Models for Overdispersed Count Time Series with Excess Zeros
Joseph E. Cavanaugh, Professor and Head
Department of Biostatistics
University of Iowa
Count time series are frequently encountered in biomedical, epidemiological, and public health applications. In principle, such series may exhibit three distinctive features: overdispersion, zero-inflation, and temporal correlation. Devising modeling frameworks that are sufficiently general to accommodate all three of these characteristics poses a daunting challenge. To address this challenge, we discuss the development of frameworks based on both observation-driven and parameter-driven modeling formulations. We illustrate the latter development by presenting a flexible class of dynamic models in the state-space framework. For parameter estimation, we derive a Monte Carlo Expectation-Maximization (MCEM) algorithm, where particle filtering and particle smoothing methods are employed to approximate the high-dimensional integrals in the E-step of the algorithm. To exemplify the proposed methodology, we consider an application based on the evaluation of a participatory ergonomics intervention, which is designed to reduce the incidence of workplace injuries among a group of hospital cleaners. The data consists of aggregated monthly counts of work-related injuries that were reported before and after the intervention.
This work is joint with Gideon Zamba, Ming Yang, and Fan Tang.