```
## 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
if (FALSE) {
if (require("HSAUR3")) {
gm2 <- glmer(outcome~treatment*visit+(1|patientID),
data=toenail,
family=binomial,nAGQ=20)
}
}
```

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