Parsimony and complexity in mixed models for longitudinal data

Model selection is an especially important problem for repeated measures data. Efficient estimation of fixed effects requires a reasonable but parsimonious model for the correlation structure. A standard approach is to fit a full model for the fixed effects, use some model selection criterion to choose a correlation model, then refine the fixed effects model conditional on that correlation model. This approach assumes that it is possible to fit large models. My talk explores model selection when large models can not be fit to the data. The motivating example is the estimation of seed burial rates, which are important quantities in the demography of agricultural weeds. The data are repeated counts of seed-like beads on the soil surface. The burial rate is estimated using generalized linear mixed models for count data. Large models can not be fit because the iterative maximization algorithm fails to converge. A reasonable model is chosen using a combination of biological considerations, two-stage estimation of variance components, and information criteria.