Estimators of Regression Coefficients in Models for Time Series of Counts

• Activity Number: 544
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Rachel Altman* and Abdollah Safari and Brian Leroux
• Companies: Simon Fraser University and Simon Fraser University and University of Washington
• Keywords: Count data ; Latent variables ; Hidden Markov models ; Generalized linear mixed models ; Generalized linear models ; Time series

Abstract

Correlated count data, in particular time series of counts, arise in many contexts. For instance, disease incidence, traffic fatalities, and lesion counts in multiple sclerosis patients may be monitored over time. Latent variable models, such as hidden Markov models and generalized linear mixed models, are one way of capturing the autocorrelation expected in such time series. However, depending on the structure of the latent variables, computing the maximum likelihood estimates of the regression coefficients may be challenging. In this talk, we will consider the case where the true model belongs to a broad class of latent variable models. We will discuss three different estimators of the regression coefficients, including an estimator based on the generalized linear model (GLM). Although the GLM estimator does not take into account the autocorrelation in the data, we show that, under some conditions, it performs well and has numerous advantages over the other estimators considered.