Modeling Longitudinal Count Data

To test for group differences in growth trajectories in mixed (fixed and random effects) models, researchers frequently interpret the coefficient of Group-by-Time product terms. While this practice is straightforward in linear mixed models, it is less so in generalized linear mixed models. Using both an empirical example and synthetic data, we show that the coefficient of Group-by-Time product terms in a specific class of mixed models—mixed Poisson models for count outcome variables—estimates the group difference in slope as the multiplicative change with respect to the baseline rates, not differences in the predicted rate of change between groups. The latter can be obtained from computing the marginal effect for the expected response with respect to time by group following model estimation. We propose and illustrate the use of marginal effects to test and interpret group differences in rate of change over time following estimation with mixed Poisson regression models.