Poisson

Poisson in Europe

Bias Effects of Overdispersed Longitudinal Count Data – a Monte Carlo Simulation

Daniel Seddig, from the University of Muenster, made a contribution to the 2012 Annual Conference of the European Society of Criminology, in the category “Criminological Theory, Research and Education,” under the title “Bias Effects of Overdispersed Longitudinal Count Data – a Monte Carlo Simulation”. Here is the abstract: Several criminological studies use growth mixture models to analyze the development of deviance and delinquency within distinct groups or classes of offenders over time. Since the application of common normal theory maximum likelihood estimation seems inappropriate for crime-related count data, a common solution is the use of the (zero-inflated) poisson growth mixture model. Still, there remains doubt if crime related count variables effectively meet the requirements of the poisson distribution, particularly the assumption of equidispersion. It has been demonstrated that the poisson based regression models may lead to biased parameter estimates and standard errors if the assumption is violated, i.e. data is overdispersed. An alternative approach is the negative binomial model that adds a dispersion parameter to the probability model. In a monte carlo simulation study the performance of poission and negative binomial estimation is tested for first and second order polynomial growth curve models (i.e. growth mixture models with one class) under varying levels of overdispersion with ex-ante generated count data. Results suggest that the poisson based parameter estimates and standard errors for intercept and slopes are severly biased in the conditions of moderate and high overdispersion, hence indicating false developmental tendencies. In contrast, estimates and standard errors of intercept and slopes based on the negative binomial model are not prone to such bias.

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Further Reading

  • “Bias Effects of Overdispersed Longitudinal Count Data – a Monte Carlo Simulation”, by Daniel Seddig (Proceedings)

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