Variable selection and prediction performance of penalized two-part regression with community-based crime data application

Seong-Tae Kim

Abstract:

Semicontinuous data are characterized by a mixture of a point probability mass at zero and a continuous distribution of positive values. This type of data is often modeled using a two-part model where the first part models the probability of dichotomous outcomes -zero or positive- and the second part models the distribution of positive values. Despite the two-part model’s popularity, variable selection in this model has not been fully addressed, especially, in high dimensional data. The objective of this study is to investigate variable selection and prediction performance of penalized regression methods in two-part models. The performance of the selected
techniques in the two-part model is evaluated via simulation studies. Our findings show that LASSO and ENET tend to select more predictors in the model than SCAD and MCP. Consequently, MCP and SCAD outperform LASSO and ENET for specificity, and LASSO and ENET perform better than MCP and SCAD with respect to the mean squared error. We find similar results when applying the penalized regression methods to the prediction of crime incidents using community-based data.