diff --git a/ChangeLog b/ChangeLog index 7a2a1e4..efdbdc4 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,28 @@ +2009-08-08 Douglas Bates + + * [r401] DESCRIPTION, inst/doc/Usinglmer.Rnw, inst/doc/Usinglmer.pdf: + New release on R-forge + * [r400] inst/doc/Usinglme.Rnw, inst/doc/Usinglme.bib, + inst/doc/Usinglmer.Rnw, inst/doc/Usinglmer.bib: Update to AFS version + +2009-08-08 Martin Maechler mmaechler + + * DESCRIPTION, man/Animal.Rd, man/AvgDailyGain.Rd, man/BIB.Rd, + man/Bond.Rd, man/Cultivation.Rd, man/Demand.Rd, man/Genetics.Rd, + man/HR.Rd, man/IncBlk.Rd, man/Mississippi.Rd, man/Multilocation.Rd, + man/PBIB.Rd, man/SIMS.Rd, man/Semi2.Rd, man/Semiconductor.Rd, + man/TeachingI.Rd, man/TeachingII.Rd, man/WWheat.Rd, man/WaferTypes.Rd, + man/Weights.Rd: update to CRAN`s version 0.4-4 (from 2008-06 !) + +2009-07-28 Martin Maechler + + * .: move mlmRev, MEMSS (and SASmixed) from + "svn.r-project.org/R-packages/trunk/" + +2006-10-23 Douglas Bates + + * [r384] Remove poorly defined example + 2006-09-09 Douglas Bates * man/BIB.Rd: Update this and all other examples for lmer back in diff --git a/DESCRIPTION b/DESCRIPTION index 1286cce..7eaec6d 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,14 +1,16 @@ Package: SASmixed -Version: 0.4-4 -Date: 2008-06-25 +Version: 0.5-1 +Date: 2009-10-21 Title: Data sets from "SAS System for Mixed Models" Maintainer: Douglas Bates Author: Original by Littel, Milliken, Stroup, and Wolfinger - modifications by Douglas Bates -Description: Data sets and sample lmer analyses corresponding - to the examples in Littel, Milliken, Stroup and Wolfinger - (1996), "SAS System for Mixed Models", SAS Institute. -Suggests: lattice, lme4 (>= 0.999375-19) + modifications by Douglas Bates +Description: Data sets and sample lmer analyses corresponding to the + examples in Littel, Milliken, Stroup and Wolfinger (1996), "SAS + System for Mixed Models", SAS Institute. +Suggests: lattice, lme4 LazyData: yes -License: GPL version 2 or later -Packaged: Wed Jun 25 12:42:15 2008; bates +License: GPL (>= 2) +Packaged: 2009-10-26 19:14:08 UTC; bates +Repository: CRAN +Date/Publication: 2009-10-26 20:51:35 diff --git a/INDEX b/INDEX new file mode 100644 index 0000000..52c9484 --- /dev/null +++ b/INDEX @@ -0,0 +1,25 @@ +Animal Animal breeding experiment +AvgDailyGain Average daily weight gain of steers on + different diets +BIB Data from a balanced incomplete block design +Bond Strengths of metal bonds +Cultivation Bacterial innoculation applied to grass + cultivars +Demand Per-capita demand deposits by state and year +Genetics Heritability data +HR Heart rates of patients on different drug + treatments +IncBlk An unbalanced incomplete block experiment +Mississippi Nitrogen concentrations in the Mississippi + River +Multilocation A multilocation trial +PBIB A partially balanced incomplete block + experiment +Semi2 Oxide layer thicknesses on semiconductors +Semiconductor Semiconductor split-plot experiment +SIMS Second International Mathematics Study data +TeachingI Teaching Methods I +TeachingII Teaching Methods II +WaferTypes Data on different types of silicon wafers +Weights Data from a weight-lifting program +WWheat Winter wheat diff --git a/inst/doc/Rplots.ps b/inst/doc/Rplots.ps deleted file mode 100644 index 61bbaf5..0000000 Binary files a/inst/doc/Rplots.ps and /dev/null differ diff --git a/inst/doc/Usinglmer.Rnw b/inst/doc/Usinglmer.Rnw index 0acdcc9..cfff415 100644 --- a/inst/doc/Usinglmer.Rnw +++ b/inst/doc/Usinglmer.Rnw @@ -45,7 +45,7 @@ A file on the SAS Institute web site (\textsf{http://www.sas.com}) contains all the data sets in the book and all the SAS programs used in \citet{litt:mill:stro:wolf:1996}. We have converted the data sets from the tabular representation used for SAS to the -\code{groupedData} objects used by \code{lmer}. To help users familiar +\code{data.frame} objects used by \code{lmer}. To help users familiar with \code{SAS PROC MIXED} get up to speed with \code{lmer} more quickly, we provide transcripts of some \code{lmer} analyses paralleling the \code{SAS PROC MIXED} analyses in \citet{litt:mill:stro:wolf:1996}. @@ -79,16 +79,17 @@ The basic specification of the model requires a linear model expression for the fixed effects and a linear model expression for the random effects. In \code{SAS PROC MIXED} the fixed-effects part is specified in the \code{model} statement and the random-effects -part in the \code{random} statement. In \code{lmer} the -arguments are called \code{fixed} and \code{random}. +part in the \code{random} statement. In \code{lmer} the fixed effects +and the random effects are both specified as terms in the +\code{formula} argument to \code{lmer}. Both \code{SAS PROC MIXED} and \code{lmer} allow a mixed-effects model to be fit by maximum likelihood (\code{method = ml} in SAS) or by maximum residual likelihood, sometimes also called restricted maximum likelihood or \textsf{REML}. This is the default criterion in \code{SAS PROC MIXED} and in \code{lmer}. To get \textsf{ML} -estimates in \code{lmer}, set the optional argument -\code{method="REML"}. +estimates use the optional argument \code{REML=FALSE} in the call to +\code{lmer}. \section{Important differences} \label{sec:differences} @@ -96,12 +97,14 @@ estimates in \code{lmer}, set the optional argument The output from \code{PROC MIXED} typically includes values of the Akaike Information Criterion (\textsf{AIC}) and Schwartz's Bayesian Criterion (\textsf{SBC}). These are used to compare different models -fit to the same data. The output of the \code{summary} function applied -to the object created by \code{lmer} also produces values of \textsf{AIC} -and \textsf{BIC} but the definitions used in \code{PROC MIXED} and in -\code{lmer} are different. In \code{lmer} the definitions are such that -``smaller is better''. In \code{PROC MIXED} the definitions are such -that ``bigger is better''. +fit to the same data. The output of the \code{summary} function +applied to the object created by \code{lmer} also produces values of +\textsf{AIC} and \textsf{BIC} but the definitions used in older +versions of \code{PROC MIXED} are different from those used in more +recent versions of \code{PROC MIXED} and in \code{lmer}. In +\code{lmer} the definitions are such that ``smaller is better''. In +some older versions of \code{PROC MIXED} the definitions are such that +``bigger is better''. When models are fit by \textsf{REML}, the values of \textsf{AIC}, \textsf{SBC} (or \textsf{BIC}) and the log-likelihood can only be @@ -111,15 +114,15 @@ compared between any models fit to the same data. That is, these quality-of-fit criteria can be used to evaluate different fixed-effects specifications or different random-effects specifications or different specifications of both fixed effects and -random effects. The greater flexibility of model comparisons when -using maximum likelihood is the reason that this is the default -criterion in \code{lmer}. +random effects. We encourage developing and testing the model using likelihood ratio tests or the \textsf{AIC} and \textsf{BIC} criteria. Once a form for both the random effects and the fixed effects has been determined, the model can be refit with \code{REML = TRUE} if the restricted -estimates of the variance components are desired. +estimates of the variance components are desired. Note that the +\code{update} function provides a convenient way of refitting a model +with changes to one or more arguments. \section{Data manipulation} \label{sec:data} @@ -152,13 +155,15 @@ data animal; would require that the \code{trait} and \code{animal} variables be specified in a class statement in any model that is fit. -In \s{} these data could be read from a file, say \texttt{animal.dat}, +In \R{} these data could be read from a file, say \texttt{animal.dat}, and converted to factors by \begin{Schunk} \begin{Sinput} -animal <- read.table("animal.dat", header = TRUE) -animal$trait <- as.factor(animal$trait) -animal$animal <- as.factor(animal$animal) +animal <- within(read.table("animal.dat", header = TRUE), + { + trait <- factor(trait) + animal <- factor(animal) + }) \end{Sinput} \end{Schunk} In general it is a good idea to check the types of variables in a data @@ -170,14 +175,6 @@ sapply(Animal, data.class) str(Animal) @ -To make specification of models in \code{lmer} easier and to make graphic -presentations more informative, we recommend converting from a -\code{data.frame} object to a \code{groupedData} object. This class of -objects contains a formula specifying the response, the primary -covariate (if there is one) and the grouping factor or factors. The -data sets from \citet{litt:mill:stro:wolf:1996} have been -converted to \code{groupedData} objects in this directory. - \subsection{Unique levels of factors} \label{sec:nested} @@ -197,14 +194,14 @@ In \code{SAS} this nesting of factors is denoted by \code{wafer(et)}. In within ET''. If both levels of nested factors are to be associated with random effects then this is all you need to know. You would use an expression with a \code{"/"} in the grouping factor part of the -formula for the \code{groupedData} object. Then the random effects -could be specified as +formula in the call to \code{lmer} object. The random effects term +would be either \begin{Example} - random = list( ET = ~ 1, Wafer = ~ 1 ) + (1 | ET/Wafer) \end{Example} or, equivalently \begin{Example} - random = ~ 1 | ET/Wafer + (1 | ET:Wafer) + (1 | ET) \end{Example} In this case, however, there would not usually be any random effects @@ -213,33 +210,31 @@ only random effects are at the \code{Wafer} level. It is necessary to create a factor that will have unique levels for each \code{Wafer} within each level of \code{ET}. One way to do this is to assign <>= -Semiconductor$Grp <- with(Semiconductor, ET:Wafer) +Semiconductor <- within(Semiconductor, Grp <- factor(ET:Wafer)) @ -%$ -after which we could specify a random effects term of \code{(1 | Grp)}. +after which we could specify a random effects term of \code{(1 | + Grp)}. Alternatively, we can use the explicit term +\begin{Example} + (1 | ET:Wafer) +\end{Example} \subsection{General approach} \label{sec:generalApproach} -As a general approach to importing data into \s{} for mixed-effects +As a general approach to importing data into \R{} for mixed-effects analysis you should: \begin{itemize} \item Create a \code{data.frame} with one row per observation and one column per variable. -\item Use \code{ordered} or \code{as.ordered} to explicitly convert any +\item Use \code{factor} or \code{as.factor} to explicitly convert any ordered factors to class \code{ordered}. \item Use \code{ordered} or \code{as.ordered} to explicitly convert any ordered factors to class \code{ordered}. -\item If necessary, use \code{getGroups} to create a factor with unique +\item If necessary, use interaction terms to create a factor with unique levels from inner nested factors. -\item Specify the formula for the response, the primary covariate and - the grouping structure to create a \code{groupedData} object from the - data frame. Labels and units for the response and the primary - covariate can also be specified at this time as can \code{outer} and - \code{inner} factor expressions. -\item Plot the data. Plot it several ways. The use of trellis - graphics is closely integrated with the \code{nlme} library. The - trellis plots can provide invaluable insight into the structure of +\item Plot the data. Plot it several ways. The use of lattice + graphics is closely integrated with the \code{lme4} library. + Lattice plots can provide invaluable insight into the structure of the data. Use them. \end{itemize} @@ -399,7 +394,7 @@ anova(fm1Mult) (fm5Mult <- lmer(Adj ~ 1 + (1|Grp), Multilocation)) anova(fm2Mult) (fm2MultR <- lmer(Adj ~ Trt + (Trt - 1|Location) + (1|Block), Multilocation, - control = list(msV = 1, niterEM = 200))) + verbose = TRUE)) @ diff --git a/inst/doc/Usinglmer.pdf b/inst/doc/Usinglmer.pdf index 2318131..3adb406 100644 Binary files a/inst/doc/Usinglmer.pdf and b/inst/doc/Usinglmer.pdf differ diff --git a/inst/doc/Usinglmer.tex b/inst/doc/Usinglmer.tex deleted file mode 100644 index fa1fcb6..0000000 --- a/inst/doc/Usinglmer.tex +++ /dev/null @@ -1,1605 +0,0 @@ -\documentclass[12pt]{article} -\usepackage{Sweave} -\usepackage{myVignette} -\usepackage[authoryear,round]{natbib} -\newcommand{\s}{\textsf{S}} -\newcommand{\R}{\textsf{R}} -\bibliographystyle{plainnat} -\DefineVerbatimEnvironment{Sinput}{Verbatim} -{formatcom={\vspace{-2.5ex}},fontshape=sl, - fontfamily=courier,fontseries=b, fontsize=\small} -\DefineVerbatimEnvironment{Example}{Verbatim} -{formatcom={\vspace{-2.5ex}}, - fontfamily=courier,fontseries=b, fontsize=\small} -\DefineVerbatimEnvironment{Soutput}{Verbatim} -{formatcom={\vspace{-2.5ex}},fontfamily=courier,fontseries=b,% - fontsize=\small} -%%\VignetteIndexEntry{lmer for SAS PROC MIXED Users} -%%\VignetteDepends{SASmixed} -%%\VignetteDepends{lattice} -\begin{document} - - -\setkeys{Gin}{width=\textwidth} -\title{\textbf{\textsf{lmer} for \textsf{SAS PROC MIXED} Users}} -\author{Douglas Bates\\Department of Statistics\\University of - Wisconsin -- Madison\\\email{Bates@wisc.edu}} -\date{} -\maketitle -\section{Introduction} -\label{sec:intro} - -The \code{lmer} function from the \code{lme4} package for \textsf{R} is used -to fit linear mixed-effects models. It is similar in scope to the -\textsf{SAS} procedure \code{PROC MIXED} described in -\citet{litt:mill:stro:wolf:1996}. - -A file on the SAS Institute web site (\textsf{http://www.sas.com}) -contains all the data sets in the book and all the SAS programs used -in \citet{litt:mill:stro:wolf:1996}. We have converted the data -sets from the tabular representation used for SAS to the -\code{groupedData} objects used by \code{lmer}. To help users familiar -with \code{SAS PROC MIXED} get up to speed with \code{lmer} more quickly, -we provide transcripts of some \code{lmer} analyses paralleling the -\code{SAS PROC MIXED} analyses in \citet{litt:mill:stro:wolf:1996}. - -In this paper we highlight some of the similarities and differences of -\code{lmer} analysis and \code{SAS PROC MIXED} analysis. - -\section{Similarities between lmer and SAS PROC MIXED} -\label{sec:similarities} - -Both \code{SAS PROC MIXED} and \code{lmer} can fit linear mixed-effects -models expressed in the Laird-Ware formulation. For a single level of -grouping \citet{lair:ware:1982} write the $n_i\/$-dimensional -response vector $\by_i$ for the $i\/$th experimental unit as -\begin{gather} - \label{eqn:oneLevel} - \by_i = \bX_i \bbeta + \bZ_i \bb_i + \beps_i,\quad i=1,\dots,M\\ - \bb_i\sim\mathcal{N}(\bzer,\bSigma), - \quad\beps_i\sim\mathcal{N}(\bzer,\sigma^2 \bI)\notag -\end{gather} -where $\bbeta$ is the $p$-dimensional vector of \emph{fixed effects}, -$\bb_i$ is the $q$-dimensional vector of \emph{random effects}, -$\bX_i$ (of size $n_i\times p$) and $\bZ_i$ (of size $n_i\times q$) -are known fixed-effects and random-effects regressor matrices, and -$\beps_i$ is the $n_i\/$-dimensional \emph{within-group error} vector -with a spherical Gaussian distribution. The assumption -$\mathrm{Var}(\beps_i)=\sigma^2\bI$ can be relaxed using additional -arguments in the model fitting. - -The basic specification of the model requires a linear model -expression for the fixed effects and a linear model expression for the -random effects. In \code{SAS PROC MIXED} the fixed-effects part is -specified in the \code{model} statement and the random-effects -part in the \code{random} statement. In \code{lmer} the -arguments are called \code{fixed} and \code{random}. - -Both \code{SAS PROC MIXED} and \code{lmer} allow a mixed-effects model -to be fit by maximum likelihood (\code{method = ml} in SAS) or by -maximum residual likelihood, sometimes also called restricted maximum -likelihood or \textsf{REML}. This is the default criterion in -\code{SAS PROC MIXED} and in \code{lmer}. To get \textsf{ML} -estimates in \code{lmer}, set the optional argument -\code{method="REML"}. - -\section{Important differences} -\label{sec:differences} - -The output from \code{PROC MIXED} typically includes values of the -Akaike Information Criterion (\textsf{AIC}) and Schwartz's Bayesian -Criterion (\textsf{SBC}). These are used to compare different models -fit to the same data. The output of the \code{summary} function applied -to the object created by \code{lmer} also produces values of \textsf{AIC} -and \textsf{BIC} but the definitions used in \code{PROC MIXED} and in -\code{lmer} are different. In \code{lmer} the definitions are such that -``smaller is better''. In \code{PROC MIXED} the definitions are such -that ``bigger is better''. - -When models are fit by \textsf{REML}, the values of \textsf{AIC}, -\textsf{SBC} (or \textsf{BIC}) and the log-likelihood can only be -compared between models with exactly the same fixed-effects structure. -When models are fit by maximum likelihood these criteria can be -compared between any models fit to the same data. That is, these -quality-of-fit criteria can be used to evaluate different -fixed-effects specifications or different random-effects -specifications or different specifications of both fixed effects and -random effects. The greater flexibility of model comparisons when -using maximum likelihood is the reason that this is the default -criterion in \code{lmer}. - -We encourage developing and testing the model using likelihood ratio -tests or the \textsf{AIC} and \textsf{BIC} criteria. Once a form -for both the random effects and the fixed effects has been determined, -the model can be refit with \code{REML = TRUE} if the restricted -estimates of the variance components are desired. - -\section{Data manipulation} -\label{sec:data} - -Both \code{PROC MIXED} and \code{lmer} work with data in a tabular form -with one row per observation. There are, however, important -differences in the internal representations of variables in the data. - -In \textsf{SAS} a qualitative factor can be stored either as numerical -values or alphanumeric labels. When a factor stored as numerical -values is used in \code{PROC MIXED} it is listed in the \code{class} -statement to indicate that it is a factor. In \s{} this information -is stored with the data itself by converting the variable to a factor -when it is first stored. If the factor represents an ordered set of -levels, it should be converted to an \code{ordered} factor. - -For example the SAS code -\begin{Example} -data animal; - input trait animal y; - datalines; -1 1 6 -1 2 8 -1 3 7 -2 1 9 -2 2 5 -2 3 . -; -\end{Example} -would require that the \code{trait} and \code{animal} variables be -specified in a class statement in any model that is fit. - -In \s{} these data could be read from a file, say \texttt{animal.dat}, -and converted to factors by -\begin{Schunk} -\begin{Sinput} -animal <- read.table("animal.dat", header = TRUE) -animal$trait <- as.factor(animal$trait) -animal$animal <- as.factor(animal$animal) -\end{Sinput} -\end{Schunk} -In general it is a good idea to check the types of variables in a data -frame before working with it. One way of doing this is to apply -the function \textsf{data.class} to each variable in turn using the -\code{sapply} function. -\begin{Schunk} -\begin{Sinput} -> sapply(Animal, data.class) -\end{Sinput} -\begin{Soutput} - Sire Dam AvgDailyGain - "factor" "factor" "numeric" -\end{Soutput} -\begin{Sinput} -> str(Animal) -\end{Sinput} -\begin{Soutput} -'data.frame': 20 obs. of 3 variables: - $ Sire : Factor w/ 5 levels "1","2","3","4",..: 1 1 1 1 2 2 2 2 3 3 ... - $ Dam : Factor w/ 2 levels "1","2": 1 1 2 2 1 1 2 2 1 1 ... - $ AvgDailyGain: num 2.24 1.85 2.05 2.41 1.99 1.93 2.72 2.32 2.33 2.68 ... - - attr(*, "ginfo")=List of 7 - ..$ formula :Class 'formula' length 3 AvgDailyGain ~ 1 | Sire/Dam - .. .. ..- attr(*, ".Environment")= - ..$ order.groups:List of 2 - .. ..$ Sire: logi TRUE - .. ..$ Dam : logi TRUE - ..$ FUN :function (x) - ..$ outer : NULL - ..$ inner : NULL - ..$ labels :List of 1 - .. ..$ AvgDailyGain: chr "Average Daily Weight Gain" - ..$ units : list() -\end{Soutput} -\end{Schunk} - -To make specification of models in \code{lmer} easier and to make graphic -presentations more informative, we recommend converting from a -\code{data.frame} object to a \code{groupedData} object. This class of -objects contains a formula specifying the response, the primary -covariate (if there is one) and the grouping factor or factors. The -data sets from \citet{litt:mill:stro:wolf:1996} have been -converted to \code{groupedData} objects in this directory. - -\subsection{Unique levels of factors} -\label{sec:nested} - -Designs with nested grouping factors are indicated differently in the -two languages. An example of such an experimental design is the -semiconductor experiment described in section 2.2 of -\citet{litt:mill:stro:wolf:1996} where twelve wafers are -assigned to four experimental treatments with three wafers per -treatment. The levels for the wafer factor are \code{1}, \code{2}, and -\code{3} but the wafer factor is only meaningful within the same level -of the treatment factor, \code{et}. There is nothing associating wafer -\code{1} of the third treatment group with wafer \code{1} of the first -treatment group. - -In \code{SAS} this nesting of factors is denoted by \code{wafer(et)}. In -\s{} the nesting is written with \code{~ ET/Wafer} and read ``wafer -within ET''. If both levels of nested factors are to be associated -with random effects then this is all you need to know. You would use -an expression with a \code{"/"} in the grouping factor part of the -formula for the \code{groupedData} object. Then the random effects -could be specified as -\begin{Example} - random = list( ET = ~ 1, Wafer = ~ 1 ) -\end{Example} -or, equivalently -\begin{Example} - random = ~ 1 | ET/Wafer -\end{Example} - -In this case, however, there would not usually be any random effects -associated with the ``experimental treatment'' or \code{ET} factor. The -only random effects are at the \code{Wafer} level. It is necessary to -create a factor that will have unique levels for each \code{Wafer} -within each level of \code{ET}. One way to do this is to assign -\begin{Schunk} -\begin{Sinput} -> Semiconductor$Grp <- with(Semiconductor, ET:Wafer) -\end{Sinput} -\end{Schunk} -%$ -after which we could specify a random effects term of \code{(1 | Grp)}. - -\subsection{General approach} -\label{sec:generalApproach} - -As a general approach to importing data into \s{} for mixed-effects -analysis you should: -\begin{itemize} -\item Create a \code{data.frame} with one row per observation and one - column per variable. -\item Use \code{ordered} or \code{as.ordered} to explicitly convert any - ordered factors to class \code{ordered}. -\item Use \code{ordered} or \code{as.ordered} to explicitly convert any - ordered factors to class \code{ordered}. -\item If necessary, use \code{getGroups} to create a factor with unique - levels from inner nested factors. -\item Specify the formula for the response, the primary covariate and - the grouping structure to create a \code{groupedData} object from the - data frame. Labels and units for the response and the primary - covariate can also be specified at this time as can \code{outer} and - \code{inner} factor expressions. -\item Plot the data. Plot it several ways. The use of trellis - graphics is closely integrated with the \code{nlme} library. The - trellis plots can provide invaluable insight into the structure of - the data. Use them. -\end{itemize} - -\section{Contrasts} -\label{sec:contrasts} - -When comparing estimates produced by \code{SAS PROC MIXED} and by -\code{lmer} one must be careful to consider the contrasts that are -used to define the effects of factors. In \textsf{SAS} a model with -an intercept and a qualitative factor is defined in terms of the -intercept and the indicator variables for all but the last level of -the factor. The default behaviour in \s{} is to use the Helmert -contrasts for the factor. On a balanced factor these provide a set of -orthogonal contrasts. In \R{} the default is the ``treatment'' -contrasts which are almost the same as the SAS parameterization except -that they drop the indicator of the first level, not the last level. - -When in doubt, check which contrasts are being used with the -\textsf{contrasts} function. - -To make comparisons easier, you may find it worthwhile to declare -\begin{Schunk} -\begin{Sinput} -> options(contrasts = c(factor = "contr.SAS", ordered = "contr.poly")) -\end{Sinput} -\end{Schunk} -at the beginning of your session. - -\bibliography{Usinglmer} -\appendix - -\section{AvgDailyGain} -\label{sec:AvgDailyGain} - -\begin{Schunk} -\begin{Sinput} -> print(xyplot(adg ~ Treatment | Block, AvgDailyGain, type = c("g", -+ "p", "r"), xlab = "Treatment (amount of feed additive)", -+ ylab = "Average daily weight gain (lb.)", aspect = "xy", -+ index.cond = function(x, y) coef(lm(y ~ x))[1])) -\end{Sinput} -\end{Schunk} -\begin{figure}[tbp] - \centering - \includegraphics{figs/f-adg1} - \caption{Average daily weight gain} - \label{fig:adg1} -\end{figure} -\begin{Schunk} -\begin{Sinput} -> (fm1Adg <- lmer(adg ~ (Treatment - 1) * InitWt + (1 | Block), -+ AvgDailyGain)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: adg ~ (Treatment - 1) * InitWt + (1 | Block) - Data: AvgDailyGain - AIC BIC logLik deviance REMLdev - 85.33 99.98 -32.66 10.10 65.33 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 0.25930 0.50921 - Residual 0.04943 0.22233 -Number of obs: 32, groups: Block, 8 - -Fixed effects: - Estimate Std. Error t value -Treatment0 0.439126 0.711093 0.6175 -Treatment10 1.426112 0.637550 2.2369 -Treatment20 0.479620 0.548890 0.8738 -Treatment30 0.200117 0.775205 0.2581 -InitWt 0.004448 0.002082 2.1368 -Treatment0:InitWt -0.002154 0.002786 -0.7732 -Treatment10:InitWt -0.003365 0.002515 -1.3381 -Treatment20:InitWt -0.001082 0.002488 -0.4351 - -Correlation of Fixed Effects: - Trtmn0 Trtm10 Trtm20 Trtm30 InitWt Tr0:IW T10:IW -Treatment10 0.039 -Treatment20 0.080 0.334 -Treatment30 0.011 0.097 0.043 -InitWt 0.050 -0.032 0.035 -0.967 -Trtmnt0:InW -0.640 0.046 -0.024 0.754 -0.780 -Trtmnt10:IW -0.021 -0.535 -0.178 0.781 -0.808 0.617 -Trtmnt20:IW -0.040 -0.106 -0.512 0.828 -0.856 0.666 0.775 -\end{Soutput} -\begin{Sinput} -> anova(fm1Adg) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Treatment 4 5.7251 1.4313 28.9552 -InitWt 1 0.5495 0.5495 11.1174 -Treatment:InitWt 3 0.1381 0.0460 0.9312 -\end{Soutput} -\begin{Sinput} -> (fm2Adg <- lmer(adg ~ InitWt + Treatment + (1 | Block), AvgDailyGain)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: adg ~ InitWt + Treatment + (1 | Block) - Data: AvgDailyGain - AIC BIC logLik deviance REMLdev - 50.34 60.6 -18.17 13.62 36.34 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 0.240833 0.49075 - Residual 0.050081 0.22379 -Number of obs: 32, groups: Block, 8 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 0.8011046 0.3556609 2.252 -InitWt 0.0027797 0.0008334 3.336 -Treatment0 -0.5520740 0.1148138 -4.808 -Treatment10 -0.0685666 0.1189697 -0.576 -Treatment20 -0.0881295 0.1162885 -0.758 - -Correlation of Fixed Effects: - (Intr) InitWt Trtmn0 Trtm10 -InitWt -0.844 -Treatment0 0.036 -0.224 -Treatment10 0.139 -0.340 0.534 -Treatment20 0.079 -0.272 0.530 0.545 -\end{Soutput} -\begin{Sinput} -> anova(fm2Adg) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -InitWt 1 0.51456 0.51456 10.275 -Treatment 3 1.52670 0.50890 10.162 -\end{Soutput} -\begin{Sinput} -> (fm3Adg <- lmer(adg ~ InitWt + Treatment - 1 + (1 | Block), -+ AvgDailyGain)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: adg ~ InitWt + Treatment - 1 + (1 | Block) - Data: AvgDailyGain - AIC BIC logLik deviance REMLdev - 50.34 60.6 -18.17 13.62 36.34 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 0.240833 0.49075 - Residual 0.050081 0.22379 -Number of obs: 32, groups: Block, 8 - -Fixed effects: - Estimate Std. Error t value -InitWt 0.0027797 0.0008334 3.336 -Treatment0 0.2490307 0.3776319 0.659 -Treatment10 0.7325380 0.3903800 1.876 -Treatment20 0.7129751 0.3827687 1.863 -Treatment30 0.8011046 0.3556609 2.252 - -Correlation of Fixed Effects: - InitWt Trtmn0 Trtm10 Trtm20 -Treatment0 -0.863 -Treatment10 -0.873 0.957 -Treatment20 -0.867 0.957 0.958 -Treatment30 -0.844 0.953 0.953 0.953 -\end{Soutput} -\end{Schunk} - - -\section{BIB} -\label{sec:BIB} -\begin{Schunk} -\begin{Sinput} -> print(xyplot(y ~ x | Block, BIB, groups = Treatment, type = c("g", -+ "p"), aspect = "xy", auto.key = list(points = TRUE, space = "right", -+ lines = FALSE))) -\end{Sinput} -\end{Schunk} -\begin{figure}[tbp] - \centering - \includegraphics{figs/f-bib1} - \caption{Balanced incomplete block design} - \label{fig:bib1} -\end{figure} -\begin{Schunk} -\begin{Sinput} -> (fm1BIB <- lmer(y ~ Treatment * x + (1 | Block), BIB)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: y ~ Treatment * x + (1 | Block) - Data: BIB - AIC BIC logLik deviance REMLdev - 124.9 136.7 -52.45 93.5 104.9 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 18.2488 4.2719 - Residual 1.2005 1.0957 -Number of obs: 24, groups: Block, 8 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 22.36787 3.10185 7.211 -Treatment1 4.42948 3.36511 1.316 -Treatment2 -0.43738 2.93326 -0.149 -Treatment3 6.27861 3.28210 1.913 -x 0.44255 0.08706 5.083 -Treatment1:x -0.22377 0.10608 -2.109 -Treatment2:x 0.05338 0.09714 0.550 -Treatment3:x -0.17918 0.11571 -1.548 - -Correlation of Fixed Effects: - (Intr) Trtmn1 Trtmn2 Trtmn3 x Trtm1: Trtm2: -Treatment1 -0.728 -Treatment2 -0.778 0.797 -Treatment3 -0.796 0.827 0.826 -x -0.859 0.797 0.865 0.886 -Treatmnt1:x 0.709 -0.979 -0.774 -0.797 -0.799 -Treatmnt2:x 0.722 -0.731 -0.965 -0.763 -0.829 0.729 -Treatmnt3:x 0.769 -0.789 -0.790 -0.976 -0.879 0.777 0.748 -\end{Soutput} -\begin{Sinput} -> anova(fm1BIB) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Treatment 3 23.447 7.816 6.5107 -x 1 136.809 136.809 113.9640 -Treatment:x 3 18.427 6.142 5.1166 -\end{Soutput} -\begin{Sinput} -> (fm2BIB <- lmer(y ~ Treatment + x:Grp + (1 | Block), BIB)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: y ~ Treatment + x:Grp + (1 | Block) - Data: BIB - AIC BIC logLik deviance REMLdev - 115.2 124.6 -49.59 94.09 99.18 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 18.5245 4.3040 - Residual 1.0379 1.0188 -Number of obs: 24, groups: Block, 8 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 20.94518 2.06228 10.156 -Treatment1 5.34143 1.97574 2.704 -Treatment2 1.13556 0.71400 1.590 -Treatment3 8.18102 1.77013 4.622 -x:Grp13 0.23952 0.04296 5.575 -x:Grp24 0.48923 0.04412 11.088 - -Correlation of Fixed Effects: - (Intr) Trtmn1 Trtmn2 Trtmn3 x:Gr13 -Treatment1 -0.501 -Treatment2 -0.431 0.559 -Treatment3 -0.527 0.942 0.581 -x:Grp13 0.027 -0.663 -0.165 -0.605 -x:Grp24 -0.639 0.651 0.452 0.688 0.042 -\end{Soutput} -\begin{Sinput} -> anova(fm2BIB) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Treatment 3 23.424 7.808 7.5233 -x:Grp 2 154.733 77.366 74.5441 -\end{Soutput} -\end{Schunk} - - -\section{Bond} -\label{sec:Bond} - -\begin{Schunk} -\begin{Sinput} -> (fm1Bond <- lmer(pressure ~ Metal + (1 | Ingot), Bond)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: pressure ~ Metal + (1 | Ingot) - Data: Bond - AIC BIC logLik deviance REMLdev - 117.8 123.0 -53.9 115.7 107.8 -Random effects: - Groups Name Variance Std.Dev. - Ingot (Intercept) 11.447 3.3833 - Residual 10.372 3.2206 -Number of obs: 21, groups: Ingot, 7 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 71.1000 1.7655 40.27 -Metalc -0.9143 1.7215 -0.53 -Metali 4.8000 1.7215 2.79 - -Correlation of Fixed Effects: - (Intr) Metalc -Metalc -0.488 -Metali -0.488 0.500 -\end{Soutput} -\begin{Sinput} -> anova(fm1Bond) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Metal 2 131.90 65.95 6.3585 -\end{Soutput} -\end{Schunk} - -\section{Cultivation} -\label{sec:Cultivation} - -\begin{Schunk} -\begin{Sinput} -> str(Cultivation) -\end{Sinput} -\begin{Soutput} -'data.frame': 24 obs. of 4 variables: - $ Block: Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 2 2 2 2 ... - $ Cult : Factor w/ 2 levels "a","b": 1 1 1 2 2 2 1 1 1 2 ... - $ Inoc : Factor w/ 3 levels "con","dea","liv": 1 2 3 1 2 3 1 2 3 1 ... - $ drywt: num 27.4 29.7 34.5 29.4 32.5 34.4 28.9 28.7 33.4 28.7 ... - - attr(*, "ginfo")=List of 7 - ..$ formula :Class 'formula' length 3 drywt ~ 1 | Block/Cult - .. .. ..- attr(*, ".Environment")= - ..$ order.groups:List of 2 - .. ..$ Block: logi TRUE - .. ..$ Cult : logi TRUE - ..$ FUN :function (x) - ..$ outer : NULL - ..$ inner :List of 1 - .. ..$ Cult:Class 'formula' length 2 ~Inoc - .. .. .. ..- attr(*, ".Environment")= - ..$ labels :List of 1 - .. ..$ drywt: chr "Yield" - ..$ units : list() -\end{Soutput} -\begin{Sinput} -> xtabs(~Block + Cult, Cultivation) -\end{Sinput} -\begin{Soutput} - Cult -Block a b - 1 3 3 - 2 3 3 - 3 3 3 - 4 3 3 -\end{Soutput} -\begin{Sinput} -> (fm1Cult <- lmer(drywt ~ Inoc * Cult + (1 | Block) + (1 | -+ Cult), Cultivation)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: drywt ~ Inoc * Cult + (1 | Block) + (1 | Cult) - Data: Cultivation - AIC BIC logLik deviance REMLdev - 86.49 97.09 -34.24 74.94 68.49 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 1.20728 1.09876 - Cult (Intercept) 0.26565 0.51541 - Residual 1.19633 1.09377 -Number of obs: 24, groups: Block, 4; Cult, 2 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 33.5250 0.9309 36.01 -Inoccon -5.5000 0.7734 -7.11 -Inocdea -2.8750 0.7734 -3.72 -Culta -0.3750 1.0628 -0.35 -Inoccon:Culta 0.2500 1.0938 0.23 -Inocdea:Culta -1.0250 1.0938 -0.94 - -Correlation of Fixed Effects: - (Intr) Inoccn Inocde Culta Incc:C -Inoccon -0.415 -Inocdea -0.415 0.500 -Culta -0.571 0.364 0.364 -Inoccon:Clt 0.294 -0.707 -0.354 -0.515 -Inocdea:Clt 0.294 -0.354 -0.707 -0.515 0.500 -\end{Soutput} -\begin{Sinput} -> anova(fm1Cult) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Inoc 2 118.176 59.088 49.3908 -Cult 1 0.657 0.657 0.5489 -Inoc:Cult 2 1.826 0.913 0.7631 -\end{Soutput} -\begin{Sinput} -> (fm2Cult <- lmer(drywt ~ Inoc + Cult + (1 | Block) + (1 | -+ Cult), Cultivation)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: drywt ~ Inoc + Cult + (1 | Block) + (1 | Cult) - Data: Cultivation - AIC BIC logLik deviance REMLdev - 87.75 96 -36.88 76.9 73.75 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 1.21283 1.10129 - Cult (Intercept) 0.25824 0.50817 - Residual 1.16299 1.07842 -Number of obs: 24, groups: Block, 4; Cult, 2 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 33.6542 0.8691 38.72 -Inoccon -5.3750 0.5392 -9.97 -Inocdea -3.3875 0.5392 -6.28 -Culta -0.6333 0.8428 -0.75 - -Correlation of Fixed Effects: - (Intr) Inoccn Inocde -Inoccon -0.310 -Inocdea -0.310 0.500 -Culta -0.485 0.000 0.000 -\end{Soutput} -\begin{Sinput} -> anova(fm2Cult) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Inoc 2 118.176 59.088 50.8069 -Cult 1 0.657 0.657 0.5647 -\end{Soutput} -\begin{Sinput} -> (fm3Cult <- lmer(drywt ~ Inoc + (1 | Block) + (1 | Cult), -+ Cultivation)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: drywt ~ Inoc + (1 | Block) + (1 | Cult) - Data: Cultivation - AIC BIC logLik deviance REMLdev - 87.68 94.75 -37.84 77.32 75.68 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 1.21285 1.10129 - Cult (Intercept) 0.10360 0.32188 - Residual 1.16300 1.07842 -Number of obs: 24, groups: Block, 4; Cult, 2 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 33.3375 0.7074 47.13 -Inoccon -5.3750 0.5392 -9.97 -Inocdea -3.3875 0.5392 -6.28 - -Correlation of Fixed Effects: - (Intr) Inoccn -Inoccon -0.381 -Inocdea -0.381 0.500 -\end{Soutput} -\begin{Sinput} -> anova(fm3Cult) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Inoc 2 118.176 59.088 50.806 -\end{Soutput} -\end{Schunk} - - - -\section{Demand} -\label{sec:Demand} - -\begin{Schunk} -\begin{Sinput} -> (fm1Demand <- lmer(log(d) ~ log(y) + log(rd) + log(rt) + -+ log(rs) + (1 | State) + (1 | Year), Demand)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: log(d) ~ log(y) + log(rd) + log(rt) + log(rs) + (1 | State) + (1 | Year) - Data: Demand - AIC BIC logLik deviance REMLdev - -224.2 -205.4 120.1 -260.5 -240.2 -Random effects: - Groups Name Variance Std.Dev. - Year (Intercept) 0.00026466 0.016268 - State (Intercept) 0.02950232 0.171762 - Residual 0.00111699 0.033421 -Number of obs: 77, groups: Year, 11; State, 7 - -Fixed effects: - Estimate Std. Error t value -(Intercept) -1.28386 0.72343 -1.775 -log(y) 1.06978 0.10393 10.294 -log(rd) -0.29533 0.05246 -5.629 -log(rt) 0.03988 0.02789 1.430 -log(rs) -0.32673 0.11438 -2.856 - -Correlation of Fixed Effects: - (Intr) log(y) lg(rd) lg(rt) -log(y) -0.976 -log(rd) 0.383 -0.227 -log(rt) 0.077 -0.062 -0.337 -log(rs) 0.444 -0.600 -0.270 -0.323 -\end{Soutput} -\end{Schunk} - -\section{HR} -\label{sec:HR} -\begin{Schunk} -\begin{Sinput} -> (fm1HR <- lmer(HR ~ Time * Drug + baseHR + (Time | Patient), -+ HR)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: HR ~ Time * Drug + baseHR + (Time | Patient) - Data: HR - AIC BIC logLik deviance REMLdev - 789.6 820.3 -383.8 788.1 767.6 -Random effects: - Groups Name Variance Std.Dev. Corr - Patient (Intercept) 60.633 7.7867 - Time 37.789 6.1473 -0.563 - Residual 24.361 4.9357 -Number of obs: 120, groups: Patient, 24 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 33.9784 10.2826 3.304 -Time -3.1970 3.0850 -1.036 -Druga 3.5991 4.2314 0.851 -Drugb 7.0912 4.2094 1.685 -baseHR 0.5434 0.1161 4.679 -Time:Druga -7.5013 4.3629 -1.719 -Time:Drugb -3.9894 4.3629 -0.914 - -Correlation of Fixed Effects: - (Intr) Time Druga Drugb baseHR Tim:Drg -Time -0.162 -Druga -0.308 0.394 -Drugb -0.244 0.396 0.501 -baseHR -0.957 0.000 0.110 0.041 -Time:Druga 0.115 -0.707 -0.557 -0.280 0.000 -Time:Drugb 0.115 -0.707 -0.278 -0.560 0.000 0.500 -\end{Soutput} -\begin{Sinput} -> anova(fm1HR) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Time 1 379.20 379.20 15.5661 -Drug 2 92.89 46.45 1.9066 -baseHR 1 533.30 533.30 21.8915 -Time:Drug 2 72.11 36.06 1.4801 -\end{Soutput} -\begin{Sinput} -> (fm3HR <- lmer(HR ~ Time + Drug + baseHR + (Time | Patient), -+ HR)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: HR ~ Time + Drug + baseHR + (Time | Patient) - Data: HR - AIC BIC logLik deviance REMLdev - 797.8 822.9 -389.9 791.2 779.8 -Random effects: - Groups Name Variance Std.Dev. Corr - Patient (Intercept) 61.560 7.8460 - Time 40.968 6.4006 -0.571 - Residual 24.361 4.9357 -Number of obs: 120, groups: Patient, 24 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 36.0471 10.1941 3.536 -Time -7.0273 1.8179 -3.866 -Druga -0.4526 3.5144 -0.129 -Drugb 4.9364 3.4879 1.415 -baseHR 0.5434 0.1161 4.679 - -Correlation of Fixed Effects: - (Intr) Time Druga Drugb -Time -0.096 -Druga -0.297 0.000 -Drugb -0.219 0.000 0.502 -baseHR -0.966 0.000 0.132 0.050 -\end{Soutput} -\begin{Sinput} -> anova(fm3HR) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Time 1 364.01 364.01 14.9423 -Drug 2 92.89 46.45 1.9066 -baseHR 1 533.29 533.29 21.8915 -\end{Soutput} -\begin{Sinput} -> (fm4HR <- lmer(HR ~ Time + baseHR + (Time | Patient), HR)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: HR ~ Time + baseHR + (Time | Patient) - Data: HR - AIC BIC logLik deviance REMLdev - 805.1 824.7 -395.6 794.3 791.1 -Random effects: - Groups Name Variance Std.Dev. Corr - Patient (Intercept) 63.026 7.9389 - Time 40.968 6.4006 -0.553 - Residual 24.361 4.9357 -Number of obs: 120, groups: Patient, 24 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 36.9321 9.9010 3.730 -Time -7.0273 1.8179 -3.866 -baseHR 0.5508 0.1175 4.686 - -Correlation of Fixed Effects: - (Intr) Time -Time -0.098 -baseHR -0.984 0.000 -\end{Soutput} -\begin{Sinput} -> anova(fm4HR) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Time 1 364.0 364.0 14.942 -baseHR 1 534.9 534.9 21.957 -\end{Soutput} -\end{Schunk} - - -\section{Mississippi} -\label{sec:Mississippi} - -\begin{Schunk} -\begin{Sinput} -> (fm1Miss <- lmer(y ~ 1 + (1 | influent), Mississippi)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: y ~ 1 + (1 | influent) - Data: Mississippi - AIC BIC logLik deviance REMLdev - 258.4 263.2 -126.2 256.6 252.4 -Random effects: - Groups Name Variance Std.Dev. - influent (Intercept) 63.313 7.9570 - Residual 42.659 6.5314 -Number of obs: 37, groups: influent, 6 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 21.223 3.429 6.19 -\end{Soutput} -\begin{Sinput} -> (fm1MLMiss <- lmer(y ~ 1 + (1 | influent), Mississippi, method = "ML")) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by maximum likelihood -Formula: y ~ 1 + (1 | influent) - Data: Mississippi - AIC BIC logLik deviance REMLdev - 262.6 267.4 -128.3 256.6 252.4 -Random effects: - Groups Name Variance Std.Dev. - influent (Intercept) 51.250 7.1589 - Residual 42.698 6.5344 -Number of obs: 37, groups: influent, 6 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 21.217 3.122 6.796 -\end{Soutput} -\begin{Sinput} -> ranef(fm1MLMiss) -\end{Sinput} -\begin{Soutput} -$influent - (Intercept) -1 0.3097835 -2 -6.5771551 -3 -3.7862180 -4 2.8826386 -5 -5.8434348 -6 13.0143857 -\end{Soutput} -\begin{Sinput} -> ranef(fm1Miss) -\end{Sinput} -\begin{Soutput} -$influent - (Intercept) -1 0.3092865 -2 -6.7192205 -3 -3.8978570 -4 2.9460546 -5 -6.0128502 -6 13.3745867 -\end{Soutput} -\begin{Sinput} -> VarCorr(fm1Miss) -\end{Sinput} -\begin{Soutput} -$influent - (Intercept) -(Intercept) 63.31329 -attr(,"stddev") -(Intercept) - 7.956965 -attr(,"correlation") - (Intercept) -(Intercept) 1 - -attr(,"sc") -sigmaREML - 6.53139 -\end{Soutput} -\begin{Sinput} -> (fm2Miss <- lmer(y ~ Type + (1 | influent), Mississippi)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: y ~ Type + (1 | influent) - Data: Mississippi - AIC BIC logLik deviance REMLdev - 244.5 252.6 -117.3 247.5 234.5 -Random effects: - Groups Name Variance Std.Dev. - influent (Intercept) 14.966 3.8686 - Residual 42.514 6.5203 -Number of obs: 37, groups: influent, 6 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 36.400 4.845 7.514 -Type1 -20.800 5.933 -3.506 -Type2 -16.462 5.516 -2.984 - -Correlation of Fixed Effects: - (Intr) Type1 -Type1 -0.816 -Type2 -0.878 0.717 -\end{Soutput} -\begin{Sinput} -> anova(fm2Miss) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Type 2 541.85 270.93 6.3726 -\end{Soutput} -\end{Schunk} - -\section{Multilocation} -\label{sec:Multilocation} - -\begin{Schunk} -\begin{Sinput} -> str(Multilocation) -\end{Sinput} -\begin{Soutput} -'data.frame': 108 obs. of 7 variables: - $ obs : num 3 4 6 7 9 10 12 16 19 20 ... - $ Location: Factor w/ 9 levels "A","B","C","D",..: 1 1 1 1 1 1 1 1 1 1 ... - $ Block : Factor w/ 3 levels "1","2","3": 1 1 1 1 2 2 2 2 3 3 ... - $ Trt : Factor w/ 4 levels "1","2","3","4": 3 4 2 1 2 1 3 4 1 2 ... - $ Adj : num 3.16 3.12 3.16 3.25 2.71 ... - $ Fe : num 7.10 6.68 6.83 6.53 8.25 ... - $ Grp : Factor w/ 27 levels "A/1","A/2","A/3",..: 1 1 1 1 2 2 2 2 3 3 ... - - attr(*, "ginfo")=List of 7 - ..$ formula :Class 'formula' length 3 Adj ~ 1 | Location/Block - .. .. ..- attr(*, ".Environment")= - ..$ order.groups:List of 2 - .. ..$ Location: logi TRUE - .. ..$ Block : logi TRUE - ..$ FUN :function (x) - ..$ outer : NULL - ..$ inner :List of 1 - .. ..$ Block:Class 'formula' length 2 ~Trt - .. .. .. ..- attr(*, ".Environment")= - ..$ labels :List of 1 - .. ..$ Adj: chr "Adjusted yield" - ..$ units : list() -\end{Soutput} -\begin{Sinput} -> Multilocation$Grp <- with(Multilocation, Block:Location) -> (fm1Mult <- lmer(Adj ~ Location * Trt + (1 | Grp), Multilocation)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: Adj ~ Location * Trt + (1 | Grp) - Data: Multilocation - AIC BIC logLik deviance REMLdev - 86.65 188.6 -5.323 -87.15 10.65 -Random effects: - Groups Name Variance Std.Dev. - Grp (Intercept) 0.0056191 0.074961 - Residual 0.0345788 0.185954 -Number of obs: 108, groups: Grp, 27 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 2.35923 0.11575 20.381 -LocationA 0.64930 0.16370 3.966 -LocationB 0.06643 0.16370 0.406 -LocationC 0.54533 0.16370 3.331 -LocationD 0.37413 0.16370 2.285 -LocationE 0.55000 0.16370 3.360 -LocationF 0.99810 0.16370 6.097 -LocationG 0.36057 0.16370 2.203 -LocationH 1.01403 0.16370 6.194 -Trt1 0.22720 0.15183 1.496 -Trt2 -0.00140 0.15183 -0.009 -Trt3 0.42323 0.15183 2.788 -LocationA:Trt1 -0.18853 0.21472 -0.878 -LocationB:Trt1 -0.27523 0.21472 -1.282 -LocationC:Trt1 -0.04000 0.21472 -0.186 -LocationD:Trt1 -0.53513 0.21472 -2.492 -LocationE:Trt1 -0.26297 0.21472 -1.225 -LocationF:Trt1 -0.27153 0.21472 -1.265 -LocationG:Trt1 0.20323 0.21472 0.946 -LocationH:Trt1 -0.14953 0.21472 -0.696 -LocationA:Trt2 -0.09347 0.21472 -0.435 -LocationB:Trt2 -0.32273 0.21472 -1.503 -LocationC:Trt2 0.08960 0.21472 0.417 -LocationD:Trt2 -0.29693 0.21472 -1.383 -LocationE:Trt2 -0.30693 0.21472 -1.429 -LocationF:Trt2 -0.30993 0.21472 -1.443 -LocationG:Trt2 -0.10860 0.21472 -0.506 -LocationH:Trt2 -0.33060 0.21472 -1.540 -LocationA:Trt3 -0.40247 0.21472 -1.874 -LocationB:Trt3 -0.56550 0.21472 -2.634 -LocationC:Trt3 -0.12247 0.21472 -0.570 -LocationD:Trt3 -0.54840 0.21472 -2.554 -LocationE:Trt3 -0.32863 0.21472 -1.531 -LocationF:Trt3 -0.46257 0.21472 -2.154 -LocationG:Trt3 -0.25297 0.21472 -1.178 -LocationH:Trt3 -0.37203 0.21472 -1.733 - -Correlation of Fixed Effects: - (Intr) LoctnA LoctnB LoctnC LoctnD LoctnE LoctnF LoctnG LoctnH -LocationA -0.707 -LocationB -0.707 0.500 -LocationC -0.707 0.500 0.500 -LocationD -0.707 0.500 0.500 0.500 -LocationE -0.707 0.500 0.500 0.500 0.500 -LocationF -0.707 0.500 0.500 0.500 0.500 0.500 -LocationG -0.707 0.500 0.500 0.500 0.500 0.500 0.500 -LocationH -0.707 0.500 0.500 0.500 0.500 0.500 0.500 0.500 -Trt1 -0.656 0.464 0.464 0.464 0.464 0.464 0.464 0.464 0.464 -Trt2 -0.656 0.464 0.464 0.464 0.464 0.464 0.464 0.464 0.464 -Trt3 -0.656 0.464 0.464 0.464 0.464 0.464 0.464 0.464 0.464 -LoctnA:Trt1 0.464 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnB:Trt1 0.464 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnC:Trt1 0.464 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnD:Trt1 0.464 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -LoctnE:Trt1 0.464 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -LoctnF:Trt1 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -LoctnG:Trt1 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -LoctnH:Trt1 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 -LoctnA:Trt2 0.464 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnB:Trt2 0.464 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnC:Trt2 0.464 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnD:Trt2 0.464 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -LoctnE:Trt2 0.464 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -LoctnF:Trt2 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -LoctnG:Trt2 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -LoctnH:Trt2 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 -LoctnA:Trt3 0.464 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnB:Trt3 0.464 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnC:Trt3 0.464 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -0.328 -LoctnD:Trt3 0.464 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -0.328 -LoctnE:Trt3 0.464 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -0.328 -LoctnF:Trt3 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -0.328 -LoctnG:Trt3 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 -0.328 -LoctnH:Trt3 0.464 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.328 -0.656 - Trt1 Trt2 Trt3 LcA:T1 LcB:T1 LcC:T1 LcD:T1 LcE:T1 LcF:T1 -LocationA -LocationB -LocationC -LocationD -LocationE -LocationF -LocationG -LocationH -Trt1 -Trt2 0.500 -Trt3 0.500 0.500 -LoctnA:Trt1 -0.707 -0.354 -0.354 -LoctnB:Trt1 -0.707 -0.354 -0.354 0.500 -LoctnC:Trt1 -0.707 -0.354 -0.354 0.500 0.500 -LoctnD:Trt1 -0.707 -0.354 -0.354 0.500 0.500 0.500 -LoctnE:Trt1 -0.707 -0.354 -0.354 0.500 0.500 0.500 0.500 -LoctnF:Trt1 -0.707 -0.354 -0.354 0.500 0.500 0.500 0.500 0.500 -LoctnG:Trt1 -0.707 -0.354 -0.354 0.500 0.500 0.500 0.500 0.500 0.500 -LoctnH:Trt1 -0.707 -0.354 -0.354 0.500 0.500 0.500 0.500 0.500 0.500 -LoctnA:Trt2 -0.354 -0.707 -0.354 0.500 0.250 0.250 0.250 0.250 0.250 -LoctnB:Trt2 -0.354 -0.707 -0.354 0.250 0.500 0.250 0.250 0.250 0.250 -LoctnC:Trt2 -0.354 -0.707 -0.354 0.250 0.250 0.500 0.250 0.250 0.250 -LoctnD:Trt2 -0.354 -0.707 -0.354 0.250 0.250 0.250 0.500 0.250 0.250 -LoctnE:Trt2 -0.354 -0.707 -0.354 0.250 0.250 0.250 0.250 0.500 0.250 -LoctnF:Trt2 -0.354 -0.707 -0.354 0.250 0.250 0.250 0.250 0.250 0.500 -LoctnG:Trt2 -0.354 -0.707 -0.354 0.250 0.250 0.250 0.250 0.250 0.250 -LoctnH:Trt2 -0.354 -0.707 -0.354 0.250 0.250 0.250 0.250 0.250 0.250 -LoctnA:Trt3 -0.354 -0.354 -0.707 0.500 0.250 0.250 0.250 0.250 0.250 -LoctnB:Trt3 -0.354 -0.354 -0.707 0.250 0.500 0.250 0.250 0.250 0.250 -LoctnC:Trt3 -0.354 -0.354 -0.707 0.250 0.250 0.500 0.250 0.250 0.250 -LoctnD:Trt3 -0.354 -0.354 -0.707 0.250 0.250 0.250 0.500 0.250 0.250 -LoctnE:Trt3 -0.354 -0.354 -0.707 0.250 0.250 0.250 0.250 0.500 0.250 -LoctnF:Trt3 -0.354 -0.354 -0.707 0.250 0.250 0.250 0.250 0.250 0.500 -LoctnG:Trt3 -0.354 -0.354 -0.707 0.250 0.250 0.250 0.250 0.250 0.250 -LoctnH:Trt3 -0.354 -0.354 -0.707 0.250 0.250 0.250 0.250 0.250 0.250 - LcG:T1 LcH:T1 LcA:T2 LcB:T2 LcC:T2 LcD:T2 LcE:T2 LcF:T2 LcG:T2 -LocationA -LocationB -LocationC -LocationD -LocationE -LocationF -LocationG -LocationH -Trt1 -Trt2 -Trt3 -LoctnA:Trt1 -LoctnB:Trt1 -LoctnC:Trt1 -LoctnD:Trt1 -LoctnE:Trt1 -LoctnF:Trt1 -LoctnG:Trt1 -LoctnH:Trt1 0.500 -LoctnA:Trt2 0.250 0.250 -LoctnB:Trt2 0.250 0.250 0.500 -LoctnC:Trt2 0.250 0.250 0.500 0.500 -LoctnD:Trt2 0.250 0.250 0.500 0.500 0.500 -LoctnE:Trt2 0.250 0.250 0.500 0.500 0.500 0.500 -LoctnF:Trt2 0.250 0.250 0.500 0.500 0.500 0.500 0.500 -LoctnG:Trt2 0.500 0.250 0.500 0.500 0.500 0.500 0.500 0.500 -LoctnH:Trt2 0.250 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 -LoctnA:Trt3 0.250 0.250 0.500 0.250 0.250 0.250 0.250 0.250 0.250 -LoctnB:Trt3 0.250 0.250 0.250 0.500 0.250 0.250 0.250 0.250 0.250 -LoctnC:Trt3 0.250 0.250 0.250 0.250 0.500 0.250 0.250 0.250 0.250 -LoctnD:Trt3 0.250 0.250 0.250 0.250 0.250 0.500 0.250 0.250 0.250 -LoctnE:Trt3 0.250 0.250 0.250 0.250 0.250 0.250 0.500 0.250 0.250 -LoctnF:Trt3 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.500 0.250 -LoctnG:Trt3 0.500 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.500 -LoctnH:Trt3 0.250 0.500 0.250 0.250 0.250 0.250 0.250 0.250 0.250 - LcH:T2 LcA:T3 LcB:T3 LcC:T3 LcD:T3 LcE:T3 LcF:T3 LcG:T3 -LocationA -LocationB -LocationC -LocationD -LocationE -LocationF -LocationG -LocationH -Trt1 -Trt2 -Trt3 -LoctnA:Trt1 -LoctnB:Trt1 -LoctnC:Trt1 -LoctnD:Trt1 -LoctnE:Trt1 -LoctnF:Trt1 -LoctnG:Trt1 -LoctnH:Trt1 -LoctnA:Trt2 -LoctnB:Trt2 -LoctnC:Trt2 -LoctnD:Trt2 -LoctnE:Trt2 -LoctnF:Trt2 -LoctnG:Trt2 -LoctnH:Trt2 -LoctnA:Trt3 0.250 -LoctnB:Trt3 0.250 0.500 -LoctnC:Trt3 0.250 0.500 0.500 -LoctnD:Trt3 0.250 0.500 0.500 0.500 -LoctnE:Trt3 0.250 0.500 0.500 0.500 0.500 -LoctnF:Trt3 0.250 0.500 0.500 0.500 0.500 0.500 -LoctnG:Trt3 0.250 0.500 0.500 0.500 0.500 0.500 0.500 -LoctnH:Trt3 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 -\end{Soutput} -\begin{Sinput} -> anova(fm1Mult) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Location 8 6.9476 0.8684 25.1149 -Trt 3 1.2217 0.4072 11.7774 -Location:Trt 24 0.9966 0.0415 1.2008 -\end{Soutput} -\begin{Sinput} -> (fm2Mult <- lmer(Adj ~ Location + Trt + (1 | Grp), Multilocation)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: Adj ~ Location + Trt + (1 | Grp) - Data: Multilocation - AIC BIC logLik deviance REMLdev - 22 59.55 3.001 -51.22 -6.001 -Random effects: - Groups Name Variance Std.Dev. - Grp (Intercept) 0.0050851 0.07131 - Residual 0.0367154 0.19161 -Number of obs: 108, groups: Grp, 27 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 2.53296 0.07599 33.33 -LocationA 0.47818 0.09752 4.90 -LocationB -0.22443 0.09752 -2.30 -LocationC 0.52712 0.09752 5.41 -LocationD 0.02902 0.09752 0.30 -LocationE 0.32537 0.09752 3.34 -LocationF 0.73709 0.09752 7.56 -LocationG 0.32098 0.09752 3.29 -LocationH 0.80099 0.09752 8.21 -Trt1 0.05834 0.05215 1.12 -Trt2 -0.18802 0.05215 -3.61 -Trt3 0.08379 0.05215 1.61 - -Correlation of Fixed Effects: - (Intr) LoctnA LoctnB LoctnC LoctnD LoctnE LoctnF LoctnG LoctnH -LocationA -0.642 -LocationB -0.642 0.500 -LocationC -0.642 0.500 0.500 -LocationD -0.642 0.500 0.500 0.500 -LocationE -0.642 0.500 0.500 0.500 0.500 -LocationF -0.642 0.500 0.500 0.500 0.500 0.500 -LocationG -0.642 0.500 0.500 0.500 0.500 0.500 0.500 -LocationH -0.642 0.500 0.500 0.500 0.500 0.500 0.500 0.500 -Trt1 -0.343 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -Trt2 -0.343 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -Trt3 -0.343 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 - Trt1 Trt2 -LocationA -LocationB -LocationC -LocationD -LocationE -LocationF -LocationG -LocationH -Trt1 -Trt2 0.500 -Trt3 0.500 0.500 -\end{Soutput} -\begin{Sinput} -> (fm3Mult <- lmer(Adj ~ Location + (1 | Grp), Multilocation)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: Adj ~ Location + (1 | Grp) - Data: Multilocation - AIC BIC logLik deviance REMLdev - 31.94 61.44 -4.968 -22.96 9.935 -Random effects: - Groups Name Variance Std.Dev. - Grp (Intercept) 3.3652e-11 5.8011e-06 - Residual 5.1642e-02 2.2725e-01 -Number of obs: 108, groups: Grp, 27 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 2.52149 0.06560 38.44 -LocationA 0.47818 0.09277 5.15 -LocationB -0.22443 0.09277 -2.42 -LocationC 0.52712 0.09277 5.68 -LocationD 0.02902 0.09277 0.31 -LocationE 0.32537 0.09277 3.51 -LocationF 0.73709 0.09277 7.95 -LocationG 0.32098 0.09277 3.46 -LocationH 0.80099 0.09277 8.63 - -Correlation of Fixed Effects: - (Intr) LoctnA LoctnB LoctnC LoctnD LoctnE LoctnF LoctnG -LocationA -0.707 -LocationB -0.707 0.500 -LocationC -0.707 0.500 0.500 -LocationD -0.707 0.500 0.500 0.500 -LocationE -0.707 0.500 0.500 0.500 0.500 -LocationF -0.707 0.500 0.500 0.500 0.500 0.500 -LocationG -0.707 0.500 0.500 0.500 0.500 0.500 0.500 -LocationH -0.707 0.500 0.500 0.500 0.500 0.500 0.500 0.500 -\end{Soutput} -\begin{Sinput} -> (fm4Mult <- lmer(Adj ~ Trt + (1 | Grp), Multilocation)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: Adj ~ Trt + (1 | Grp) - Data: Multilocation - AIC BIC logLik deviance REMLdev - 43.51 59.6 -15.75 14.95 31.51 -Random effects: - Groups Name Variance Std.Dev. - Grp (Intercept) 0.110920 0.33305 - Residual 0.036716 0.19161 -Number of obs: 108, groups: Grp, 27 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 2.86567 0.07395 38.75 -Trt1 0.05834 0.05215 1.12 -Trt2 -0.18802 0.05215 -3.61 -Trt3 0.08379 0.05215 1.61 - -Correlation of Fixed Effects: - (Intr) Trt1 Trt2 -Trt1 -0.353 -Trt2 -0.353 0.500 -Trt3 -0.353 0.500 0.500 -\end{Soutput} -\begin{Sinput} -> (fm5Mult <- lmer(Adj ~ 1 + (1 | Grp), Multilocation)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: Adj ~ 1 + (1 | Grp) - Data: Multilocation - AIC BIC logLik deviance REMLdev - 53.33 61.37 -23.66 43.75 47.33 -Random effects: - Groups Name Variance Std.Dev. - Grp (Intercept) 0.107489 0.32785 - Residual 0.050439 0.22459 -Number of obs: 108, groups: Grp, 27 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 2.85419 0.06669 42.8 -\end{Soutput} -\begin{Sinput} -> anova(fm2Mult) -\end{Sinput} -\begin{Soutput} -Analysis of Variance Table - Df Sum Sq Mean Sq F value -Location 8 7.3768 0.9221 25.115 -Trt 3 1.2217 0.4072 11.092 -\end{Soutput} -\begin{Sinput} -> (fm2MultR <- lmer(Adj ~ Trt + (Trt - 1 | Location) + (1 | -+ Block), Multilocation, control = list(msV = 1, niterEM = 200))) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: Adj ~ Trt + (Trt - 1 | Location) + (1 | Block) - Data: Multilocation - AIC BIC logLik deviance REMLdev - 33.41 76.32 -0.7036 -13.38 1.407 -Random effects: - Groups Name Variance Std.Dev. Corr - Location Trt1 1.3589e-01 3.6863e-01 - Trt2 1.0700e-01 3.2710e-01 0.989 - Trt3 1.1909e-01 3.4509e-01 0.998 0.996 - Trt4 1.1411e-01 3.3780e-01 0.927 0.972 0.948 - Block (Intercept) 2.3486e-14 1.5325e-07 - Residual 3.7773e-02 1.9435e-01 -Number of obs: 108, groups: Location, 9; Block, 3 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 2.86567 0.11865 24.152 -Trt1 0.05834 0.07012 0.832 -Trt2 -0.18802 0.05921 -3.176 -Trt3 0.08379 0.06447 1.300 - -Correlation of Fixed Effects: - (Intr) Trt1 Trt2 -Trt1 -0.150 -Trt2 -0.306 0.620 -Trt3 -0.236 0.682 0.620 -\end{Soutput} -\end{Schunk} - - -\section{PBIB} -\label{sec:PBIB} - -\begin{Schunk} -\begin{Sinput} -> str(PBIB) -\end{Sinput} -\begin{Soutput} -'data.frame': 60 obs. of 3 variables: - $ response : num 2.4 2.5 2.6 2 2.7 2.8 2.4 2.7 2.6 2.8 ... - $ Treatment: Factor w/ 15 levels "1","10","11",..: 7 15 1 5 11 13 14 1 2 1 ... - $ Block : Factor w/ 15 levels "1","10","11",..: 1 1 1 1 8 8 8 8 9 9 ... - - attr(*, "ginfo")=List of 7 - ..$ formula :Class 'formula' length 3 response ~ Treatment | Block - .. .. ..- attr(*, ".Environment")= - ..$ order.groups: logi TRUE - ..$ FUN :function (x) - ..$ outer : NULL - ..$ inner : NULL - ..$ labels : list() - ..$ units : list() -\end{Soutput} -\begin{Sinput} -> (fm1PBIB <- lmer(response ~ Treatment + (1 | Block), PBIB)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: response ~ Treatment + (1 | Block) - Data: PBIB - AIC BIC logLik deviance REMLdev - 85.98 121.6 -25.99 22.83 51.98 -Random effects: - Groups Name Variance Std.Dev. - Block (Intercept) 0.046519 0.21568 - Residual 0.085560 0.29251 -Number of obs: 60, groups: Block, 15 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 2.891309 0.166413 17.374 -Treatment1 -0.073788 0.222062 -0.332 -Treatment10 -0.400249 0.222062 -1.802 -Treatment11 0.007392 0.222062 0.033 -Treatment12 0.161514 0.222062 0.727 -Treatment13 -0.273542 0.222062 -1.232 -Treatment14 -0.400000 0.227201 -1.761 -Treatment15 -0.032076 0.222062 -0.144 -Treatment2 -0.485995 0.222062 -2.189 -Treatment3 -0.436366 0.222062 -1.965 -Treatment4 -0.107474 0.227201 -0.473 -Treatment5 -0.086411 0.222062 -0.389 -Treatment6 0.019385 0.222062 0.087 -Treatment7 -0.102323 0.222062 -0.461 -Treatment8 -0.109705 0.222062 -0.494 - -Correlation of Fixed Effects: - (Intr) Trtmn1 Trtm10 Trtm11 Trtm12 Trtm13 Trtm14 Trtm15 Trtmn2 -Treatment1 -0.667 -Treatment10 -0.667 0.500 -Treatment11 -0.667 0.477 0.500 -Treatment12 -0.667 0.500 0.500 0.500 -Treatment13 -0.667 0.500 0.500 0.500 0.500 -Treatment14 -0.683 0.512 0.512 0.512 0.512 0.512 -Treatment15 -0.667 0.500 0.477 0.500 0.500 0.500 0.512 -Treatment2 -0.667 0.500 0.500 0.500 0.477 0.500 0.512 0.500 -Treatment3 -0.667 0.500 0.500 0.500 0.500 0.477 0.512 0.500 0.500 -Treatment4 -0.683 0.512 0.512 0.512 0.512 0.512 0.500 0.512 0.512 -Treatment5 -0.667 0.500 0.477 0.500 0.500 0.500 0.512 0.477 0.500 -Treatment6 -0.667 0.477 0.500 0.477 0.500 0.500 0.512 0.500 0.500 -Treatment7 -0.667 0.500 0.500 0.500 0.477 0.500 0.512 0.500 0.477 -Treatment8 -0.667 0.500 0.500 0.500 0.500 0.477 0.512 0.500 0.500 - Trtmn3 Trtmn4 Trtmn5 Trtmn6 Trtmn7 -Treatment1 -Treatment10 -Treatment11 -Treatment12 -Treatment13 -Treatment14 -Treatment15 -Treatment2 -Treatment3 -Treatment4 0.512 -Treatment5 0.500 0.512 -Treatment6 0.500 0.512 0.500 -Treatment7 0.500 0.512 0.500 0.500 -Treatment8 0.477 0.512 0.500 0.500 0.500 -\end{Soutput} -\end{Schunk} - - -\section{SIMS} -\label{sec:SIMS} - -\begin{Schunk} -\begin{Sinput} -> str(SIMS) -\end{Sinput} -\begin{Soutput} -'data.frame': 3691 obs. of 3 variables: - $ Pretot: num 29 38 31 31 29 23 23 33 30 32 ... - $ Gain : num 2 0 6 6 5 9 7 2 1 3 ... - $ Class : Factor w/ 190 levels "1","10","100",..: 1 1 1 1 1 1 1 1 1 1 ... - - attr(*, "ginfo")=List of 7 - ..$ formula :Class 'formula' length 3 Gain ~ Pretot | Class - .. .. ..- attr(*, ".Environment")= - ..$ order.groups: logi TRUE - ..$ FUN :function (x) - ..$ outer : NULL - ..$ inner : NULL - ..$ labels :List of 2 - .. ..$ Pretot: chr "Sum of pre-test core item scores" - .. ..$ Gain : chr "Gain in mathematics achievement score" - ..$ units : list() -\end{Soutput} -\begin{Sinput} -> (fm1SIMS <- lmer(Gain ~ Pretot + (Pretot | Class), SIMS)) -\end{Sinput} -\begin{Soutput} -Linear mixed model fit by REML -Formula: Gain ~ Pretot + (Pretot | Class) - Data: SIMS - AIC BIC logLik deviance REMLdev - 22393 22430 -11190 22373 22381 -Random effects: - Groups Name Variance Std.Dev. Corr - Class (Intercept) 14.489586 3.806519 - Pretot 0.009206 0.095947 -0.641 - Residual 22.235943 4.715500 -Number of obs: 3691, groups: Class, 190 - -Fixed effects: - Estimate Std. Error t value -(Intercept) 7.0595 0.3659 19.29 -Pretot -0.1860 0.0161 -11.55 - -Correlation of Fixed Effects: - (Intr) -Pretot -0.760 -\end{Soutput} -\end{Schunk} -\end{document} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: t -%%% End: diff --git a/inst/doc/figs/f-adg1.pdf b/inst/doc/figs/f-adg1.pdf index e558d5d..6f66b8e 100644 Binary files a/inst/doc/figs/f-adg1.pdf and b/inst/doc/figs/f-adg1.pdf differ diff --git a/inst/doc/figs/f-bib1.pdf b/inst/doc/figs/f-bib1.pdf index e14d25e..0cb21b8 100644 Binary files a/inst/doc/figs/f-bib1.pdf and b/inst/doc/figs/f-bib1.pdf differ