Multiple Inflation Negative Binomial Model with L1 Regularization

• Activity Number: 186
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Arvind Tripathi*+ and Kui Zhang and Xiaogang Su
• Companies: University of Alabama at Birmingham and University of Alabama at Birmingham and University of Texas at El Paso
• Keywords: Count data ; Negative binomial distribution ; Multiple inflation ; L1 regularization

Abstract

In modeling count data, often times, difficulties arise when the outcome variable is not only dispersed but also has more than one inflated counts. Analogous to the Multiple-Inflation Poisson model (Su et al., 2013 Statistica Sinica), we propose a multiple inflation negative binomial (MINB) regression model by using mixture of a cumulative logit model and negative binomial model, whereas the mixing probabilities are formulated with a logistic regression. An EM algorithm is developed to obtain maximum-likelihood estimates. Moreover, the L1 regularization, yet with important modifications, is adapted to aid in the variable selection issues with the MINB model. Both simulation and real data examples will be used to assess the performance of the proposed model and compare it with the other available competitive count models.