Regularization and model selection for quantile varying coefficient model with categorical effect modifiers

A varying coefficient model with categorical effect modifiers is an effective modeling strategy when the data set includes categorical variables. With categorial predictors the number of parameters can become very large. This paper focuses on the model selection problem for varying coefficient model with categorical effect modifiers under the framework of quantile regression. After distinguishing between nominal and ordinal effect modifiers, a unified (adaptive-) Lasso-type regularization technique is proposed that allows for selection of covariates and fusion of categories of categorical effect modifiers, which can identify whether the coefficient functions are really varying with the level of a potentially effect modifying factor and provide a sparse model at different quantile levels. Moreover, the large sample properties are derived under appropriate conditions including a fixed bound on the number of parameters. The proposed methods are illustrated and investigated by extensive simulation studies and two real data evaluations.