Summary: The dependence of multiple interrelated responses on a set of covariates can be efficiently and parsimoniously modeled using reduced-rank methods. Two forms of reduced-rank models are possible depending on assumptions about response error correlations. When the response outcomes are binary, a minimum distance estimator based on first-stage marginal probit regressions can be used to estimate the reduced-rank models. The alternative models and the estimation procedure are illustrated using a data set on the dietary fats and cholesterol knowledge of a sample of U.S. household meal planners.