Variable selection for varying coefficient models with the sparse regularization

Varying-coefficient models are useful tools for analyzing longitudinal data. They can effectively describe a relationship between predictors and responses repeatedly measured. We consider the problem of selecting variables in the varying-coefficient models via the adaptive elastic net regularization. Coefficients given as functions are expressed by basis expansions, and then parameters involved in the model are estimated by the penalized likelihood method using the coordinate descent algorithm derived for solving the problem of sparse regularization. We examine the effectiveness of our modeling procedure through Monte Carlo simulations and real data analysis.