Fit a generalized linear mixed-effects model (GLMM). Both fixed
effects and random effects are specified via the model formula.
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)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.
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).
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.
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.
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.
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.)
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.
an optional vector of ‘prior weights’ to be used
in the fitting process. Should be NULL or a numeric
vector.
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.
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.
an optional list. See the contrasts.arg of
model.matrix.default.
optional starting values on the scale of the
conditional mean, as in glm; see there for
details.
optional starting values on the scale of the unbounded
predictor as in glm; see there for details.
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).
An object of class merMod (more specifically,
an object of subclass glmerMod) for which many
methods are available (e.g. methods(class="merMod"))
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.
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.
# NOT RUN {
## 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.
## 'verbose = 1' monitors iteratin a bit; (verbose = 2 does more):
(gm1a <- glmer(cbind(incidence, size - incidence) ~ period + (1 | herd),
cbpp, binomial, verbose = 1, 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("HSAUR3")) {
gm2 <- glmer(outcome~treatment*visit+(1|patientID),
data=toenail,
family=binomial,nAGQ=20)
}
# }
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