Generalized linear mixed models and modified AIC

The paper by Austin et al. refers repeatedly to generalized linear mixed models, or GLMMs. Example. Suppose we are doing a simple observational study. We observe some species of animal. N animals are selected at random and tracked. They may be observed visually, or by some sort of attached sensor. The position is recorded at short regular intervals. Say, once a minute. The variable of interest (Y ) is the number of times an individual moves between observations in a set period of time. The period could be an hour or a day. It should be much longer than the interval of observation. For predictors, we will use mean temperature (t) and mean nearness to food resources (n) over a period. For simplicity, we will assume that n is numerical. We can assume that each animal reacts to external conditions in its own way. So the individual animal is also a predictor. This predictor would have number of levels equal to the number of animals observed. Y is a count. we’ll assume Y has a Poisson distribution: P (Y = n) = e−η η n! , n = 0, 1, . . .