Simulation Study for the Zero-Inflated Negative Binomial

• Activity Number: 194
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jelani Wiltshire*+ and David Oakes
• Companies: University of Rochester and Univ of Rochester Medical Center
• Keywords: zero inflated negative binomial ; excessive zeros ; zero inflated poisson ; longitudinal study

Abstract

In count data there are numerous applications in which the number of observed zeros are substantially larger than the predicted number of zeros under the traditional count data probability models. A popular approach used to model this type of data has been the application of the zero inflated Poisson (ZIP) model. We applied a variant of the ZIP model, the zero inflated negative binomial model with random effects, to a data set from a longitudinal study. We have found that the variance estimates of the some coefficients in the model were unstable. The variance estimate of the intercept parameter in the logistic part of the model was unusually large. There were also several covariates in the model for which the variance of the coefficients were underestimated. In this paper we seek to understand the properties of the variance estimates under this model through the forms of parameter estimation which include maximum likelihood and generalized estimation equations. This was done through a simulation study which reflected the complex structure of the data in the longitudinal study. We also studied various missing data paradigms to see how they impacted the variance estimates.