  We propose a unified multinomial link model for analyzing categorical
responses. It not only covers the existing multinomial logistic models and
their extensions as special cases, but also includes new models that can
incorporate the observations with NA or Unknown responses in the data analysis.
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 on estimating parameters of cumulative link models. The
applications to real datasets show that the new models can fit the data
significantly better, and the corresponding data analysis may correct the
misleading conclusions due to missing responses.
