Fitting Linear Mixed-Effects Models Using lme4
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abstract
Maximum likelihood or restricted maximum likelihood (REML) estimates of
the parameters in linear mixed-effects models can be determined using the
lmer function in the lme4 package for R. As for most model-fitting
functions in R, the model is described in an lmer call by a formula, in
this case including both fixed- and random-effects terms. The formula and
data together determine a numerical representation of the model from which
the profiled deviance or the profiled REML criterion can be evaluated as a
function of some of the model parameters. The appropriate criterion is
optimized, using one of the constrained optimization functions in R, to
provide the parameter estimates. We describe the structure of the model,
the steps in evaluating the profiled deviance or REML criterion, and the
structure of classes or types that represents such a model. Sufficient
detail is included to allow specialization of these structures by users
who wish to write functions to fit specialized linear mixed models, such
as models incorporating pedigrees or smoothing splines, that are not
easily expressible in the formula language used by lmer.
