A model selection method based on the adaptive LASSO-penalized GEE and weighted Gaussian pseudo-likelihood BIC in longitudinal robust analysis

In this article, a new robust variable selection approach is introduced by combining the robust generalized estimating equations and adaptive LASSO penalty function for longitudinal generalized linear models. Then, an efficient weighted Gaussian pseudo-likelihood version of the BIC (WGBIC) is proposed to choose the tuning parameter in the process of robust variable selection and to select the best working correlation structure simultaneously. Meanwhile, the oracle properties of the proposed robust variable selection method are established and an efficient algorithm combining the iterative weighted least squares and minorization–maximization is proposed to implement robust variable selection and parameter estimation.