Multinomial Link Models

We propose a new class of regression models for analyzing categorical responses, called multinomial link models. It consists of four subclasses, including mixed-link models that generalize existing multinomial logistic models and their extensions, two-group models that can incorporate the observations with NA or unknown responses, multinomial conditional link models that handle longitudinal categorical responses, and po-npo mixture models that extend partial proportional odds models. We provide explicit formulae and detailed algorithms for finding the maximum likelihood estimates of the model parameters and computing the Fisher information matrix. Our algorithms solve the infeasibility issue of existing statistical software when estimating parameters of cumulative link models. The applications to real datasets show that the new models can fit the data significantly better, correct misleading conclusions due to missing responses, and make more informative inference.