R: Fit Generalized Linear Mixed-Effects Models

glmer {lme4}

R Documentation

Fit Generalized Linear Mixed-Effects Models

Description

Fit a generalized linear mixed model (GLMM)

Usage

  glmer(formula, data = NULL, family = gaussian,
    control = glmerControl(), start = NULL, verbose = 0L,
    nAGQ = 1L, subset, weights, na.action, offset,
    contrasts = NULL, mustart, etastart,
    devFunOnly = FALSE, ...)

Arguments

`family`	a GLM family, see `glm` and `family`.
`nAGQ`	integer scalar - the number of points per axis for evaluating the adaptive Gauss-Hermite approximation to the log-likelihood. Defaults to 1, corresponding to the Laplace approximation. Values greater than 1 produce greater accuracy in the evaluation of the log-likelihood at the expense of speed. A value of zero uses a faster but less exact form of parameter estimation for GLMMs by optimizing the random effects and the fixed-effects coefficients in the penalized iteratively reweighted least squares step.
`start`	a named list of starting values for the parameters in the model, or a numeric vector. A numeric `start` argument will be used as the starting value of `theta`. If `start` is a list, the `theta` element (a numeric vector) is used as the starting value for the first optimization step (default=1 for diagonal elements and 0 for off-diagonal elements of the lower Cholesky factor); the fitted value of `theta` from the first step, plus `start[["fixef"]]`, are used as starting values for the second optimization step. If `start` has both `fixef` and `theta` elements, the first optimization step is skipped. For more details or finer control of optimization, see `modular`.
`mustart`	optional starting values on the scale of the conditional mean, as in `glm`; see there for details.
`etastart`	optional starting values on the scale of the unbounded predictor as in `glm`; see there for details.
`...`	other potential arguments. A `method` argument was used in earlier versions of the package. Its functionality has been replaced by the `nAGQ` argument.
`formula`	a two-sided linear formula object describing both the fixed-effects and fixed-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.
`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).
`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.
`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 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.
`na.action`	a function that indicates what should happen when the data contain `NA`s. 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).

Details

Fit a generalized linear mixed model, which incorporates both fixed-effects parameters and random effects in a linear predictor, via maximum likelihood. The linear predictor is related to the conditional mean of the response through the inverse link function defined in the GLM family.

The expression for the likelihood of a mixed-effects model is an integral over the random effects space. For a linear mixed-effects model (LMM), as fit by lmer, this integral can be evaluated exactly. For a GLMM the integral must be approximated. The most reliable approximation for GLMMs with a single grouping factor for the random effects is adaptive Gauss-Hermite quadrature. The nAGQ argument controls the number of nodes in the quadrature formula. A model with a single, scalar random-effects term could reasonably use up to 25 quadrature points per scalar integral.

With vector-valued random effects the complexity of the Gauss-Hermite quadrature formulas increases dramatically with the dimension. For a 3-dimensional vector-valued random effect nAGQ=5 requires 93 evaluations of the GLM deviance per evaluation of the approximate GLMM deviance. For 20-dimensional evaluations of the GLM deviance per evaluation of the approximate GLMM deviance.

The default approximation is the Laplace approximation, corresponding to nAGQ=1.

Value

An object of class glmerMod, for which many methods are available (e.g. methods(class="glmerMod"))

Examples

## generalized linear mixed model
library(lattice)
xyplot(incidence/size ~ period|herd, cbpp, type=c('g','p','l'),
       layout=c(3,5), index.cond = function(x,y)max(y))
(gm1 <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
              data = cbpp, family = binomial))
## using nAGQ=0 only gets close to the optimum
(gm1a <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
               cbpp, binomial, nAGQ = 0))
## using  nAGQ = 9  provides a better evaluation of the deviance
## Currently the internal calculations use the sum of deviance residuals,
## which is not directly comparable with the nAGQ=0 or nAGQ=1 result.
(gm1a <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
               cbpp, binomial, nAGQ = 9))

## GLMM with individual-level variability (accounting for overdispersion)
## For this data set the model is the same as one allowing for a period:herd
## interaction, which the plot indicates could be needed.
cbpp$obs <- 1:nrow(cbpp)
(gm2 <- glmer(cbind(incidence, size - incidence) ~ period +
    (1 | herd) +  (1|obs),
              family = binomial, data = cbpp))
anova(gm1,gm2)

## glmer and glm log-likelihoods are consistent
gm1Devfun <- update(gm1,devFunOnly=TRUE)
gm0 <- glm(cbind(incidence, size - incidence) ~ period,
           family = binomial, data = cbpp)
## evaluate GLMM deviance at RE variance=theta=0, beta=(GLM coeffs)
gm1Dev0 <- gm1Devfun(c(0,coef(gm0)))
## compare
stopifnot(all.equal(gm1Dev0,c(-2*logLik(gm0))))

[Package lme4 version 1.1-5 Index]