We propose a unified multinomial link model for analyzing categorical responses. It not only covers the existing multinomial logistic models and their extensions as a special class, but also allows the observations with NA or Unknown responses to be incorporated as a special category in the data analysis. We provide explicit formulae for computing the likelihood gradient and Fisher information matrix, as well as detailed algorithms for finding the maximum likelihood estimates of the model parameters. 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 proposed multinomial link models can fit the data significantly better, and the corresponding data analysis may correct the misleading conclusions due to missing data.

翻译：我们提出了一种用于分析分类响应的统一多项式链接模型。该模型不仅将现有的多项式逻辑模型及其扩展作为特例涵盖在内，还允许将带有NA或未知响应的观测数据作为特殊类别纳入数据分析中。我们提供了计算似然梯度与费希尔信息矩阵的显式公式，以及寻找模型参数极大似然估计的详细算法。所提出的算法解决了现有统计软件在估计累积链接模型参数时存在的不可行性问题。实际数据应用表明，所提出的多项式链接模型能显著更好地拟合数据，其对应的数据分析可能纠正因数据缺失导致的误导性结论。