glmer
From lme4 v1.1-13
by Ben Bolker
Fitting Generalized Linear Mixed-Effects Models
Fit a generalized linear mixed-effects model (GLMM). Both fixed
effects and random effects are specified via the model formula.
- Keywords
- models
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
- 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. - data
- an optional data frame containing the variables named in
formula. By default the variables are taken from the environment from whichlmeris called. Whiledatais optional, the package authors strongly recommend its use, especially when later applying methods such asupdateanddrop1to the fitted model (such methods are not guaranteed to work properly ifdatais omitted). Ifdatais omitted, variables will be taken from the environment offormula(if specified as a formula) or from the parent frame (if specified as a character vector). - family
- a GLM family, see
glmandfamily. - control
- a list (of correct class, resulting from
lmerControl()orglmerControl()respectively) containing control parameters, including the nonlinear optimizer to be used and parameters to be passed through to the nonlinear optimizer, see the*lmerControldocumentation for details. - start
- a named list of starting values for the parameters in the
model, or a numeric vector. A numeric
startargument will be used as the starting value oftheta. Ifstartis a list, thethetaelement (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 ofthetafrom the first step, plusstart[["fixef"]], are used as starting values for the second optimization step. Ifstarthas bothfixefandthetaelements, the first optimization step is skipped. For more details or finer control of optimization, seemodular. - verbose
- integer scalar. If
> 0verbose output is generated during the optimization of the parameter estimates. If> 1verbose output is generated during the individual PIRLS steps. - 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. (See Details.)
- subset
- an optional expression indicating the subset of the rows
of
datathat 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
NULLor a numeric vector. - 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 ofgetOption("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
NULLor a numeric vector of length equal to the number of cases. One or moreoffsetterms can be included in the formula instead or as well, and if more than one is specified their sum is used. Seemodel.offset. - contrasts
- an optional list. See the
contrasts.argofmodel.matrix.default. - 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. - 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).
- …
- other potential arguments. A
methodargument was used in earlier versions of the package. Its functionality has been replaced by thenAGQargument.
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
is adaptive Gauss-Hermite quadrature,
at present implemented only for models with
a single scalar random effect. 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.
Value
An object of class merMod (more specifically,
an object of subclass glmerMod) for which many
methods are available (e.g. methods(class="merMod"))
See Also
lmer (for details on formulas and
parameterization); glm for Generalized Linear
Models (without random effects).
nlmer for nonlinear mixed-effects models. glmer.nb to fit negative binomial GLMMs.
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))))
## the toenail oncholysis data from Backer et al 1998
## these data are notoriously difficult to fit
## Not run: ------------------------------------
# if (require("HSAUR2")) {
# gm2 <- glmer(outcome~treatment*visit+(1|patientID),
# data=toenail,
# family=binomial,nAGQ=20)
# }
## ---------------------------------------------
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