In high-dimensional longitudinal data with multinomial response, the number of covariates is always much larger than the number of subjects and when modelling such data, variable selection is always an important issue. In this study, we developed the penalized generalized estimating equation for multinomial responses for identifying important variables and estimation of their regression coefficients simultaneously. An iterative algorithm is used to solve the penalized estimating equation by combining the Fisher-scoring algorithm and minorization-maximization algorithm. We used a penalty term to regularize the slope part only because category-specific intercept terms should be included in the multinomial model. We conducted a simulation study to investigate the performance of the proposed method and demonstrated its performance using real dataset.

在具有多项响应的高维纵向数据中，协变量的数量总是远大于受试者的数量，在对此类数据进行建模时，变量选择始终是一个重要问题。在这项研究中，我们开发了多项式响应的惩罚广义估计方程，用于同时识别重要变量和估计其回归系数。结合Fisher-scoring算法和minorization-maximization算法，采用迭代算法求解惩罚估计方程。我们使用惩罚项来正则化斜率部分只是因为特定于类别的截距项应包含在多项式模型中。我们进行了模拟研究以研究所提出方法的性能，并使用真实数据集证明其性能。