Analyzing count variables in individuals and groups: Single level and multilevel models

Abstract

We address two challenges in data analysis of group research. First, data may be clustered (i.e., responses of individual group members are correlated). Second, some dependent variables may consist of integer counts of number of occurrences of an event. Familiar ANOVA and regression models provide nonoptimal analyses in both cases. Standard multilevel (mixed) models yield accurate inference for clustered normally distributed data. Generalized linear models (GLMs), specifically Poisson regression and related models, yield accurate inference for nonclustered count data. New generalized linear mixed models (GLMMs) integrate GLMs with multilevel models, addressing both challenges and yielding accurate inferences for grouped count outcomes. To provide the necessary background for understanding GLMMs, we first introduce GLMs, with detailed coverage in an example of Poisson regression. We then introduce multilevel models. Finally, we develop GLMMs and illustrate in an example their application to clustered count data. Group research may benefit from the flexibility provided by GLMMs.