Abstract
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.
Highlights
Modern research studies routinely collect information on a broad array of outcomes including count measurements with excess amount of zeros
We propose a set of Expectation Maximization (EM) adaptive LASSO methods using a variety of data-adaptive weights
Tang et al [6] showed that the EM adaptive LASSO (i.e., AMAZonn - EM AL) enjoys the so-called oracle properties, i.e., the estimator is able to identify the true model consistently, and the resulting estimator is as efficient as oracle
Summary
JP Morgan Chase & Co., USA NBCUniversal, USA Department of Biostatistics, Harvard T.H. Chan School of Public Health, USA Program in Medical and Population Genetics, Broad Institute of MIT and Harvard, USA Department of Genetics and Genomic Sciences, Icahn School of Medicine at Mount Sinai, USA Eli Lilly and Company, USA. 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. The methods are further evaluated through extensive synthetic experiments and applied to a German health care demand dataset
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