Variable selection and structure identification for additive models with longitudinal data

This paper proposes a polynomial structure identification (PSI) method for variable selection and model structure identification of additive models with longitudinal data. First, the backfitting algorithm and zero-order local polynomial smoothing method are used to select important variables in the additive model, and the importance of variables is determined through the inverse of the bandwidth parameter in the nonparametric partial kernel function. Second, the backfitting algorithm and Q-order local polynomial smoothing method are utilized to identify the specific structure of each selected predictor. To incorporate correlations within longitudinal data, a two-stage estimation method is proposed for estimating the regression parameters of the identified important variables: (i) Parameter estimators of the important variables are firstly obtained under an independence working model assumption; (ii) Generalized estimating equations with a working correlation matrix based on B-splines are constructed to obtain the final estimators of the parameters, which improve the efficiency of parameter estimation. Finally, simulation studies are carried out to evaluate the performance of the proposed method, followed by the presentation of two real-world examples for illustration.