Loglinear analysis is most useful when we have two or more categorical response variables. Loglinear analysis, however, requires categorical predictor variables, such that the data can be represented in a contingency table. Researchers often have a mix of categorical and numerical predictors. We present a new statistical methodology for the analysis of multiple categorical response variables with a mix of numeric and categorical predictor variables. Therefore, the stereotype model, a reduced rank regression model for multinomial outcome variables, is extended with a design matrix for the profile scores and one for the dependencies among the responses. An MM algorithm is presented for estimation of the model parameters. Three examples are presented. The first shows that our method is equivalent to loglinear analysis when we only have categorical variables. With the second example, we show the differences between marginal logit models and our extended stereotype model, which is a conditional model. The third example is more extensive, and shows how to analyze a data set, how to select a model, and how to interpret the final model.

翻译：对数线性分析在处理两个或多个分类响应变量时最为有效。然而，对数线性分析要求预测变量为分类变量，以便数据能够以列联表形式呈现。研究者通常面临分类预测变量与数值预测变量的混合情况。我们提出了一种新的统计方法，用于分析涉及数值与分类预测变量混合的多个分类响应变量。为此，我们将刻板印象模型（一种针对多项结果变量的降秩回归模型）进行扩展，为其引入设计矩阵，分别处理轮廓得分及响应变量间的依赖关系。我们提出了一种MM算法用于模型参数估计。通过三个实例进行验证：第一个实例表明，当仅使用分类变量时，我们的方法等价于对数线性分析；第二个实例展示了边际对数模型与我们提出的条件型扩展刻板印象模型之间的差异；第三个实例更为复杂，展示了数据分析、模型选择及最终模型解释的完整流程。