A note on comparing the estimates of models for cluster-correlated or longitudinal data with binary or ordinal outcomes

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for binary or ordered-categorical outcomes, however, comparisons between such models are impeded by the implicit rescaling of the model estimates that takes place with the inclusion of new predictors and/or random effects. This paper presents an approach for putting the estimates on a common scale to facilitate relative comparisons between models fit to binary or ordinal outcomes. The approach is developed for both population-average and unit-specific models. Key words: categorical data, mixed model, multilevel model, ordinal, binary. Clustered and longitudinal data are quite common in psychology, social science, and health research. A common feature of both data structures is dependence among the observations within units. Two general approaches for modeling dependent data are to fit a population-average model that permits the model residuals to correlate within units, for instance, using Generalized Esti-mating Equations (GEE) (Liang & Zeger, 1986), or to fit a unit-specific model with random effects, as in the Generalized Linear Mixed Model (GLMM) (McCulloch & Searle, 2001). Thes