\HeaderA{glmmPQL}{Fit Generalized Linear Mixed Models via PQL}{glmmPQL}
\keyword{models}{glmmPQL}
\begin{Description}\relax
Fit a GLMM model with multivariate normal random effects, using
Penalized Quasi-Likelihood.
\end{Description}
\begin{Usage}
\begin{verbatim}
glmmPQL(fixed, random, family, data, correlation, weights,
        control, niter = 10, verbose = TRUE, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{fixed}] a two-sided linear formula giving fixed-effects part of the model.

\item[\code{random}] a formula or list of formulae describing the random effects.

\item[\code{family}] a GLM family.

\item[\code{data}] an optional data frame used as the first place to find
variables in the formulae.

\item[\code{correlation}] an optional correlation structure.

\item[\code{weights}] optional case weights as in \code{glm}.

\item[\code{control}] an optional argument to be passed to \code{lme}.

\item[\code{niter}] maximum number of iterations.

\item[\code{verbose}] logical: print out record of iterations?

\item[\code{...}] Further arguments for \code{lme}.

\end{ldescription}
\end{Arguments}
\begin{Details}\relax
\code{glmmPQL} works by repeated calls to \code{\LinkA{lme}{lme}}, so
package \code{nlme} will be loaded at first use if necessary.
\end{Details}
\begin{Value}
A object of class \code{"lme"}: see \code{\LinkA{lmeObject}{lmeObject}}.
\end{Value}
\begin{References}\relax
Schall, R. (1991) Estimation in generalized linear models with
random effects.
\emph{Biometrika}
\bold{78}, 719--727.

Breslow, N. E. and Clayton, D. G. (1993) Approximate inference in
generalized linear mixed models.
\emph{Journal of the American Statistical Association}
\bold{88}, 9--25.

Wolfinger, R. and O'Connell, M. (1993) Generalized linear mixed models: a
pseudo-likelihood approach.
\emph{Journal of Statistical Computation and Simulation}
\bold{48}, 233--243.

Venables, W. N. and Ripley, B. D. (2002)
\emph{Modern Applied Statistics with S.} Fourth edition.  Springer.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{lme}{lme}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
library(nlme) # will be loaded automatically if omitted
summary(glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID,
                family = binomial, data = bacteria))
\end{ExampleCode}
\end{Examples}

