A Multicollinearity-Adjusted Adaptive LASSO for Zero-Infated Count Regression

• Activity Number: 395 - Recent Advances in Zero-Inflated Regression Models
• Type: Topic Contributed
• Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Prithish Banerjee* and Broti Garai and Shrabanti Chowdhury and Himel Mallick
• Companies: Wayne State University School of Medicine and West Virginia University and Wayne State University and Harvard University
• Keywords: Zero-Inflated Poisson ; Zero-Inflated Negative Binomial ; LASSO ; Adaptive LASSO ; EM Algorithm ; Variable Selection

Abstract

Recently, various regularization methods have been extensively developed for variable selection in zero-inflated count models. Among these, the EM Adaptive LASSO is a variable selection method for zero-inflated count outcomes, which is shown to be both consistent in variable selection and asymptotically normal in coefficient estimation. However, actual variable selection performance of the EM Adaptive LASSO depends on the adaptive choice of the weight vector in the penalty function. Here we show that the data-adaptive weight calculation using the MLE estimate can result in very poor performance when multicollinearity of the design matrix is a concern. To achieve better variable selection results, we take into account the standard errors of the MLE estimate for weight construction, and propose a new variable selection method for the zero-inflated Poisson and zero-inflated negative binomial regression models. The method is evaluated through extensive numerical experiments with comparisons to the EM Adaptive LASSO method, and is applied to a health care dataset, which reveal favorable finite-sample performance while maintaining the theoretical properties of the EM Adaptive LASSO.