Modeling a categorical variable allowing arbitrarily many category choices

This article discusses the modeling of a categorical variable for which subjects can select any number of categories. For c categories, the response variable consists of a cross-classification of c binary components, one pertaining to each category. Using data from a survey (Loughin, T. M. and Scherer, P. N., 1998, Biometrics, 54, 630-687) in which Kansas farmers indicated their primacy sources of veterinary information, we discuss simultaneous logit modeling of the binary components of the multivariate response. The use of maximum likelihood or quasi-likelihood fitting provides chi-squared tests with degrees of freedom df = c(r - I) for testing the independence between each of the c response components and an explanatory variable with T categories. These tests are alternatives to the weighted chi-squared test and the bootstrap test proposed by Loughin and Scherer for this hypothesis.