Multinomial Link Models

We propose a new family of regression models for analyzing categorical responses, called multinomial link models. It consists of four classes, namely, 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, dichotomous conditional link models that handle longitudinal binary responses, and po-npo mixture models that are more flexible than partial proportional odds models. By characterizing the feasible parameter space, deriving necessary and sufficient conditions, and developing validated algorithms to guarantee the finding of feasible maximum likelihood estimates, we solve the infeasibility issue of existing statistical software when estimating parameters for cumulative link models. We also provide explicit formulae and detailed algorithms for computing the Fisher information matrix and selecting the best models among the new family. 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 statistical inference.