Analysis of Zero-Inflated Count Time Series: A Partial Likelihood Approach

• Activity Number: 421
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Ming Yang*+ and Gideon Zamba and Joseph Cavanaugh
• Companies: University of Iowa and University of Iowa and University of Iowa
• Keywords: Count time series ; EM algorithm ; Partial likelihood ; Zero-inflation

Abstract

Count data with excess zeros are common in many biomedical and public health applications. The zero-inflated Poisson (ZIP) regression model has been widely used in practice to analyze such data. In this paper, we extend the ordinary ZIP regression framework to model zero-inflated count time series. An observation-driven model is presented and developed, and the partial likelihood is employed for statistical inference. Partial likelihood inference has been successfully applied in modeling time series where the conditional distribution of the response lies within the exponential family. Extending this approach to ZIP time series poses methodological and theoretical challenges, since the ZIP distribution is a mixture and therefore lies outside the exponential family. We establish the asymptotic theory of the maximum partial likelihood estimator (MPLE) under mild regularity conditions, and investigate its finite sample behavior in a simulation study. We outline the computation of the MPLE and its standard error. Finally, we present an epidemiological application to illustrate the proposed methodology.