Multinomial regression models based on continuation ratios

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Abstract

This paper concerns continuation ratio models for multinomial responses. These are conditional probabilities used in logit models to define the dependence of the multinomial proportions on explanatory variables and unknown parameters. A distinctive feature of these models is that if one models the various continuation ratios separately, then resulting estimates and test statistics are asymptotically independent. This allows the partitioning of likelihood ratio statistics and the search for effects in specific categories of an ordinal response variable. Models that use the same parameters for different continuation ratios are suitable for estimating more global differences. The fitting of these models to actual data is illustrated, including an example from a pharmaceutical study. The results show that different models are suitable for modelling complementary sorts of differences between multinomial response distributions.

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