The handling of overdispersion on Poisson regression model with the generalized Poisson regression model

Abstract

Regression model is used to model the relationship between predictor variables and response variable. In case that the response variable are Poisson distributed, Poisson regression model can be used to model the relationship. An assumption that must be fulfilled on Poisson distribution is the mean value of data equals to the variance value (or so- called equidispersion). If the variance value is greater than the mean value, it is called overdispersion. Overdispersion occurs due to such factors as the presence greater variance of response variable caused by other variables unobserved heterogeneity, the influence of other variables which leads to dependence of the probability of an event on previous events, the presence of outliers, the existence of excess zeros on response variable. If the equidispersion is not met, the Poisson regression is no longer appropriate to model the data. Moreover, the resulted model will yield biased parameter estimation and underestimated standard error, leading to invalid conclusions. To handle overdispersion, the generalized Poisson regression model can be employed. The present study seeks to overcome overdispersion of the Poisson regression model using generalized Poisson regression model and to apply it to data of maternal deaths in Central Java. The study found out the generalized Poisson regression model, its parameter estimation using maximum likelihood estimation (MLE), as well as iterative solution using Newton-Raphson method. The iterative estimation obtained is α^(t+1)=α(t)−H(t)−1G(t) and β^(t+1)=β(t)−H(t)−1G(t), where t represents the number of iterations required and α is dispersion parameter. The analysis results in the generalized Poisson regression model, expressed as Y^i=exp(β^0+β^1X1i+β^2X2i+…+β^pXpi).