Intra-class Correlation in Random-effects Models for Binary Data

We review the concept of intra-class correlation in random-effects models for binary outcomes as estimated by Stata's xtprobit, xtlogit, and xtclog. We consider the usual measures of correlation based on a latent variable formulation of these models and note corrections to the last two procedures. We also discuss alternative measures of association based on manifest variables or actual outcomes and introduce a new command xtrho for computing these measures for all three types of models.