Penalized generalized estimating equations approach to longitudinal data with multinomial responses

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.