Feature screening for generalized varying coefficient models with application to dichotomous responses

Generalized varying coefficient model (GVCM) is an important extension of generalized linear model and varying coefficient model. It has been widely applied in many areas. This paper mainly considers the variable screening problem with dichotomous response data under GVCM, where a spline approximation is employed to estimate the coefficient function for each covariate. Two screening procedures based on marginal maximum likelihood estimation and marginal likelihood ratio statistics are studied. The sure independence screening property and the ranking consistency of these two approaches are established under some technical conditions. Some refined algorithms are presented to control the false selection rate. Extensive numerical studies are conducted to evaluate the performance of the proposed methodology.