Estimating λ from a Generalized Poisson-Multinomial Mixture Model and an Application to Alcohol Drinking

• In Event: 368 - Section on Alcohol, Drugs, and Tobacco Refereed Roundtable Session and Business Meeting
  In Refereed Roundtable 60min: Table 06. Adolescent Alcohol Use

Abstract

Although count data is often collected in social, psychological and epidemiological surveys in grouped and right-truncated categories, there is a lack of statistical methods simultaneously taking both grouping and right-truncation into account. In this research, we propose a new generalized Poisson-multinomial mixture approach to model grouped and right-truncated (GRT) count data. Based on a mixed Poisson-multinomial process for conceptualizing grouped and right-truncated count data, we prove that the new maximum-likelihood estimator (MLE-GRT) is consistent and asymptotically normally distributed for both Poisson and zero-inflated Poisson models. The use of the MLE-GRT, implemented in an R package, is illustrated by both statistical simulation and empirical examples. This research provides a tool for epidemiologists to estimate incidence from grouped and right-truncated count data and lays a foundation for regression analyses of such data structure.

Authors

• Qiang Fu, The University of British Columbia

• Xin Guo, The Hong Kong Polytechnic University

• Kenneth C. Land