diff --git a/DESCRIPTION b/DESCRIPTION index 3c80724..1286cce 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,6 +1,6 @@ Package: SASmixed -Version: 0.4-2 -Date: 2006-10-19 +Version: 0.4-4 +Date: 2008-06-25 Title: Data sets from "SAS System for Mixed Models" Maintainer: Douglas Bates Author: Original by Littel, Milliken, Stroup, and Wolfinger @@ -8,7 +8,7 @@ Author: Original by Littel, Milliken, Stroup, and Wolfinger 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 (>= 0.9975-4) +Suggests: lattice, lme4 (>= 0.999375-19) LazyData: yes License: GPL version 2 or later -Packaged: Thu Oct 19 13:21:37 2006; bates +Packaged: Wed Jun 25 12:42:15 2008; bates diff --git a/INDEX b/INDEX deleted file mode 100644 index 14d2201..0000000 --- a/INDEX +++ /dev/null @@ -1,25 +0,0 @@ -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 -SIMS Second International Mathematics Study data -Semi2 Oxide layer thicknesses on semiconductors -Semiconductor Semiconductor split-plot experiment -TeachingI Teaching Methods I -TeachingII Teaching Methods II -WWheat Winter wheat -WaferTypes Data on different types of silicon wafers -Weights Data from a weight-lifting program diff --git a/inst/doc/Rplots.ps b/inst/doc/Rplots.ps new file mode 100644 index 0000000..61bbaf5 Binary files /dev/null and b/inst/doc/Rplots.ps differ diff --git a/inst/doc/Usinglme.Rnw b/inst/doc/Usinglmer.Rnw similarity index 99% rename from inst/doc/Usinglme.Rnw rename to inst/doc/Usinglmer.Rnw index 635d643..0acdcc9 100644 --- a/inst/doc/Usinglme.Rnw +++ b/inst/doc/Usinglmer.Rnw @@ -36,7 +36,7 @@ library(lme4) \section{Introduction} \label{sec:intro} -The \code{lmer} function from the \code{Matrix} library for \textsf{R} is used +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}. @@ -266,7 +266,7 @@ options(contrasts = c(factor = "contr.SAS", ordered = "contr.poly")) @ at the beginning of your session. -\bibliography{Usinglme} +\bibliography{Usinglmer} \appendix \section{AvgDailyGain} diff --git a/inst/doc/Usinglme.bib b/inst/doc/Usinglmer.bib similarity index 88% rename from inst/doc/Usinglme.bib rename to inst/doc/Usinglmer.bib index 8f4238b..6223ae4 100644 --- a/inst/doc/Usinglme.bib +++ b/inst/doc/Usinglmer.bib @@ -1,5 +1,3 @@ -@String{id = "$Id: Usinglme.bib,v 1.1 1999/10/13 00:50:09 saikat Exp $"} - @Article{ lair:ware:1982, author = {Laird, Nan M. and Ware, James H.}, title = {Random-effects Models for Longitudinal Data}, diff --git a/inst/doc/Usinglme.pdf b/inst/doc/Usinglmer.pdf similarity index 52% rename from inst/doc/Usinglme.pdf rename to inst/doc/Usinglmer.pdf index bb5023b..2318131 100644 Binary files a/inst/doc/Usinglme.pdf and b/inst/doc/Usinglmer.pdf differ diff --git a/inst/doc/Usinglmer.tex b/inst/doc/Usinglmer.tex new file mode 100644 index 0000000..fa1fcb6 --- /dev/null +++ b/inst/doc/Usinglmer.tex @@ -0,0 +1,1605 @@ +\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 c2a963c..e558d5d 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 e90a819..e14d25e 100644 Binary files a/inst/doc/figs/f-bib1.pdf and b/inst/doc/figs/f-bib1.pdf differ diff --git a/man/Animal.Rd b/man/Animal.Rd index 009b662..76cb395 100644 --- a/man/Animal.Rd +++ b/man/Animal.Rd @@ -1,6 +1,5 @@ \name{Animal} \alias{Animal} -\non_function{} \title{Animal breeding experiment} \description{ The \code{Animal} data frame has 20 rows and 3 columns giving the diff --git a/man/AvgDailyGain.Rd b/man/AvgDailyGain.Rd index 76ba110..71395ce 100644 --- a/man/AvgDailyGain.Rd +++ b/man/AvgDailyGain.Rd @@ -1,6 +1,5 @@ \name{AvgDailyGain} \alias{AvgDailyGain} -\non_function{} \title{Average daily weight gain of steers on different diets} \description{ The \code{AvgDailyGain} data frame has 32 rows and 6 columns. diff --git a/man/BIB.Rd b/man/BIB.Rd index 950ae3c..866f0a3 100644 --- a/man/BIB.Rd +++ b/man/BIB.Rd @@ -1,6 +1,5 @@ \name{BIB} \alias{BIB} -\non_function{} \title{Data from a balanced incomplete block design} \description{ The \code{BIB} data frame has 24 rows and 5 columns. diff --git a/man/Bond.Rd b/man/Bond.Rd index 7484918..ccd2e05 100644 --- a/man/Bond.Rd +++ b/man/Bond.Rd @@ -1,6 +1,5 @@ \name{Bond} \alias{Bond} -\non_function{} \title{Strengths of metal bonds} \description{ The \code{Bond} data frame has 21 rows and 3 columns of data on the diff --git a/man/Cultivation.Rd b/man/Cultivation.Rd index 7344456..9f639fc 100644 --- a/man/Cultivation.Rd +++ b/man/Cultivation.Rd @@ -1,6 +1,5 @@ \name{Cultivation} \alias{Cultivation} -\non_function{} \title{Bacterial innoculation applied to grass cultivars} \description{ The \code{Cultivation} data frame has 24 rows and 4 columns of data diff --git a/man/Demand.Rd b/man/Demand.Rd index f74226f..8674244 100644 --- a/man/Demand.Rd +++ b/man/Demand.Rd @@ -1,6 +1,5 @@ \name{Demand} \alias{Demand} -\non_function{} \title{Per-capita demand deposits by state and year} \description{ The \code{Demand} data frame has 77 rows and 8 columns of data on diff --git a/man/Genetics.Rd b/man/Genetics.Rd index bf1c9a9..0ca727f 100644 --- a/man/Genetics.Rd +++ b/man/Genetics.Rd @@ -1,6 +1,5 @@ \name{Genetics} \alias{Genetics} -\non_function{} \title{Heritability data} \description{ The \code{Genetics} data frame has 60 rows and 4 columns. diff --git a/man/HR.Rd b/man/HR.Rd index 192f71d..dd656ed 100644 --- a/man/HR.Rd +++ b/man/HR.Rd @@ -1,6 +1,5 @@ \name{HR} \alias{HR} -\non_function{} \title{Heart rates of patients on different drug treatments} \description{ The \code{HR} data frame has 120 rows and 5 columns of the heart diff --git a/man/IncBlk.Rd b/man/IncBlk.Rd index 3577a82..5a8304d 100644 --- a/man/IncBlk.Rd +++ b/man/IncBlk.Rd @@ -1,6 +1,5 @@ \name{IncBlk} \alias{IncBlk} -\non_function{} \title{An unbalanced incomplete block experiment} \description{ The \code{IncBlk} data frame has 24 rows and 4 columns. diff --git a/man/Mississippi.Rd b/man/Mississippi.Rd index f1a1818..af9b6ba 100644 --- a/man/Mississippi.Rd +++ b/man/Mississippi.Rd @@ -1,6 +1,5 @@ \name{Mississippi} \alias{Mississippi} -\non_function{} \title{Nitrogen concentrations in the Mississippi River} \description{ The \code{Mississippi} data frame has 37 rows and 3 columns. diff --git a/man/Multilocation.Rd b/man/Multilocation.Rd index d9d4387..d624a03 100644 --- a/man/Multilocation.Rd +++ b/man/Multilocation.Rd @@ -1,6 +1,5 @@ \name{Multilocation} \alias{Multilocation} -\non_function{} \title{A multilocation trial} \description{ The \code{Multilocation} data frame has 108 rows and 7 columns. diff --git a/man/PBIB.Rd b/man/PBIB.Rd index ccc4c17..4b9dc05 100644 --- a/man/PBIB.Rd +++ b/man/PBIB.Rd @@ -1,6 +1,5 @@ \name{PBIB} \alias{PBIB} -\non_function{} \title{A partially balanced incomplete block experiment} \description{ The \code{PBIB} data frame has 60 rows and 3 columns. diff --git a/man/SIMS.Rd b/man/SIMS.Rd index 6b45711..f9695d7 100644 --- a/man/SIMS.Rd +++ b/man/SIMS.Rd @@ -1,6 +1,5 @@ \name{SIMS} \alias{SIMS} -\non_function{} \title{Second International Mathematics Study data} \description{ The \code{SIMS} data frame has 3691 rows and 3 columns. @@ -19,8 +18,7 @@ } } } -\details{ -} +%\details{} \source{ Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), \emph{SAS System for Mixed Models}, SAS Institute diff --git a/man/Semi2.Rd b/man/Semi2.Rd index 61c1d15..0fab436 100644 --- a/man/Semi2.Rd +++ b/man/Semi2.Rd @@ -1,6 +1,5 @@ \name{Semi2} \alias{Semi2} -\non_function{} \title{Oxide layer thicknesses on semiconductors} \description{ The \code{Semi2} data frame has 72 rows and 5 columns. diff --git a/man/Semiconductor.Rd b/man/Semiconductor.Rd index f8f536c..bcacc12 100644 --- a/man/Semiconductor.Rd +++ b/man/Semiconductor.Rd @@ -1,6 +1,5 @@ \name{Semiconductor} \alias{Semiconductor} -\non_function{} \title{Semiconductor split-plot experiment} \description{ The \code{Semiconductor} data frame has 48 rows and 5 columns. @@ -26,8 +25,7 @@ } } } -\details{ -} +%\details{} \source{ Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), \emph{SAS System for Mixed Models}, SAS Institute diff --git a/man/TeachingI.Rd b/man/TeachingI.Rd index 24dc367..e69f7b7 100644 --- a/man/TeachingI.Rd +++ b/man/TeachingI.Rd @@ -1,6 +1,5 @@ \name{TeachingI} \alias{TeachingI} -\non_function{} \title{Teaching Methods I} \description{ The \code{TeachingI} data frame has 96 rows and 7 columns. diff --git a/man/TeachingII.Rd b/man/TeachingII.Rd index e986fde..0e6dc39 100644 --- a/man/TeachingII.Rd +++ b/man/TeachingII.Rd @@ -1,6 +1,5 @@ \name{TeachingII} \alias{TeachingII} -\non_function{} \title{Teaching Methods II} \description{ The \code{TeachingII} data frame has 96 rows and 6 columns. diff --git a/man/WWheat.Rd b/man/WWheat.Rd index 3d611a2..e212979 100644 --- a/man/WWheat.Rd +++ b/man/WWheat.Rd @@ -1,6 +1,5 @@ \name{WWheat} \alias{WWheat} -\non_function{} \title{Winter wheat} \description{ The \code{WWheat} data frame has 60 rows and 3 columns. @@ -19,7 +18,6 @@ } } } -%\details{} \source{ Littel, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), \emph{SAS System for Mixed Models}, SAS Institute diff --git a/man/WaferTypes.Rd b/man/WaferTypes.Rd index 57b7e73..bb1fda6 100644 --- a/man/WaferTypes.Rd +++ b/man/WaferTypes.Rd @@ -1,6 +1,5 @@ \name{WaferTypes} \alias{WaferTypes} -\non_function{} \title{Data on different types of silicon wafers} \description{ The \code{WaferTypes} data frame has 144 rows and 8 columns. diff --git a/man/Weights.Rd b/man/Weights.Rd index 98b0c68..2e34ac3 100644 --- a/man/Weights.Rd +++ b/man/Weights.Rd @@ -1,6 +1,5 @@ \name{Weights} \alias{Weights} -\non_function{} \title{Data from a weight-lifting program} \description{ The \code{Weights} data frame has 399 rows and 5 columns.