The R Book

Use of lmer with Complex Nesting

In this section we have count data (snails) so we want to use family = poisson. But we have complicated spatial pseudoreplication arising from a split-plot design, so we cannot use a GLM. The answer is to use generalized mixed models, lmer. The default method for a generalized linear model fit with lmer has been switched from PQL to the Laplace method. The Laplace method is more reliable than PQL, and is not so much slower to as to preclude its routine use (Doug Bates, personal communication).

The syntax is extended in the usual way to accommodate the random effects (Chapter 19), with slashes showing the nesting of the random effects, and with the factor associated with the largest plot size on the left and the smallest on the right. We revisit the splitplot experiment on biomass (p. 469) and analyse the count data on snails captured from each plot. The model we want to fit is a generalized mixed model with Poisson errors (because the data are counts) with complex nesting to take account of the four-level split-plot design (Rabbit exclusion within Blocks, Lime treatment within Rabbit plots, 3 Competition treatments within each Lime plot and 4 nutrient regimes within each Competition plot):

counts<-read.table("c:\\temp\\splitcounts.txt",header=T)
attach(counts)
names(counts)

[1] "vals"      "Block"      "Rabbit" "Lime"
[5]  "Competition"   "Nutrient"

The syntax within lmer is very straightforward: fixed effects after the tilde ~, then random effects inside ...