Abstract
As in a Poisson generalized linear mixed model (GLMM), one can also add into a binomial generalized linear model (GLM) random variation beyond what is stipulated by the binomial distribution. The chapter examines the relationship between precipitation during the breeding season and reproductive success; wet springs are likely to depress the proportion of successful nests. One can assume that all shrike populations have the same relation- ship between breeding success and standardized spring precipitation, but at different levels, corresponding to a random-intercepts model. This means assuming that every shrike population has a specific response to precipitation but that both intercept and slope are “similar” among populations. As for the Poisson case, the introduction of random effects into a binomial GLM in WinBUGS is particularly straightforward and transparent. Fitting the resulting binomial GLMM in WinBUGS is very helpful for the general understanding of this class of models.
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