Two-part quantile regression analysis with variable selection for complex data and its application

Semi-continuous data, also known as zero-inflated non-negative continuous data, are commonly observed in various fields such as biomedicine, environmental science, and ecology. Such data exhibit a combination of zero values and positive continuous values that are right-skewed and heteroscedastic. In this study, we present a novel approach for analyzing complex semi-continuous data using a two-part quantile regression method. In addition, we investigate variable selection techniques using least absolute shrinkage and selection operator, smoothly clipped absolute deviation, and minimax concave penalty methods within the framework of two-part quantile regression. Simulation studies are then conducted to evaluate the effectiveness of the proposed methods. Finally, we apply these methods to examine the determinants of health care spending decisions in American households.