Regression Models for Multiple Category Response Data
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The generalization of categorical data from two categories (the binomial random variable) to multiple categories (the multinomial random variable) is a fundamental step in the analysis of contingency tables, allowing (for example) generalization of analysis for 2 × 2 tables to I × J tables. The need for such generalizations carries over to regression analysis as well. In a clinical trial context, for example, investigation of the effectiveness of a treatment might be the goal of the analysis, but the effects of a treatment might have several levels, such as ineffective, moderately effective with side effects, moderately effective without side effects, completely effective with side effects, and completely effective without side effects. This multinomial target variable is obviously different from a binary success/failure target, but the goal remains the same: to develop a model relating predictors to the probability of falling in each of the levels of the target. Depending on the structure of the response variable (nominal or ordinal), different generalizations are possible.
KeywordsMultinomial Logit Model Asbestos Exposure Daily News Proportional Odds Model Baseline Category
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