A random-effects probit model is developed for the case in which the outcome of interest is a series of correlated binary responses. These responses can be obtained as the product of a longitudinal response process where an individual is repeatedly classified on a binary outcome variable (e.g., sick or well on occasion t), or in “multilevel” or “clustered” problems in which individuals within groups (e.g., firms, classes, families, or clinics) are considered to share characteristics that produce similar responses. Both examples produce potentially correlated binary responses and modeling these person- or cluster-specific effects is required. The general model permits analysis at both the level of the individual and cluster and at the level at which experimental manipulations are applied (e.g., treatment group). The model provides maximum likelihood estimates for time-varying and time-invariant covariates in the longitudinal case and covariates which vary at the level of the individual and at the cluster level for multilevel problems. A similar number of individuals within clusters or number of measurement occasions within individuals is not required. Empirical Bayesian estimates of person-specific trends or cluster-specific effects are provided. Models are illustrated with data from mental health research.

There has been considerable interest in random-effects models for longitudinal and hierarchical, clustered, or multilevel data in the statistical literatures for biology (Jennrich & Schluchter, 1986; Laird & Ware, 1982; Ware, 1985; Waternaux, Laird, & Ware, 1989; Hedeker & Gibbons, 1994), education (Bock, 1989; Goldstein, 1987), psychology (Bryk & Raudenbush, 1987; Willett, Ayoub, & Robinson, 1991), biomedicine (Gibbons, Hedeker, Waternaux, & Davis, 1988; Hedeker, Gibbons, Waternaux, & Davis, 1989; Gibbons et al., 1993), and actuarial and risk assessment (Gibbons, Hedeker, Charles, & Frisch, in press). Much of the work cited here has been focused on continuous and...