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.