# Fit Linear Mixed Models via REML.

### Description

Function fits Linear Mixed Models (LMM) using Restricted Maximum Likelihood (REML).

### Usage

1 |

### 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 warning, which will be issued otherwise |

### 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=σ^2/se(σ^2)*, and *σ^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).

### Author(s)

Andre Schuetzenmeister andre.schuetzenmeister@roche.com

### See Also

`remlVCA`

, `VCAinference`

, `ranef.VCA`

, `residuals.VCA`

,
`anovaVCA`

, `anovaMM`

, `plotRandVar`

, `test.fixef`

,
`test.lsmeans`

, `lmer`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 | ```
## 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+Sex:age2+(Subject)+(Subject):age2, 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)
``` |