A Note on the Adaptive LASSO for Zero-Inflated Poisson Regression

• Published in: Journal of probability and statistics Vol. 2018; no. 2018; pp. 1 - 9
• Main Authors: Chowdhury, Shrabanti, Mallick, Himel, Garai, Broti, Banerjee, Prithish, Chatterjee, Saptarshi
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2018; Hindawi; John Wiley & Sons, Inc
• Subjects: Economic models; Generalized linear models; Identification methods; Medical research; Parameter estimation; Poisson density functions; Population; Regularization; Regularization methods; Software; Statistical analysis; Statistical methods
• ISSN: 1687-952X; 1687-9538
• DOI: 10.1155/2018/2834183

We consider the problem of modelling count data with excess zeros using Zero-Inflated Poisson (ZIP) regression. Recently, various regularization methods have been developed for variable selection in ZIP models. Among these, EM LASSO is a popular method for simultaneous variable selection and parameter estimation. However, EM LASSO suffers from estimation inefficiency and selection inconsistency. To remedy these problems, we propose a set of EM adaptive LASSO methods using a variety of data-adaptive weights. We show theoretically that the new methods are able to identify the true model consistently, and the resulting estimators can be as efficient as oracle. The methods are further evaluated through extensive synthetic experiments and applied to a German health care demand dataset.