# Fit Linear Mixed Models via REML Function fits Linear Mixed Models (LMM) using Restricted Maximum Likelihood (REML). ```r remlMM( form, Data, by = NULL, VarVC = TRUE, cov = TRUE, quiet = FALSE, order.data = TRUE ) ``` ## Arguments - `form`: (formula) specifying the model to be fit, a response variable left of the '~' is mandatory, random terms have to be enclosed in brackets (see details for definition of valid model terms) - `Data`: (data.frame) containing all variables referenced in 'form' - `by`: (factor, character) variable specifying groups for which the analysis should be performed individually, i.e. by-processing - `VarVC`: (logical) TRUE = the variance-covariance matrix of variance components will be approximated using the method found in Giesbrecht & Burns (1985), which also serves as basis for applying a Satterthwaite approximation of the degrees of freedom for each variance component, FALSE = leaves out this step, no confidence intervals for VC will be available - `cov`: (logical) TRUE = in case of non-zero covariances a block diagonal matrix will be constructed, FALSE = a diagonal matrix with all off-diagonal element being equal to zero will be contructed - `quiet`: (logical) TRUE = will suppress any messages or warning, which will be issued otherwise - `order.data`: (logical) TRUE = class-variables will be ordered increasingly, FALSE = ordering of class-variables will remain as is ## Details The model is formulated exactly as in function `anovaMM`, i.e. random terms need be enclosed by round brackets. All terms appearing in the model (fixed or random) need to be compliant with the regular expression "^[^[\.]]?[[:alnum:]_\.]*$", i.e. they may not start with a dot and may then only consist of alpha-numeric characters, dot and underscore. Otherwise, an error will be issued. Here, a LMM is fitted by REML using the `lmer` function of the `lme4`-package. For all models the Giesbrechnt & Burns (1985) approximation of the variance-covariance matrix of variance components (VC) can be applied ('VarVC=TRUE'). A Satterthwaite approximation of the degrees of freedom for all VC and total variance is based on this approximated matrix using $df=2Z^2$, where $Z$ is the Wald statistic $Z=\sigma^2/se(\sigma^2)$, and $\sigma^2$ is here used for an estimated variance. The variance of total variability, i.e. the sum of all VC is computed via summing up all elements of the variance-covariance matrix of the VC. One can constrain the variance-covariance matrix of random effects $G$ to be either diagonal ('cov=FALSE'), i.e. all random effects are indpendent of each other (covariance is 0). If 'cov=TRUE' (the default) matrix $G$ will be constructed as implied by the model returned by function `lmer`. As for objects returned by function `anovaMM` linear hypotheses of fixed effects or LS Means can be tested with functions `test.fixef` and `test.lsmeans`. Note, that option "contain" does not work for LMM fitted via REML. Note, that for large datasets approximating the variance-covariance matrix of VC is computationally expensive and may take very long. There is no Fisher-information matrix available for 'merMod' objects, which can serve as approximation. To avoid this time-consuming step, use argument 'VarVC=FALSE' but remember, that no confidence intervals for any VC will be available. If you use Microsoft's R Open, formerly known as Revolution-R, which comes with Intel's Math Kernel Library (MKL), this will be automatically detected and an environment-optimized version will be used, reducing the computational time considerably (see examples). ## Examples ```r ## Not run: data(dataEP05A2_2) # assuming 'day' as fixed, 'run' as random remlMM(y~day/(run), dataEP05A2_2) # assuming both as random leads to same results as # calling anovaVCA remlMM(y~(day)/(run), dataEP05A2_2) anovaVCA(y~day/run, dataEP05A2_2) remlVCA(y~day/run, dataEP05A2_2) # fit a larger random model data(VCAdata1) fitMM1 <- remlMM(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 <- remlMM(y~(lot+(device))/(day)/(run), VCAdata1[VCAdata1$sample==2,]) # the following model definition is equivalent to the one above, # since a single random term in an interaction makes the interaction # random (see the 3rd reference for details on this topic) fitMM3 <- remlMM(y~(lot+(device))/day/run, VCAdata1[VCAdata1$sample==2,]) # fit same model for each sample using by-processing lst <- remlMM(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 for using 'remlMM' Ortho <- Orthodont Ortho$age2 <- Ortho$age - 11 Ortho$Subject <- factor(as.character(Ortho$Subject)) fit.remlMM1 <- remlMM(distance~Sex*age2+(Subject)*age2, Ortho) # use simplified formula avoiding unnecessary terms fit.remlMM2 <- remlMM(distance~Sex+age2+Sex:age2+(Subject)+age2:(Subject), Ortho) # and exclude intercept fit.remlMM3 <- remlMM(distance~Sex+Sex:age2+(Subject)+(Subject):age2-1, Ortho) # now use exclude covariance of per-subject intercept and slope # as for models fitted by function 'anovaMM' fit.remlMM4 <- remlMM(distance~Sex+Sex:age2+(Subject)+(Subject):age2-1, Ortho, cov=FALSE) # compare results fit.lme fit.remlMM1 fit.remlMM2 fit.remlMM3 fit.remlMM4 # are there a sex-specific differences? cmat <- getL(fit.remlMM3, c("SexMale-SexFemale", "SexMale:age2-SexFemale:age2")) cmat test.fixef(fit.remlMM3, L=cmat) ## End(Not run) ``` ## See Also `remlVCA`, `VCAinference`, `ranef.VCA`, `residuals.VCA`, `anovaVCA`, `anovaMM`, `plotRandVar`, `test.fixef`, `test.lsmeans`, `lmer` ## Author(s) Andre Schuetzenmeister andre.schuetzenmeister@roche.com

remlMM function