume = {10}, + number = {3}, + pages = {e1421}, + doi = {10.1002/wics.1421}, + url = {https://doi.org/10.1002/wics.1421}, + year = {2018} +} + +@article{tukey1963less, + title={Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/Winsorization 1}, + author={Tukey, John W and McLaughlin, Donald H}, + journal={Sankhy{\=a}: The Indian Journal of Statistics, Series A}, + pages={331--352}, + year={1963}, + publisher={JSTOR} +} + +@article{van1995statistical, + title={Statistical mimicking of reaction time data: Single-process models, parameter variability, and mixtures}, + author={Van Zandt, Trisha and Ratcliff, Roger}, + journal={Psychonomic Bulletin \& Review}, + volume={2}, + number={1}, + pages={20--54}, + year={1995}, + publisher={Springer}, + doi = {10.3758/BF03214411} +} + +@article{ratcliff1993methods, + title={Methods for dealing with reaction time outliers.}, + author={Ratcliff, Roger}, + journal={Psychological bulletin}, + volume={114}, + number={3}, + pages={510}, + year={1993}, + publisher={American Psychological Association}, + doi = {10.1037/0033-2909.114.3.510} +} + +@book{mcelreath2020statistical, + title={Statistical rethinking: A Bayesian course with examples in {R} and Stan}, + author={McElreath, Richard}, + year={2020}, + publisher={CRC press} +} + +@Manual{rcore, + title = {{R}: A Language and Environment for Statistical Computing}, + author = {{R Core Team}}, + organization = {R Foundation for Statistical Computing}, + address = {Vienna, Austria}, + year = {2021}, + url = {https://www.R-project.org/} +} \ No newline at end of file

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a/papers/Mathematics/paper.Rmd +++ b/papers/JOSE/paper_longform.Rmd @@ -1,42 +1,48 @@ --- title: "Check your outliers! An introduction to identifying statistical outliers in R with *easystats*" -author: +tags: + - R + - univariate outliers + - multivariate outliers + - robust detection methods + - easystats +authors: - name: Rémi Thériault - affil: 1,* orcid: 0000-0003-4315-6788 + affiliation: 1 - name: Mattan S. Ben-Shachar - affil: 2 orcid: 0000-0002-4287-4801 + affiliation: 2 - name: Indrajeet Patil - affil: 3 orcid: 0000-0003-1995-6531 + affiliation: 3 - name: Daniel Lüdecke - affil: 4 orcid: 0000-0002-8895-3206 + affiliation: 4 - name: Brenton M. Wiernik - affil: 5 orcid: 0000-0001-9560-6336 + affiliation: 5 - name: Dominique Makowski - affil: 6 orcid: 0000-0001-5375-9967 -affiliation: - - num: 1 - address: Department of Psychology, Université du Québec à Montréal, Montréal, Québec, Canada - - num: 2 - address: Independent Researcher - - num: 3 - address: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany - - num: 4 - address: Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, Germany - - num: 5 - address: Independent Researcher, Tampa, FL, USA - - num: 6 - address: School of Psychology, University of Sussex, Brighton, UK + affiliation: 6 +affiliations: + - index: 1 + name: Department of Psychology, Université du Québec à Montréal, Montréal, Québec, Canada + - index: 2 + name: Independent Researcher + - index: 3 + name: Center for Humans and Machines, Max Planck Institute for Human Development, Berlin, Germany + - index: 4 + name: Institute of Medical Sociology, University Medical Center Hamburg-Eppendorf, Germany + - index: 5 + name: Independent Researcher, Tampa, FL, USA + - index: 6 + name: School of Psychology, University of Sussex, Brighton, UK correspondence: theriault.remi@courrier.uqam.ca. -journal: "mathematics" type: article status: submit -bibliography: mybibfile.bib +date: 7 June 2023 +bibliography: paper.bib simplesummary: | The *{performance}* package from the *easystats* ecosystem makes it easy to diagnose outliers in R and according to current best practices thanks to the @@ -45,7 +51,7 @@ abstract: | Beyond the challenge of keeping up-to-date with current best practices regarding the diagnosis and treatment of outliers, an additional difficulty arises concerning the mathematical implementation of the recommended methods. - In this paper, we provide an overview of current recommandations and best + In this paper, we provide an overview of current recommendations and best practices and demonstrate how they can easily and conveniently be implemented in the R statistical computing software, using the *{performance}* package of the *easystats* ecosystem. We cover univariate, multivariate, and @@ -53,7 +59,7 @@ abstract: | threshold, standard output, and plotting methods. We conclude with recommendations on the handling of outliers: the different theoretical types of outliers, whether to exclude or winsorize them, and the importance of - transparency. + transparency. keywords: | univariate outliers; multivariate outliers; robust detection methods; R; easystats acknowledgement: | @@ -90,7 +96,10 @@ abbreviations: long: invariant coordinate selection - short: OSF long: Open Science Framework -output: rticles::mdpi_article +output: + rticles::joss_article: + journal: "JOSE" +csl: apa.csl --- ```{r setup, include=FALSE} @@ -107,9 +116,9 @@ library(see) library(datawizard) ``` -# Introduction +# Statement of Need -Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" are hard to define. +Real-life data often contain observations that can be considered *abnormal* when compared to the main population. The cause of it---be it because they belong to a different distribution (originating from a different generative process) or simply being extreme cases, statistically rare but not impossible---can be hard to assess, and the boundaries of "abnormal" difficult to define. Nonetheless, the improper handling of these outliers can substantially affect statistical model estimations, biasing effect estimations and weakening the models' predictive performance. It is thus essential to address this problem in a thoughtful manner. Yet, despite the existence of established recommendations and guidelines, many researchers still do not treat outliers in a consistent manner, or do so using inappropriate strategies [@simmons2011false; @leys2013outliers]. @@ -155,12 +164,21 @@ data_clean <- data[-which(outliers), ] All `check_outliers()` output objects possess a `plot()` method, meaning it is also possible to visualize the outliers: -```{r univariate, fig.cap = "Visual depiction of outliers using the robust z-score method."} +```{r univariate, eval=FALSE} library(see) plot(outliers) ``` +```{r univariate_implicit, fig.cap = "Visual depiction of outliers using the robust z-score method. The distance represents an aggregate score for variables mpg, cyl, disp, and hp.", echo=FALSE} +library(see) + +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 +)) +``` + Other univariate methods are available, such as using the interquartile range (IQR), or based on different intervals, such as the Highest Density Interval (HDI) or the Bias Corrected and Accelerated Interval (BCI). These methods are documented and described in the function's [help page](). ## Multivariate Outliers @@ -173,13 +191,22 @@ One common approach for this is to compute multivariate distance metrics such as In *{performance}*'s `check_outliers()`, one can use this approach with `method = "mcd"`.^[Our default threshold for the MCD method is defined by `stats::qchisq(p = 1 - 0.001, df = ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] -```{r multivariate, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance."} +```{r multivariate} outliers <- check_outliers(data, method = "mcd") outliers +``` +```{r multivariate_plot, eval=FALSE} plot(outliers) ``` +```{r multivariate_implicit, fig.cap = "Visual depiction of outliers using the Minimum Covariance Determinant (MCD) method, a robust version of the Mahalanobis distance. The distance represents the MCD scores for variables mpg, cyl, disp, and hp.", echo=FALSE} +plot(outliers) + + ggplot2::theme(axis.text.x = ggplot2::element_text( + angle = 45, size = 7 +)) +``` + Other multivariate methods are available, such as another type of robust Mahalanobis distance that in this case relies on an orthogonalized Gnanadesikan-Kettenring pairwise estimator [@gnanadesikan1972robust]. These methods are documented and described in the function's [help page](https://easystats.github.io/performance/reference/check_outliers.html). ## Model-Based Outliers @@ -188,7 +215,7 @@ Working with regression models creates the possibility of using model-based SOD In {performance}, two such model-based SOD methods are currently available: Cook's distance, for regular regression models, and Pareto, for Bayesian models. As such, `check_outliers()` can be applied directly on regression model objects, by simply specifying `method = "cook"` (or `method = "pareto"` for Bayesian models).^[Our default threshold for the Cook method is defined by `stats::qf(0.5, ncol(x), nrow(x) - ncol(x))`, which again is an approximation of the critical value for _p_ < .001 consistent with the thresholds of our other methods.] -```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals)."} +```{r model, fig.cap = "Visual depiction of outliers based on Cook's distance (leverage and standardized residuals), based on the fitted model."} model <- lm(disp ~ mpg * disp, data = data) outliers <- check_outliers(model, method = "cook") outliers @@ -218,7 +245,7 @@ knitr::kable( caption = "Summary of Statistical Outlier Detection Methods Recommendations.", longtable = TRUE) ``` -### Cook's Distance vs. MCD +## Cook's Distance vs. MCD @leys2018outliers report a preference for the MCD method over Cook's distance. This is because Cook's distance removes one observation at a time and checks its corresponding influence on the model each time [@cook1977detection], and flags any observation that has a large influence. In the view of these authors, when there are several outliers, the process of removing a single outlier at a time is problematic as the model remains "contaminated" or influenced by other possible outliers in the model, rendering this method suboptimal in the presence of multiple outliers. @@ -242,7 +269,7 @@ which(outliers) In contrast, the model-based detection method displays the desired behaviour: it correctly flags the person who is very tall but very light, without flagging the person who is both tall and heavy. -```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation)."} +```{r model2, fig.cap = "The leverage method (Cook's distance) correctly distinguishes the true outlier from the model-consistent extreme observation), based on the fitted model."} outliers <- check_outliers(model, method = "cook") which(outliers) plot(outliers) @@ -250,9 +277,9 @@ plot(outliers) Finally, unusual observations happen naturally: extreme observations are expected even when taken from a normal distribution. While statistical models can integrate this "expectation", multivariate outlier methods might be too conservative, flagging too many observations despite belonging to the right generative process. For these reasons, we believe that model-based methods are still preferable to the MCD when using supported regression models. Additionally, if the presence of multiple outliers is a significant concern, regression methods that are more robust to outliers should be considered---like _t_ regression or quantile regression---as they render their precise identification less critical [@mcelreath2020statistical]. -## Multiple Methods +## Composite Outlier Score -An alternative approach that is possible is to combine several methods, based on the assumption that different methods provide different angles of looking at the problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. +The *{performance}* package also offers an alternative, consensus-based approach that combines several methods, based on the assumption that different methods provide different angles of looking at a given problem. By applying a variety of methods, one can hope to "triangulate" the true outliers (those consistently flagged by multiple methods) and thus attempt to minimize false positives. In practice, this approach computes a composite outlier score, formed of the average of the binary (0 or 1) classification results of each method. It represents the probability that each observation is classified as an outlier by at least one method. The default decision rule classifies rows with composite outlier scores superior or equal to 0.5 as outlier observations (i.e., that were classified as outliers by at least half of the methods). In *{performance}*'s `check_outliers()`, one can use this approach by including all desired methods in the corresponding argument. @@ -269,7 +296,7 @@ attributes(outliers)$outlier_var$zscore_robust An example sentence for reporting the usage of the composite method could be: -> Based on a composite outlier score (see the 'check_outliers()' function in the 'performance' R package, [@ludecke2021performance]) obtained via the joint application of multiple outliers detection algorithms ((a) median absolute deviation (MAD)-based robust _z_ scores, [@leys2013outliers]; (b) Mahalanobis minimum covariance determinant (MCD), [@leys2019outliers]; and (c) Cook's distance, [@cook1977detection]), we excluded two participants that were classified as outliers by at least half of the methods used. +> Based on a composite outlier score [see the 'check_outliers()' function in the 'performance' R package, @ludecke2021performance] obtained via the joint application of multiple outliers detection algorithms [(a) median absolute deviation (MAD)-based robust _z_ scores, @leys2013outliers; (b) Mahalanobis minimum covariance determinant (MCD), @leys2019outliers; and (c) Cook's distance, @cook1977detection], we excluded two participants that were classified as outliers by at least half of the methods used. # Handling Outliers @@ -279,7 +306,7 @@ The above section demonstrated how to identify outliers using the `check_outlier @leys2019outliers distinguish between error outliers, interesting outliers, and random outliers. _Error outliers_ are likely due to human error and should be corrected before data analysis or outright removed since they are invalid observations. _Interesting outliers_ are not due to technical error and may be of theoretical interest; it might thus be relevant to investigate them further even though they should be removed from the current analysis of interest. _Random outliers_ are assumed to be due to chance alone and to belong to the correct distribution and, therefore, should be retained. -It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion. +It is recommended to _keep_ observations which are expected to be part of the distribution of interest, even if they are outliers [@leys2019outliers]. However, if it is suspected that the outliers belong to an alternative distribution, then those observations could have a large impact on the results and call into question their robustness, especially if significance is conditional on their inclusion, so should be removed. On the other hand, there are also outliers that cannot be detected by statistical tools, but should be found and removed. For example, if we are studying the effects of X on Y among teenagers and we have one observation from a 20-year-old, this observation might not be a _statistical outlier_, but it is an outlier in the _context_ of our research, and should be discarded to allow for valid inferences. @@ -302,9 +329,26 @@ winsorized_data[1501:1502, ] ## The Importance of Transparency -Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified; (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. +Once again, it is a critical part of a sound outlier treatment that regardless of which SOD method used, it should be reported in a reproducible manner. Ideally, the handling of outliers should be specified *a priori* with as much detail as possible, and preregistered, to limit researchers' degrees of freedom and therefore risks of false positives [@leys2019outliers]. This is especially true given that interesting outliers and random outliers are often times hard to distinguish in practice. Thus, researchers should always prioritize transparency and report all of the following information: (a) how many outliers were identified (including percentage); (b) according to which method and criteria, (c) using which function of which R package (if applicable), and (d) how they were handled (excluded or winsorized, if the latter, using what threshold). If at all possible, (e) the corresponding code script along with the data should be shared on a public repository like the Open Science Framework (OSF), so that the exclusion criteria can be reproduced precisely. # Conclusion In this paper, we have showed how to investigate outliers using the `check_outliers()` function of the *{performance}* package while following current good practices. However, best practice for outlier treatment does not stop at using appropriate statistical algorithms, but entails respecting existing recommendations, such as preregistration, reproducibility, consistency, transparency, and justification. Ideally, one would additionally also report the package, function, and threshold used (linking to the full code when possible). We hope that this paper and the accompanying `check_outlier()` function of *easystats* will help researchers engage in good research practices while providing a smooth outlier detection experience. +### Contributions + +R.T. drafted the paper; all authors contributed to both the writing of the paper and the conception of the software. + +### Acknowledgements + +*{performance}* is part of the collaborative [*easystats*](https://github.com/easystats/easystats) ecosystem [@easystatspackage]. Thus, we thank all [members of easystats](https://github.com/orgs/easystats/people), contributors, and users alike. + +### Funding information + +This research received no external funding. + +### Competing Interests + +The authors declare no conflict of interest + +# References \ No newline at end of file diff --git a/papers/JOSE/table1.jpg b/papers/JOSE/table1.jpg new file mode 100644 index 0000000000000000000000000000000000000000..5f29d676ef62503650e56f1de8ae6d5328ea1d4f GIT binary patch literal 393255 zcmeFZ1yo#JlQ!A}2niYpt_cv_-8+Qf0fIXOr)e5@>p+6LClK5n0t9!51Zgz5y9cLf z{?0r9H}kETZ|>ZG=H9vMu1T}b>D_YroZ6@MQ&mq@aX)jv40xg-BQFC$K|uk$L;eBo zR{)mM9w18qKuHO}0ssIW0nkv$0qDpP3UZS`q4?*q3)F8sWaq+RXW{aUpM#4-7;rxakOJUhVqs%F#>K|Meu9UKPeeyT^zL5}ZJErF~bqaWlNlZdYM*f0b zHOR)<#nsK-!_(`-$H1WAkkGKW_=Loyh9_7 z>mL||jZaKYP0#$CU0GdQ-`L#R-q}4l{dIPJad~xp^II+y0O~)9_0N+1E4lEIay>vp zLq)^*Ef>lIcjShOkB0u7`yqj(Du#*UQ(7MXM})6pv#L5C)A6bu6PY@VVG`5xt-Lt- 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} - 'skip$ - if$ - namesleft #1 > - { "; " * t * } - { - s nameptr "{ll}" format.name$ duplicate$ "others" = - { 't := } - { pop$ } - if$ - numnames #2 > - { "" * } - 'skip$ - if$ - t "others" = - {"; " * " et~al." * } - { "; " * t * } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {format.key} -{ empty$ - { key field.or.null } - { "" } - if$ -} - -FUNCTION {format.authors} -{ author empty$ - { "" } - { author format.names } - if$ -} - -FUNCTION {format.editors} -{ editor empty$ - { "" } - { editor format.names - editor num.names$ #1 > - { ", Eds." * } - { ", Ed." * } - if$ - } - if$ -} - - - - -FUNCTION {format.title} -{ title empty$ - { "" } - { title} - if$ -} - -FUNCTION {format.number.patent} -{ number empty$ - { "" } - { nationality empty$ - { number} - { nationality " " * number *} - if$ - } - if$ -} - -FUNCTION {format.full.names} -{'s := - #1 'nameptr := - s num.names$ 'numnames := - numnames 'namesleft := - { namesleft #0 > } - { s nameptr - "{vv~}{ll}" format.name$ 't := - nameptr #1 > - { - namesleft #1 > - { ", " * t * } - { - numnames #2 > - { "," * } - 'skip$ - if$ - t "others" = - { " et~al." * } - { " and " * t * } - if$ - } - if$ - } - 't - if$ - nameptr #1 + 'nameptr := - namesleft #1 - 'namesleft := - } - while$ -} - -FUNCTION {author.editor.full} -{ author empty$ - { editor empty$ - { "" } - { editor format.full.names } - if$ - } - { author format.full.names } - if$ -} - - - -FUNCTION {author.full} -{ author empty$ - { "" } - { author format.full.names } - if$ -} - -FUNCTION {editor.full} -{ editor empty$ - { "" } - { editor format.full.names } - if$ -} - -FUNCTION {make.full.names} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.full - { type$ "proceedings" = - 'editor.full - 'author.full - if$ - } - if$ -} - -FUNCTION {output.bibitem} -{ newline$ - "\bibitem[" write$ - label write$ - ")" make.full.names duplicate$ short.list = - { pop$ } - { * } - if$ - "]{" * write$ - cite$ write$ - "}" write$ - newline$ - "" - before.all 'output.state := -} - -FUNCTION {n.dashify} -{ 't := - "" - { t empty$ not } - { t #1 #1 substring$ "-" = - { t #1 #2 substring$ "--" = not - { "--" * - t #2 global.max$ substring$ 't := - } - { { t #1 #1 substring$ "-" = } - { "-" * - t #2 global.max$ substring$ 't := - } - while$ - } - if$ - } - { t #1 #1 substring$ * - t #2 global.max$ substring$ 't := - } - if$ - } - while$ -} - - -FUNCTION {format.date} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { " " year embolden * } - if$ -} - -FUNCTION {format.bdate} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { " " year * } - if$ -} - -FUNCTION {format.pdate} -{ year empty$ - { month empty$ - { "" } - { "there's a month but no year in " cite$ * warning$ - month - } - if$ - } - { month empty$ - { " " year * } - { " " month * ", " * year * } - if$} - if$ -} - -FUNCTION {format.btitle} -{ title emphasize -} - -FUNCTION {tie.or.space.connect} -{ duplicate$ text.length$ #3 < - { "~" } - { " " } - if$ - swap$ * * -} - -FUNCTION {either.or.check} -{ empty$ - 'pop$ - { "can't use both " swap$ * " fields in " * cite$ * warning$ } - if$ -} - -FUNCTION {format.bvolume} -{ volume empty$ - { "" } - { "Vol." volume tie.or.space.connect - series empty$ - 'skip$ - { ", " * series emphasize * } - if$ - "volume and number" number either.or.check - } - if$ -} - -FUNCTION {format.number.series} -{ volume empty$ - { number empty$ - { series field.or.null } - { output.state mid.sentence = - { "number" } - { "Number" } - if$ - number tie.or.space.connect - series empty$ - { "there's a number but no series in " cite$ * warning$ } - { " in " * series * } - if$ - } - if$ - } - { "" } - if$ -} - -FUNCTION {format.edition} -{ edition empty$ - { "" } - { output.state mid.sentence = - { edition "l" change.case$ " ed." * } - { edition "t" change.case$ " ed." * } - if$ - } - if$ -} - -INTEGERS { multiresult } - -FUNCTION {multi.page.check} -{ 't := - #0 'multiresult := - { multiresult not - t empty$ not - and - } - { t #1 #1 substring$ - duplicate$ "-" = - swap$ duplicate$ "," = - swap$ "+" = - or or - { #1 'multiresult := } - { t #2 global.max$ substring$ 't := } - if$ - } - while$ - multiresult -} - -FUNCTION {format.pages} -{ pages empty$ - { "" } - { pages multi.page.check - { "pp." pages n.dashify tie.or.space.connect } - { "p." pages tie.or.space.connect } - if$ - } - if$ -} - -FUNCTION {format.vol.num.pages} -{ volume emphasize field.or.null - number empty$ - 'skip$ - { - volume empty$ - { "there's a number but no volume in " cite$ * warning$ } - 'skip$ - if$ - } - if$ - pages empty$ - 'skip$ - { duplicate$ empty$ - { pop$ format.pages } - { ",~" * pages n.dashify * } - if$ - } - if$ -} - -FUNCTION {format.chapter.pages} -{ chapter empty$ - 'format.pages - { type empty$ - { "chapter" } - { type "l" change.case$ } - if$ - chapter tie.or.space.connect - pages empty$ - 'skip$ - { ", " * format.pages * } - if$ - } - if$ -} - -FUNCTION {format.in.ed.booktitle} -{ booktitle empty$ - { "" } - { editor empty$ - { edition empty$ - {"In " booktitle emphasize *} - {"In " booktitle emphasize * ", " * edition * " ed." *} - if$ - } - { edition empty$ - {"In " booktitle emphasize * "; " * format.editors * } - {"In " booktitle emphasize * ", " * edition * " ed." * "; " * format.editors * } - if$ - } - if$ - } - if$ -} - -FUNCTION {format.in.ed.booktitle.proc} -{ booktitle empty$ - { "" } - { editor empty$ - { edition empty$ - {"In Proceedings of the " booktitle *} - {"In Proceedings of the " booktitle * ", " * edition * " ed." *} - if$ - } - { edition empty$ - {"In Proceedings of the " booktitle * "; " * format.editors * } - {"In Proceedings of the " booktitle * ", " * edition * " ed." * "; " * format.editors * } - if$ - } - if$ - } - if$ -} - -FUNCTION {format.publisher.and.address} -{ publisher empty$ - {""} - { address empty$ - {publisher } - {publisher ": " * address *} - if$ - } - if$ -} - - - -FUNCTION {empty.misc.check} -{ author empty$ title empty$ howpublished empty$ - month empty$ year empty$ note empty$ - and and and and and - { "all relevant fields are empty in " cite$ * warning$ } - 'skip$ - if$ -} - -FUNCTION {format.thesis.type} -{ type empty$ - 'skip$ - { pop$ - type "t" change.case$ - } - if$ -} - -FUNCTION {format.tr.number} -{ type empty$ - { "Technical Report" } - 'type - if$ - number empty$ - { "t" change.case$ } - { number tie.or.space.connect } - if$ -} - -FUNCTION {format.article.crossref} -{ key empty$ - { journal empty$ - { "need key or journal for " cite$ * " to crossref " * crossref * - warning$ - "" - } - { "In \emph{" journal * "}" * } - if$ - } - { "In " } - if$ - " \citet{" * crossref * "}" * -} - - - -FUNCTION {format.book.crossref} -{ volume empty$ - { "empty volume in " cite$ * "'s crossref of " * crossref * warning$ - "In " - } - { "Vol." volume tie.or.space.connect - " of " * - } - if$ - editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { series empty$ - { "need editor, key, or series for " cite$ * " to crossref " * - crossref * warning$ - "" * - } - { "{\em " * series * "\/}" * } - if$ - } - { key * } - if$ - } - { "" * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.incoll.inproc.crossref} -{ editor empty$ - editor field.or.null author field.or.null = - or - { key empty$ - { booktitle empty$ - { "need editor, key, or booktitle for " cite$ * " to crossref " * - crossref * warning$ - "" - } - { "In {\em " booktitle * "\/}" * } - if$ - } - { "In " key * } - if$ - } - { "In " * } - if$ - " \cite{" * crossref * "}" * -} - -FUNCTION {format.website} -{ url empty$ - { "" } - { "" url website * - urldate empty$ - {"there is url but no urldate in " cite$ * warning$} - { ", accessed on " * urldate *} - if$ - } - if$ -} - - -%% the following function is modified from kp.bst at http://arxiv.org/hypertex/bibstyles/ -FUNCTION {format.eprint} -{eprint empty$ - { ""} - {primaryClass empty$ - {" \href{http://xxx.lanl.gov/abs/" eprint * "}" * "{{\normalfont " * "[" * eprint * "]" * "}}" *} - {archivePrefix empty$ - {" \href{http://xxx.lanl.gov/abs/" eprint * "}" * "{{\normalfont " * "[" * "arXiv:" * primaryClass * "/" * eprint * "]" * "}}" *} - {" \href{http://xxx.lanl.gov/abs/" eprint * "}" * "{{\normalfont " * "[" * archivePrefix * ":" * primaryClass * "/" * eprint * "]" * "}}" *} - if$ - } - if$ - } -if$ -} - - -%% For printing DOI numbers (it is a hyperlink but printed in black) -FUNCTION {formatfull.doi} -{ doi empty$ - { "" } - {"{\url{https://doi.org/" doi * "}}" * } - if$ -} - - - -FUNCTION {article} -{ output.bibitem - format.authors "author" output.check - author format.key output - new.block - format.title "title" output.check - new.block - crossref missing$ - { journal emphasize "journal" output.check - format.date * format.vol.num.pages "" * output - } - { format.article.crossref output.nonnull - format.pages output - } - if$ -format.eprint output -new.block -note output -formatfull.doi output -fin.entry -} - -FUNCTION {book} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ - new.block - format.btitle "title" output.check - format.edition output - after.item 'output.state := - crossref missing$ - { format.bvolume output - format.number.series output - format.publisher.and.address "publisher" output.check -%%% address output - } - { - format.book.crossref output.nonnull - } - if$ - format.bdate "year" output.check - after.item 'output.state := - format.chapter.pages output - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {booklet} -{ output.bibitem - format.authors output - new.block - format.title "title" output.check - howpublished address new.block.checkb - howpublished output - address output - format.bdate output - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {inbook} -{ output.bibitem - author empty$ - { format.editors "author and editor" output.check } - { format.authors output.nonnull - crossref missing$ - { "author and editor" editor either.or.check } - 'skip$ - if$ - } - if$ -%%% new.block - format.title "title" output.check - new.block - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - after.item 'output.state := - format.number.series output -%% new.sentence - format.publisher.and.address "publisher" output.check - format.bdate "year" output.check - after.item 'output.state := - format.bvolume output - format.chapter.pages "chapter and pages" output.check - - } - { format.chapter.pages "chapter and pages" output.check - new.block - format.book.crossref output.nonnull - format.bdate "year" output.check - } - if$ - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {incollection} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.sentence - crossref missing$ - { format.in.ed.booktitle "booktitle" output.check - after.item 'output.state := - format.number.series output -% new.sentence - format.publisher.and.address "publisher" output.check - format.bdate "year" output.check - after.item 'output.state := - format.bvolume output - format.chapter.pages output - } - { format.incoll.inproc.crossref output.nonnull - format.chapter.pages output - } - if$ - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {inproceedings} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - crossref missing$ - { format.in.ed.booktitle.proc "booktitle" output.check - address empty$ - { organization publisher new.sentence.checkb - organization output - publisher output - format.bdate "year" output.check - } - { after.item 'output.state := - organization output - format.publisher.and.address output.nonnull - format.bdate "year" output.check - after.item 'output.state := - } - if$ - format.number.series output - format.bvolume output - format.pages output - } - { format.incoll.inproc.crossref output.nonnull - format.pages output - } - if$ - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {conference} { inproceedings } - -FUNCTION {manual} -{ output.bibitem - author empty$ - { organization empty$ - 'skip$ - { organization output.nonnull - address output - } - if$ - } - { format.authors output.nonnull } - if$ - new.block - format.btitle "title" output.check - author empty$ - { organization empty$ - { address new.block.checka - address output - } - 'skip$ - if$ - } - { organization address new.block.checkb - organization output - address output - } - if$ - format.edition output - format.bdate output - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {mastersthesis} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - "Master's thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.bdate "year" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {misc} -{ output.bibitem - format.authors output - title howpublished new.block.checkb - format.title output - howpublished new.block.checka - howpublished output - format.bdate output - format.eprint output - new.block - note output - formatfull.doi output - fin.entry - empty.misc.check -} - -FUNCTION {phdthesis} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - "PhD thesis" format.thesis.type output.nonnull - school "school" output.check - address output - format.bdate "year" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {proceedings} -{ output.bibitem - editor empty$ - { organization output } - { format.editors output.nonnull } - if$ - new.block - format.btitle "title" output.check - format.bvolume output - format.number.series output - address empty$ - { editor empty$ - { publisher new.sentence.checka } - { organization publisher new.sentence.checkb - organization output - } - if$ - publisher output - format.bdate "year" output.check - } - { address output.nonnull - format.bdate "year" output.check - new.sentence - editor empty$ - 'skip$ - { organization output } - if$ - publisher output - } - if$ - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {techreport} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - format.tr.number output.nonnull - institution "institution" output.check - address output - format.bdate "year" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {unpublished} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {www} -{ output.bibitem - format.authors "author" output.checkwoa - new.block - format.title "title" output.check - new.block - format.website "url" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -FUNCTION {patent} -{ output.bibitem - format.authors "author" output.check - new.block - format.title "title" output.check - new.block - format.number.patent "number" output.check - mid.sentence 'output.state := - format.pdate "date" output.check - format.eprint output - new.block - note output - formatfull.doi output - fin.entry -} - -READ - -FUNCTION {sortify} -{ purify$ - "l" change.case$ -} - - -INTEGERS { len } - -FUNCTION {chop.word} -{ 's := - 'len := - s #1 len substring$ = - { s len #1 + global.max$ substring$ } - 's - if$ -} - - -FUNCTION {format.lab.names} -{ 's := - s #1 "{vv~}{ll}" format.name$ - s num.names$ duplicate$ - #2 > - { pop$ " \em{et~al.}" * } - { #2 < - 'skip$ - { s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" = - { " \em{et~al.}" * } - { " and " * s #2 "{vv~}{ll}" format.name$ * } - if$ - } - if$ - } - if$ -} - - -FUNCTION {author.key.label} -{ author empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {author.editor.key.label} -{ author empty$ - { editor empty$ - { key empty$ - { cite$ #1 #3 substring$ } - 'key - if$ - } - { editor format.lab.names } - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {author.key.organization.label} -{ author empty$ - { key empty$ - { organization empty$ - { cite$ #1 #3 substring$ } - { "The " #4 organization chop.word #3 text.prefix$ } - if$ - } - 'key - if$ - } - { author format.lab.names } - if$ -} - -FUNCTION {editor.key.organization.label} -{ editor empty$ - { key empty$ - { organization empty$ - { cite$ #1 #3 substring$ } - { "The " #4 organization chop.word #3 text.prefix$ } - if$ - } - 'key - if$ - } - { editor format.lab.names } - if$ -} - -FUNCTION {calc.short.authors} -{ type$ "book" = - type$ "inbook" = - or - 'author.editor.key.label - { type$ "proceedings" = - 'editor.key.organization.label - { type$ "manual" = - 'author.key.organization.label - 'author.key.label - if$ - } - if$ - } - if$ - 'short.list := -} - -FUNCTION {calc.label} -{ calc.short.authors - short.list - "(" - * - year duplicate$ empty$ - short.list key field.or.null = or - { pop$ "" } - 'skip$ - if$ - * - 'label := -} - -INTEGERS { seq.num } - -FUNCTION {init.seq} -{ #0 'seq.num :=} - -EXECUTE {init.seq} - -FUNCTION {int.to.fix} -{ "000000000" swap$ int.to.str$ * - #-1 #10 substring$ -} - - -FUNCTION {presort} -{ calc.label - label sortify - " " - * - seq.num #1 + 'seq.num := - seq.num int.to.fix - 'sort.label := - sort.label * - #1 entry.max$ substring$ - 'sort.key$ := -} - -ITERATE {presort} - - -STRINGS { longest.label last.label next.extra } - -INTEGERS { longest.label.width last.extra.num number.label } - -FUNCTION {initialize.longest.label} -{ "" 'longest.label := - #0 int.to.chr$ 'last.label := - "" 'next.extra := - #0 'longest.label.width := - #0 'last.extra.num := - #0 'number.label := -} - -FUNCTION {forward.pass} -{ last.label label = - { last.extra.num #1 + 'last.extra.num := - last.extra.num int.to.chr$ 'extra.label := - } - { "a" chr.to.int$ 'last.extra.num := - "" 'extra.label := - label 'last.label := - } - if$ - number.label #1 + 'number.label := -} - -FUNCTION {reverse.pass} -{ next.extra "b" = - { "a" 'extra.label := } - 'skip$ - if$ - extra.label 'next.extra := - extra.label - duplicate$ empty$ - 'skip$ - { "{\natexlab{" swap$ * "}}" * } - if$ - 'extra.label := - label extra.label * 'label := -} - -EXECUTE {initialize.longest.label} - -ITERATE {forward.pass} - -REVERSE {reverse.pass} - -FUNCTION {begin.bib} -{ "\begin{thebibliography}{999}" - write$ newline$ -} - -EXECUTE {begin.bib} - -EXECUTE {init.state.consts} - -ITERATE {call.type$} - -FUNCTION {end.bib} -{ newline$ - "\end{thebibliography}" write$ newline$ -} - -EXECUTE {end.bib} - - diff --git a/papers/Mathematics/mdpi.cls b/papers/Mathematics/mdpi.cls deleted file mode 100644 index aad304f8c..000000000 --- a/papers/Mathematics/mdpi.cls +++ /dev/null @@ -1,1176 +0,0 @@ -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -%% %% MDPI class for LaTeX files 15.2.2019 b -%% %% For any information please send an e-mail to: -%% %% latex@mdpi.com -%% %% -%% %% Initial class provided by: -%% %% Stefano Mariani -%% %% Modified by: -%% %% Dietrich Rordorf -%% %% Peter Harremoes -%% %% Zeno Schumacher -%% %% Maddalena Giulini -%% %% Andres Gartmann -%% %% Dr. Janine Daum -%% %% Versions: -%% %% v1.0 before Dr. Janine Daum -%% %% v2.0 when Dr. Janine Daum started (March 2013) -%% %% v3.0 after layout change (September 2015) -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%% IDENTIFICATION -\NeedsTeXFormat{LaTeX2e} -\ProvidesClass{mdpi}[15/02/2019 MDPI paper class] - -%%%% Copyright and citebox - \AtEndDocument{\par \cright} - -%% PRELIMINARY DECLARATIONS -\LoadClass[10pt,a4paper]{article} -\RequirePackage[T1]{fontenc} -\RequirePackage[utf8]{inputenc} -\RequirePackage{calc} -\RequirePackage{indentfirst} -\RequirePackage{fancyhdr} -\RequirePackage{graphicx,epstopdf} -\RequirePackage{lastpage} -\RequirePackage{ifthen} -\RequirePackage{float} -\RequirePackage{amsmath} -% TODO: Currently lineno needs to be loaded after amsmath because of conflict -% https://github.com/latex-lineno/lineno/issues/5 -\RequirePackage{lineno} -\RequirePackage{setspace} -\RequirePackage{enumitem} -\RequirePackage{mathpazo} -\RequirePackage{booktabs} % For \toprule etc. in tables -\RequirePackage[largestsep]{titlesec} -\RequirePackage{etoolbox} % For \AtBeginDocument etc. -\RequirePackage{tabto} % To use tab for alignment on first page -\RequirePackage[table]{xcolor} % To provide color for soul (for english editing) and provide coloring for tables (author request) -\RequirePackage{soul} % To highlight text -\newcommand{\highlight}[1]{\colorbox{yellow}{#1}} -\RequirePackage{multirow} -\RequirePackage{microtype} % For command \textls[]{} -\RequirePackage{tikz} % For \foreach used for Orcid icon -\RequirePackage{totcount} % To enable extracting the value of the counter "page" - - -%% OPTIONS -%% To choose the journal -% All journals (website name, full name, short name, DOI abbreviation, and ISSN) are defined in an extra file. -% This is the same as for mdpi.cls. -\input{journalnames} -\DeclareOption{journal}{\ClassWarning{mdpi}{You used an invalid journal name or you have not specified the journal. The first option of the documentclass command specifies the journal. The word 'journal' should be replaced by one of the journal names specified in template.tex (in the comment 'Choose between the following MDPI journal').}} - -%% To choose the type of manuscript -\DeclareOption{abstract}{\gdef\@arttype{Abstract}} -\DeclareOption{addendum}{\gdef\@arttype{Addendum}} -\DeclareOption{article}{\gdef\@arttype{Article}} -\DeclareOption{benchmark}{\gdef\@arttype{Benchmark}} -\DeclareOption{book}{\gdef\@arttype{Book}} -\DeclareOption{bookreview}{\gdef\@arttype{Book Review}} -\DeclareOption{briefreport}{\gdef\@arttype{Brief Report}} -\DeclareOption{casereport}{\gdef\@arttype{Case Report}} -\DeclareOption{changes}{\gdef\@arttype{Changes}} -\DeclareOption{comment}{\gdef\@arttype{Comment}} -\DeclareOption{commentary}{\gdef\@arttype{Commentary}} -\DeclareOption{communication}{\gdef\@arttype{Communication}} -\DeclareOption{conceptpaper}{\gdef\@arttype{Concept Paper}} -\DeclareOption{conferenceproceedings}{\gdef\@arttype{Proceedings}} -\DeclareOption{correction}{\gdef\@arttype{Correction}} -\DeclareOption{conferencereport}{\gdef\@arttype{Conference Report}} -\DeclareOption{expressionofconcern}{\gdef\@arttype{Expression of Concern}} -\DeclareOption{extendedabstract}{\gdef\@arttype{Extended Abstract}} -\DeclareOption{meetingreport}{\gdef\@arttype{Meeting Report}} -\DeclareOption{creative}{\gdef\@arttype{Creative}} -\DeclareOption{datadescriptor}{\gdef\@arttype{Data Descriptor}} -\DeclareOption{discussion}{\gdef\@arttype{Discussion}} -\DeclareOption{editorial}{\gdef\@arttype{Editorial}} -\DeclareOption{essay}{\gdef\@arttype{Essay}} -\DeclareOption{erratum}{\gdef\@arttype{Erratum}} -\DeclareOption{hypothesis}{\gdef\@arttype{Hypothesis}} -\DeclareOption{interestingimages}{\gdef\@arttype{Interesting Images}} -\DeclareOption{letter}{\gdef\@arttype{Letter}} -\DeclareOption{meetingreport}{\gdef\@arttype{Meeting Report}} -\DeclareOption{newbookreceived}{\gdef\@arttype{New Book Received}} -\DeclareOption{obituary}{\gdef\@arttype{Obituary}} -\DeclareOption{opinion}{\gdef\@arttype{Opinion}} -\DeclareOption{projectreport}{\gdef\@arttype{Project Report}} -\DeclareOption{reply}{\gdef\@arttype{Reply}} -\DeclareOption{retraction}{\gdef\@arttype{Retraction}} -\DeclareOption{review}{\gdef\@arttype{Review}} -\DeclareOption{perspective}{\gdef\@arttype{Perspective}} -\DeclareOption{protocol}{\gdef\@arttype{Protocol}} -\DeclareOption{shortnote}{\gdef\@arttype{Short Note}} -\DeclareOption{supfile}{\gdef\@arttype{Supfile}} -\DeclareOption{technicalnote}{\gdef\@arttype{Technical Note}} -\DeclareOption{viewpoint}{\gdef\@arttype{Viewpoint}} - -%% To choose the status of the manuscript -\DeclareOption{submit}{\gdef\@status{submit}} -\DeclareOption{accept}{\gdef\@status{accept}} - -%% To choose the whether there is one or more authors -\DeclareOption{oneauthor}{\gdef\@authornum{author}} -\DeclareOption{moreauthors}{\gdef\@authornum{authors}} - -%% Add the chosen options to the class -\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}} - -%% Defaults -\ExecuteOptions{notspecified,10pt,a4paper,article,submit,oneauthor} - -%% Process options -\ProcessOptions\relax - -%% MORE DECLARATIONS -%%%% Maths environments -\RequirePackage{amsthm} -\newtheoremstyle{mdpi}% name -{12pt}% space above -{12pt}% space below -{\itshape}% body font -{}% indent amount 1 -{\bfseries}% theorem head font -{.}% punctuation after theorem head -{.5em}% space after theorem head -{}% theorem head spec (can be left empty, meaning `normal') - -\renewcommand{\qed}{\unskip\nobreak\quad\qedsymbol} %% This places the symbol right after the text instead of placing it at the end on the line. - -\renewenvironment{proof}[1][\proofname]{\par %% \proofname allows to have "Proof of my theorem" - \pushQED{\qed}% - \normalfont \topsep6\p@\@plus6\p@\relax - \trivlist - \item[\hskip\labelsep - \bfseries %% "Proof" is bold - #1\@addpunct{.}]\ignorespaces %% Period instead of colon -}{% - \popQED\endtrivlist\@endpefalse -} - - \theoremstyle{mdpi} - \newcounter{theorem} - \setcounter{theorem}{0} - \newtheorem{Theorem}[theorem]{Theorem} - - \newcounter{lemma} - \setcounter{lemma}{0} - \newtheorem{Lemma}[lemma]{Lemma} - - \newcounter{corollary} - \setcounter{corollary}{0} - \newtheorem{Corollary}[corollary]{Corollary} - - \newcounter{proposition} - \setcounter{proposition}{0} - \newtheorem{Proposition}[proposition]{Proposition} - - \newcounter{characterization} - \setcounter{characterization}{0} - \newtheorem{Characterization}[characterization]{Characterization} - - \newcounter{property} - \setcounter{property}{0} - \newtheorem{Property}[property]{Property} - - \newcounter{problem} - \setcounter{problem}{0} - \newtheorem{Problem}[problem]{Problem} - - \newcounter{example} - \setcounter{example}{0} - \newtheorem{Example}[example]{Example} - - \newcounter{examplesanddefinitions} - \setcounter{examplesanddefinitions}{0} - \newtheorem{ExamplesandDefinitions}[examplesanddefinitions]{Examples and Definitions} - - \newcounter{remark} - \setcounter{remark}{0} - \newtheorem{Remark}[remark]{Remark} - - \newcounter{definition} - \setcounter{definition}{0} - \newtheorem{Definition}[definition]{Definition} - - \newcounter{hypothesis} - \setcounter{hypothesis}{0} - \newtheorem{Hypothesis}[hypothesis]{Hypothesis} - - \newcounter{notation} - \setcounter{notation}{0} - \newtheorem{Notation}[notation]{Notation} - -%%%% Hyphenation -\RequirePackage[none]{hyphenat} -\sloppy - -%%%% References -\RequirePackage[sort&compress,sectionbib]{natbib} % option sectionbib is for optionally organizing references using sections (author request) - -\ifthenelse{\equal{\@journal}{admsci} -\OR \equal{\@journal}{arts} -\OR \equal{\@journal}{econometrics} -\OR \equal{\@journal}{economies} -\OR \equal{\@journal}{genealogy} -\OR \equal{\@journal}{humanities} -\OR \equal{\@journal}{ijfs} -\OR \equal{\@journal}{jrfm} -\OR \equal{\@journal}{languages} -\OR \equal{\@journal}{laws} -\OR \equal{\@journal}{religions} -\OR \equal{\@journal}{risks} -\OR \equal{\@journal}{socsci}}{% - \bibliographystyle{chicago2} - \bibpunct{(}{)}{;}{x}{}{}% - }{% - \bibliographystyle{mdpi} - \bibpunct{[}{]}{,}{n}{}{}% - }% - -\renewcommand\NAT@set@cites{% - \ifNAT@numbers - \ifNAT@super \let\@cite\NAT@citesuper - \def\NAT@mbox##1{\unskip\nobreak\textsuperscript{##1}}% - \let\citeyearpar=\citeyear - \let\NAT@space\relax - \def\NAT@super@kern{\kern\p@}% - \else - \let\NAT@mbox=\mbox - \let\@cite\NAT@citenum - \let\NAT@space\relax - \let\NAT@super@kern\relax - \fi - \let\@citex\NAT@citexnum - \let\@biblabel\NAT@biblabelnum - \let\@bibsetup\NAT@bibsetnum - \renewcommand\NAT@idxtxt{\NAT@name\NAT@spacechar\NAT@open\NAT@num\NAT@close}% - \def\natexlab##1{}% - \def\NAT@penalty{\penalty\@m}% - \else - \let\@cite\NAT@cite - \let\@citex\NAT@citex - \let\@biblabel\NAT@biblabel - \let\@bibsetup\NAT@bibsetup - \let\NAT@space\NAT@spacechar - \let\NAT@penalty\@empty - \renewcommand\NAT@idxtxt{\NAT@name\NAT@spacechar\NAT@open\NAT@date\NAT@close}% - \def\natexlab##1{##1}% - \fi} - -%%%%% Hyperlinks -%% Define color for citations -\definecolor{bluecite}{HTML}{0875b7} - -\ifthenelse{\equal{\@arttype}{Book}}{ - \RequirePackage[unicode=true, - bookmarksopen={true}, - pdffitwindow=true, - colorlinks=true, - linkcolor=black, - citecolor=black, - urlcolor=black, - hyperfootnotes=false, - pdfstartview={FitH}, - pdfpagemode=UseNone]{hyperref} - }{ - \RequirePackage[unicode=true, - bookmarksopen={true}, - pdffitwindow=true, - colorlinks=true, - linkcolor=bluecite, - citecolor=bluecite, - urlcolor=bluecite, - hyperfootnotes=false, - pdfstartview={FitH}, - pdfpagemode= UseNone]{hyperref} -} - -%% To have the possibility to change the urlcolor -\newcommand{\changeurlcolor}[1]{\hypersetup{urlcolor=#1}} - -%% Metadata -\newcommand{\org@maketitle}{}% LATEX-Check -\let\org@maketitle\maketitle -\def\maketitle{% - \hypersetup{ - pdftitle={\@Title}, - pdfsubject={\@abstract}, - pdfkeywords={\@keyword}, - pdfauthor={\@AuthorNames} - }% - \org@maketitle -} - -%%%% Footnotes -\RequirePackage[hang]{footmisc} -\setlength{\skip\footins}{1.2cm} -\setlength{\footnotemargin}{5mm} -\def\footnoterule{\kern-14\p@ -\hrule \@width 2in \kern 11.6\p@} - -%%%% URL -\RequirePackage{url} -\urlstyle{same} -\g@addto@macro{\UrlBreaks}{\UrlOrds} - -%%%% Widows & orphans -\clubpenalty=10000 -\widowpenalty=10000 -\displaywidowpenalty=10000 - -%%%% Front matter -\newcommand{\firstargument}{} -\newcommand{\Title}[1]{\gdef\@Title{#1}}% -\newcommand{\Author}[1]{\gdef\@Author{#1}}% -\def\@AuthorNames{} -\newcommand{\AuthorNames}[1]{\gdef\@AuthorNames{#1}}% -\newcommand{\firstpage}[1]{\gdef\@firstpage{#1}} -\newcommand{\doinum}[1]{\gdef\@doinum{#1}} - -% DOI number -\newcommand\twodigits[1]{% -\ifnum#1<10 -0\number#1 - \else -\number#1 -\fi -} - -\newcommand\fourdigits[1]{% -\ifnum#1<10 000\number#1 - \else - \ifnum#1<100 00\number#1 - \else - \ifnum#1<1000 0\number#1 - \else - \ifnum#1<10000 \number#1 - \else - error - \fi - \fi - \fi - \fi -} - - -\ifthenelse{\equal{\@journal}{molbank}}{ - \doinum{10.3390/\@articlenumber} - }{ - \doinum{10.3390/\@doiabbr\@pubvolume\twodigits\@issuenum\fourdigits\@articlenumber} -} - - -\newcommand{\pubvolume}[1]{\gdef\@pubvolume{#1}} -\newcommand{\pubyear}[1]{\gdef\@pubyear{#1}} -\newcommand{\copyrightyear}[1]{\gdef\@copyrightyear{#1}} -\newcommand{\address}[2][]{\renewcommand{\firstargument}{#1}\gdef\@address{#2}} -\newcommand{\corresfirstargument}{} -\def\@corres{} -\newcommand{\corres}[2][]{\renewcommand{\corresfirstargument}{#1}\gdef\@corres{#2}} -\def\@conference{} -\newcommand{\conference}[1]{\gdef\@conference{#1}}% -\def\@abstract{} -\renewcommand{\abstract}[1]{\gdef\@abstract{#1}} -\def\@externaleditor{} -\newcommand{\externaleditor}[1]{\gdef\@externaleditor{#1}} -\def\@LSID{} -\newcommand{\LSID}[1]{\gdef\@LSID{#1}} -\newcommand{\history}[1]{\gdef\@history{#1}} -\def\@pacs{} -\newcommand{\PACS}[1]{\gdef\@pacs{#1}} -\def\@msc{} -\newcommand{\MSC}[1]{\gdef\@msc{#1}} -\def\@jel{} -\newcommand{\JEL}[1]{\gdef\@jel{#1}} -\def\@keyword{} -\newcommand{\keyword}[1]{\gdef\@keyword{#1}} -\def\@dataset{} -\newcommand{\dataset}[1]{\gdef\@dataset{#1}} -\def\@datasetlicense{} -\newcommand{\datasetlicense}[1]{\gdef\@datasetlicense{#1}} -\def\@featuredapplication{} -\newcommand{\featuredapplication}[1]{\gdef\@featuredapplication{#1}} -\def\@keycontribution{} -\newcommand{\keycontribution}[1]{\gdef\@keycontribution{#1}} - - -\def\@issuenum{} -\newcommand{\issuenum}[1]{\gdef\@issuenum{#1}} -\def\@updates{} -\newcommand{\updates}[1]{\gdef\@updates{#1}} - -\def\@firstnote{} -\newcommand{\firstnote}[1]{\gdef\@firstnote{#1}} -\def\@secondnote{} -\newcommand{\secondnote}[1]{\gdef\@secondnote{#1}}% -\def\@thirdnote{} -\newcommand{\thirdnote}[1]{\gdef\@thirdnote{#1}}% -\def\@fourthnote{} -\newcommand{\fourthnote}[1]{\gdef\@fourthnote{#1}}% -\def\@fifthnote{} -\newcommand{\fifthnote}[1]{\gdef\@fifthnote{#1}}% -\def\@sixthnote{} -\newcommand{\sixthnote}[1]{\gdef\@sixthnote{#1}}% -\def\@seventhnote{} -\newcommand{\seventhnote}[1]{\gdef\@seventhnote{#1}}% -\def\@eighthnote{} -\newcommand{\eighthnote}[1]{\gdef\@eighthnote{#1}}% - -\def\@simplesumm{} -\newcommand{\simplesumm}[1]{\gdef\@simplesumm{#1}} -\newcommand{\articlenumber}[1]{\gdef\@articlenumber{#1}} - -\def\@externalbibliography{} -\newcommand{\externalbibliography}[1]{\gdef\@externalbibliography{#1}} - -\def\@reftitle{} -\newcommand{\reftitle}[1]{\gdef\@reftitle{#1}} - -% For transition period to change back to continuous page numbers -\def\@continuouspages{} -\newcommand{\continuouspages}[1]{\gdef\@continuouspages{#1}} - - -%% ORCID -% Make Orcid icon -\newcommand{\orcidicon}{\includegraphics[width=0.32cm]{logo-orcid.pdf}} - -% Define link and button for each author -\foreach \x in {A, ..., Z}{% -\expandafter\xdef\csname orcid\x\endcsname{\noexpand\href{https://orcid.org/\csname orcidauthor\x\endcsname}{\noexpand\orcidicon}} -} - -%%%% Journal name for the header -\newcommand{\journalname}{\@journalshort} - - -\regtotcounter{page} % to enable extracting the value of the counter "page" using the totcount package - -%%%% Header and footer on first page -%% The plain page style needs to be redefined because with \maketitle in the article class, LaTeX applies the the plain page style automatically to the first page. -\ifthenelse{\equal{\@journal}{preprints} % - \OR \equal{\@arttype}{Book}}{% - \fancypagestyle{plain}{% - \fancyhf{} - \ifthenelse{\equal{\@arttype}{Book}}{ - \fancyfoot[C]{\footnotesize\thepage} - }{% - } - } - }{% - \ifthenelse{\equal{\@arttype}{Supfile}}{ - \fancypagestyle{plain}{ - \fancyhf{} - \fancyhead[R]{ - \footnotesize % - S\thepage{} of S\pageref*{LastPage}% - }% - \fancyhead[L]{ - \footnotesize % - \ifthenelse{\equal{\@status}{submit}}{% - Version {\@ \today} submitted to {\em\journalname}% - }{% - {\em \journalname} % - {\bfseries \@pubyear}, % - {\em \@pubvolume}, % - \ifthenelse{\equal{\@continuouspages}{\@empty}}{% - \@firstpage --\pageref*{LastPage}% - }{% - \@articlenumber% - }% - ; doi:{\changeurlcolor{black}% - \href{http://dx.doi.org/\@doinum}% - {\@doinum}}% - }% - }% - }% - }{ - \fancypagestyle{plain}{ - \fancyhf{} - \fancyfoot[L]{ - \footnotesize% - \ifthenelse{\equal{\@status}{submit}}{% - Submitted to {\em\journalname}, % - pages \thepage \ -- \color{black}{\pageref*{LastPage}}% - }{ - {\em \journalname}\ % - {\bfseries \@pubyear}, % - {\em \@pubvolume}, % - \ifthenelse{\equal{\@continuouspages}{\@empty}}{% - \@articlenumber% - 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