Interpreting parameters in the logistic regression model with random effects

Logistic regression with random effects is used to study the relationship b etween explanatory variables and a binary outcome in cases with nonindepend ent outcomes. In this paper, we examine in detail the interpretation of bot h fixed effects and random effects parameters. As heterogeneity measures, t he random effects parameters included in the model are not easily interpret ed. 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 o f well-known odds ratios, that greatly facilitates communication between th e data analyst and the subject-matter researcher. Three examples from diffe rent subject areas, mainly taken from our own experience, serve to motivate and illustrate different aspects of parameter interpretation in these mode ls.