Variable selection for additive models with missing data via multiple imputation

We present a method for variable selection for additive models under the condition that the predictors have missing values. The multiple imputation is used for missing data completion, and then the sparse estimation is applied to the additive model for variable selection. Multiple imputation random lasso (MIRL) is a method that combines multiple imputation and aggregation of the sparse estimators of the bootstrap samples, which is applicable to both low- and high-dimensional linear regression problems for data with missing values in predictors. In this work, we extend the MIRL so that it can appropriately select variables in the additive model. The nonlinear structure of the additive model is expressed by basis expansions, and their coefficients are estimated via the group lasso regularization. We call the proposed method multiple imputation random group lasso (MIRGL). We numerically verify the effectiveness of the proposed method through the analysis of simulation and real data.