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.

翻译：我们提出了一种用于分析分类响应的统一多项链接模型。该模型不仅将现有的多项逻辑模型及其扩展作为特例涵盖，还包含了能够在数据分析中处理具有NA或未知响应观测值的新模型。我们提供了用于寻找模型参数最大似然估计和计算费希尔信息矩阵的显式公式及详细算法。我们的算法解决了现有统计软件在估计累积链接模型参数时的不可行性问题。实际数据集的应用表明，新模型能够显著提升数据拟合效果，相应的数据分析可以修正因缺失响应而导致的误导性结论。