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, 630 637) in which Kansas farmers indicated their primary 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 - 1) for testing the independence between each of the c response components and an explanatory variable with r categories. These tests are alternatives to the weighted chi-squared test and the bootstrap test proposed by Loughin and Scherer for this hypothesis.