# formula with offset

data$log.time[data$visit==0] <- log(8)
data$log.time[data$visit!=0] <- log(2)

formula <- y ~ offset(log.time) + as.factor(visit) + as.factor(trt) + as.factor(visit):as.factor(trt) + (1 | subject)

# Poisson random intercept model

fit.glmm.p <- glmer(formula,
              data = data ,
              family = poisson)
summary(fit.glmm.p)
AIC(fit.glmm.p)

# Negative binomial random intercept model

fit.glmm.nb <- (glmer.nb(formula,
                 data = data))

summary(fit.glmm.nb)
AIC(fit.glmm.nb)