In this paper, we propose the generalized mixed reduced rank regression method, GMR$^3$ for short. GMR$^3$ is a regression method for a mix of numeric, binary and ordinal response variables. The predictor variables can be a mix of binary, nominal, ordinal, and numeric variables. For dealing with the categorical predictors we use optimal scaling. A majorization-minimization algorithm is derived for maximum likelihood estimation under a local independence assumption. We discuss in detail model selection for the dimensionality or rank, and the selection of predictor variables. We show an application of GMR$^3$ using the Eurobarometer Surveys data set of 2023.

翻译：本文提出了一种广义混合降秩回归方法，简称GMR$^3$。GMR$^3$是一种适用于数值型、二值型及有序响应变量混合的回归方法。预测变量可为二值型、名义型、有序型及数值型变量的混合。为处理分类预测变量，我们采用最优标度方法。在局部独立性假设下，我们推导出用于最大似然估计的优化-最小化算法。我们详细讨论了维度（或秩）的模型选择以及预测变量的选择问题。通过使用2023年欧洲晴雨表调查数据集，我们展示了GMR$^3$的实际应用。