Strategies for Modeling a Categorical Variable Allowing Multiple Category Choices

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Abstract
This article discusses strategies for modeling a categorical variable when subjects can select any subset of the categories. With c outcome categories, the models relate to a c-dimensional binary response, with each component indicating whether a particular category is chosen. The strategies are the following: (1) Using logit models directly for the marginal distribution of each component; this accounts for dependence among the component responses but does not treat the dependence as an integral part of the model. (2) Using logit models containing subject random effects to generate the dependence among the components; this approach is limited by implying nonnegative associations having a certain exchangeability. (3) Using loglinear modeling; quasi-symmetric ones are useful but are limited to estimation of within-subject effects. Marginal logit models less fully describe the dependence patterns for the data but require fewer assumptions and focus more directly on the effects of greatest substantive interest.