Fit Linear Mixed-Effects Models

This function overloads lmer from the lme4-package (lme4::lmer) and adds a couple of slots needed for the computation of Satterthwaite denominator degrees of freedom. All arguments are the same as for lme4::lmer and all the usual lmer-methods work.

Usage

lmer(
  formula,
  data = NULL,
  REML = TRUE,
  control = lmerControl(),
  start = NULL,
  verbose = 0L,
  subset,
  weights,
  na.action,
  offset,
  contrasts = NULL,
  devFunOnly = FALSE
)

Arguments

formula

a two-sided linear formula object describing both the fixed-effects and random-effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars (|) separating expressions for design matrices from grouping factors. By default, non-scalar random effects (where the design matrix has more than one column, e.g. (1+x|f)) are fitted with unstructured (general positive semidefinite) covariance matrices.

Two vertical bars (||) can be used to specify multiple uncorrelated random effects for the same grouping variable. With default settings, the ||-syntax works only for design matrices containing numeric (continuous) predictors; to fit models with independent categorical effects, use diag(f|g) or set options(lme4.doublevert.default = "diag_special") (see help(getDoublevertDefault) in lme4 version 2.0-0 or higher).
Tags preceding a random effect term specify covariance structure:
- us (default: us(f|g) is equivalent to (f|g)): unstructured, positive semi-definite
- diag: diagonal (all correlations set to zero). Specify diag(f|g, hom = TRUE) to fit a homogeneous diagonal covariance matrix
- cs: compound symmetric (all pairwise correlations set identical). Specify cs(f|g, hom = TRUE) for homogeneous variances.
- ar1: autoregressive order 1. Note that AR1 models are homogeneous by default; specify ar1(f|g, hom = FALSE) for heterogeneous variances.

data

an optional data frame containing the variables named in formula. By default the variables are taken from the environment from which lmer is called. While data is optional, the package authors strongly recommend its use, especially when later applying methods such as update and drop1 to the fitted model (such methods are not guaranteed to work properly if data is omitted). If data is omitted, variables will be taken from the environment of formula (if specified as a formula) or from the parent frame (if specified as a character vector).

REML

logical scalar - Should the estimates be chosen to optimize the REML criterion (as opposed to the log-likelihood)?

control

a list (of correct class, resulting from lmerControl() or glmerControl() respectively) containing control parameters, including the nonlinear optimizer to be used and parameters to be passed through to the nonlinear optimizer, see the *lmerControl documentation for details.

start

a numeric vector or a named list with one optional component named par or theta, giving starting values for covariance parameters. Numeric start is equivalent to list(par = start). Parameters corresponding to unstructured covariance matrices are on the scale of the Cholesky factor of the relative covariance matrix. By default, all relative covariance matrices are identity matrices.

verbose

integer scalar. If > 0 verbose output is generated during the optimization of the parameter estimates. If > 1 verbose output is generated during the individual penalized iteratively reweighted least squares (PIRLS) steps.

subset

an optional expression indicating the subset of the rows of data that should be used in the fit. This can be a logical vector, or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default.

weights

an optional vector of ‘prior weights’ to be used in the fitting process. Should be NULL or a numeric vector. Prior weights are not normalized or standardized in any way. In particular, the diagonal of the residual covariance matrix is the squared residual standard deviation parameter sigma times the vector of inverse weights. Therefore, if the weights have relatively large magnitudes, then in order to compensate, the sigma parameter will also need to have a relatively large magnitude.

na.action

a function that indicates what should happen when the data contain NAs. The default action (na.omit, inherited from the 'factory fresh' value of getOption("na.action")) strips any observations with any missing values in any variables.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. One or more offset terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See model.offset.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

devFunOnly

logical - return only the deviance evaluation function. Note that because the deviance function operates on variables stored in its environment, it may not return exactly the same values on subsequent calls (but the results should always be within machine tolerance).

Value

an S4 object of class "lmerModLmerTest"

Details

For details about lmer see lmer (help(lme4::lmer)). The description of all arguments below is taken verbatim and unedited from the lme4-package.

In cases when a valid lmer-object (lmerMod) is produced, but when the computations needed for Satterthwaite df fails, the lmerMod object is returned - not an lmerModLmerTest object.

Author

Rune Haubo B. Christensen and Alexandra Kuznetsova for the overload in lmerTest – lme4-authors for the underlying implementation in lme4.

Examples


data("sleepstudy", package="lme4")
m <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
class(m) # lmerModLmerTest
#> [1] "lmerModLmerTest"
#> attr(,"package")
#> [1] "lmerTest"