关键词: 零膨胀泊松模型, 变量选择, 联合建模

Abstract: Zero-inflated count data damage the mean-variance relation in Poisson distribution, which can be explained by the mixture distribution composed pro rata of data subject to Poisson distribution and zero-valued observations (degradation distribution). This paper studies the joint modeling and variable selection from zero-inflated count data based on the adaptive elastic-net technique. As to the zero-inflated Poisson distribution, some latent variables are induced into constructing a complete likelihood of the regression model, consisted of two components (zero-inflated and Poisson). Taking the possible collinearity and sparsity of covariates into account, the objective function is obtained by adding the adaptive elastic-net penalty to the likelihood function. Then the sparse estimator of the regression coefficient is achieved by using the EM algorithm to optimize the objective function. The Bayesian information criterion (BIC) is employed to determine the optimal tuning parameter. This paper also presents the performance of the proposed estimator with large sample properties through a theoretical demonstration and simulation study, and then applied to the practical issues with the real data.

Key words: Zero-inflated Poisson Model, Variable Selection, Joint Modeling