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library(lme4)
library(broom)
library(broom.mixed)
library(dotwhisker)

Overview

Most aspects of GLMMs are carried over from LMMs (random effects) and GLMs (families and links).

integration methods

You do have to decide on an approximation method.

In lme4, use the nAGQ= argument; nAGQ=1 (default) corresponds to Laplace approximation

integration rules

Laplace-approximation diagnostics

library(lattice)
aspect <- 0.6
xlab <- "z"; ylab <- "density"; type <- c("g","l"); scaled <- FALSE
mm <- readRDS("../data/toenail_lapldiag.rds")
print(xyplot(y ~ zvals|id, data=mm,
             type=type, aspect=aspect,
             xlab=xlab,ylab=ylab,
             as.table=TRUE,
             panel=function(x,y,...){
    if (!scaled) {
        panel.lines(x, dnorm(x), lty=2)
    } else {
        panel.abline(h=1, lty=2)
    }
    panel.xyplot(x,y,...)
}))

comparing integration methods

g1 <- glmer(incidence/size ~ period + (1|herd),
            family=binomial,
            data=cbpp,
            weights=size)
g2 <- update(g1,nAGQ=5)
g3 <- update(g1,nAGQ=10)
g4 <- MASS:::glmmPQL(incidence/size ~ period,
                     random = ~1|herd,
                     data=cbpp,
                     family=binomial,
                     weights=size)
## iteration 1
## iteration 2
## iteration 3
## iteration 4
dwplot(list(Laplace=g1,AGQ5=g2,AGQ10=g3,glmmPQL=g4))

overdispersion

dealing with overdispersion

other diagnostics

zero-inflation

Complete separation

Brooks, Mollie E., Kasper Kristensen, Koen J. van Benthem, Arni Magnusson, Casper W. Berg, Anders Nielsen, Hans J. Skaug, Martin Maechler, and Benjamin M. Bolker. 2017. “Modeling Zero-Inflated Count Data With glmmTMB.” BioRxiv, May, 132753. doi:10.1101/132753.

Elston, D. A., R. Moss, T. Boulinier, C. Arrowsmith, and X. Lambin. 2001. “Analysis of Aggregation, a Worked Example: Numbers of Ticks on Red Grouse Chicks.” Parasitology 122 (5): 563–69.