Interpreting parameters in the logistic regression model with random effects

Logistic regression with random effects is used to study the relationship between explanatory variables and a binary outcome in cases with nonindependent outcomes. In this paper, we examine in detail the interpretation of both fixed effects and random effects parameters. As heterogeneity measures, the random effects parameters included in the model are not easily interpreted. We discuss different alternative measures of heterogeneity and suggest using a median odds ratio measure that is a function of the original random effects parameters. The measure allows a simple interpretation, in terms of well-known odds ratios, that greatly facilitates communication between the data analyst and the subject-matter researcher. Three examples from different subject areas, mainly taken from our own experience, serve to motivate and illustrate different aspects of parameter interpretation in these models.