# Fit Linear Mixed Model by ANOVA or REML Function serves as interface to functions `anovaMM` and `remlMM` for fitting a linear mixed model (LMM) either by ANOVA or REML. All arguments applicable to either one of these functions can be specified (see `anovaMM` or `remlMM` for details). ```r fitLMM( form, Data, method = c("anova", "reml"), scale = TRUE, VarVC = TRUE, ... ) ``` ## Arguments - `form`: (formula) specifiying the linear mixed model, random effects need to be identified by enclosing them in round brackets, i.e. ~a/(b) will model factor 'a' as fixed and 'b' as random - `Data`: (data.frame) containing all variables referenced in 'form', note that variables can only be of type "numeric", "factor" or "character". The latter will be automatically converted to "factor" - `method`: (character) either "anova" to use ANOVA Type-I estimation of variance components or "reml" to use restricted maximum likelihood (REML) estimation of variance component - `scale`: (logical) TRUE = scale values of the response aiming to avoid numerical problems when numbers are either very small or very large, FALSE = use original scale - `VarVC`: (logical) TRUE = variance-covariance matrix of variance components will be computed, FALSE = it will not be computed - `...`: additional arguments to be passed to function `anovaMM` or function `remlMM`. ## Details Besides offering a convenient interface to both functions for fitting a LMM, this function also provides all elements required for standard task of fitted models, e.g. prediction, testing general linear hypotheses via R-package `multcomp`, etc. (see examples). ## Examples ```r ## Not run: data(dataEP05A2_2) # assuming 'day' as fixed, 'run' as random # Note: default method is "anova" fitLMM(y~day/(run), dataEP05A2_2) # explicitly request "reml" fitLMM(y~day/(run), dataEP05A2_2, method="reml") # assuming both as random leads to same results as # calling anovaVCA (ANOVA is the default) fitLMM(y~(day)/(run), dataEP05A2_2) anovaVCA(y~day/run, dataEP05A2_2) # now using REML-estimation fitLMM(y~(day)/(run), dataEP05A2_2, "reml") remlVCA(y~day/run, dataEP05A2_2) # use different approaches to estimating the covariance of # variance components (covariance parameters) # create unbalanced data dat.ub <- dataEP05A2_2[-c(11,12,23,32,40,41,42),] m1.ub <- fitLMM(y~day/(run), dat.ub, VarVC.method="scm") # VarVC.method="gb" is an approximation not relying on quadratic forms m2.ub <- fitLMM(y~day/(run), dat.ub, VarVC.method="gb") # REML-estimated variance components usually differ from ANOVA-estimates # and so do the variance-covariance matrices m3.ub <- fitLMM(y~day/(run), dat.ub, "reml", VarVC=TRUE) V1.ub <- round(vcovVC(m1.ub), 12) V2.ub <- round(vcovVC(m2.ub), 12) V3.ub <- round(vcovVC(m3.ub), 12) # fit a larger random model data(VCAdata1) fitMM1 <- fitLMM(y~((lot)+(device))/(day)/(run), VCAdata1[VCAdata1$sample==1,]) fitMM1 # now use function tailored for random models fitRM1 <- anovaVCA(y~(lot+device)/day/run, VCAdata1[VCAdata1$sample==1,]) fitRM1 # there are only 3 lots, take 'lot' as fixed fitMM2 <- fitLMM(y~(lot+(device))/(day)/(run), VCAdata1[VCAdata1$sample==2,]) # use REML on this (balanced) data fitMM2.2 <- fitLMM(y~(lot+(device))/(day)/(run), VCAdata1[VCAdata1$sample==2,], "reml") # the following model definition is equivalent to the one above, # since a single random term in an interaction makes the interaction # random (see the 3rd reference for details on this topic) fitMM3 <- fitLMM(y~(lot+(device))/day/run, VCAdata1[VCAdata1$sample==2,]) # fit same model for each sample using by-processing lst <- fitLMM(y~(lot+(device))/day/run, VCAdata1, by="sample") lst # fit mixed model originally from 'nlme' package library(nlme) data(Orthodont) fit.lme <- lme(distance~Sex*I(age-11), random=~I(age-11)|Subject, Orthodont) # re-organize data Ortho <- Orthodont Ortho$age2 <- Ortho$age - 11 Ortho$Subject <- factor(as.character(Ortho$Subject)) fit.anovaMM1 <- fitLMM(distance~Sex*age2+(Subject)*age2, Ortho) # use simplified formula avoiding unnecessary terms fit.anovaMM2 <- fitLMM(distance~Sex+Sex:age2+(Subject)+(Subject):age2, Ortho) # and exclude intercept fit.anovaMM3 <- fitLMM(distance~Sex+Sex:age2+(Subject)+(Subject):age2-1, Ortho) # compare results fit.lme fit.anovaMM1 fit.anovaMM2 fit.anovaMM3 # are there a sex-specific differences? cmat <- getL(fit.anovaMM3, c("SexMale-SexFemale", "SexMale:age2-SexFemale:age2")) cmat test.fixef(fit.anovaMM3, L=cmat) # fit LMM with fixed lot and device effects and test for lot-differences data(VCAdata1) fitS5 <- fitLMM(y~(lot+device)/(day)/(run), subset(VCAdata1, sample==5), "reml") fitS5 # apply Tukey-HSD test to screen for lot differences library(multcomp) res.tuk <- glht(fitS5, linfct=mcp(lot="Tukey")) summary(res.tuk) # compact letter display res.tuk.cld <- cld(res.tuk, col=paste0("gray", c(90,60,75))) plot(res.tuk.cld) ## End(Not run) ``` ## See Also `fitVCA`, `anovaMM`, `remlMM` ## Author(s) Andre Schuetzenmeister andre.schuetzenmeister@roche.com

fitLMM function