Evaluation of Overdispersed Data Set by Using Generalized Linear Mixed Model Approach

Abstract

The aim of this study is to investigate the problem of overdispersion frequently observed in the data sets having Poisson distribution, in which the variation is larger than the mean. Data taken Turkish Statistical Institute (TUIK) covered between 2010 and 2015 were consist of kids reared in eighteen city of Turkey. Three different model algorithm are generated in the generalized linear mixed model approach to eliminate the problem of overdispersion in the data set. The study was conducted in two steps. In the first step, we specified the model algorithm showing overdispersion case. In the second step, however, we used the two model algorithm to overcome the elimination of this overdispersion problem. The standard errors estimated in the case of overdispersion were smaller than the case where overdispersion was eliminated. Nevertheless, in case of overdispersion in the data set, it was determined that there were statistically significant differences among factors of years for population size of kid (P<0.0001), whereas these differences among years for population size of kids were not significant when overdispersion were eliminated statistically. Consequently, the present results showed that overdispersion in data set can led to important misunderstandings, if the case of this overdispersion that data sets is ignored. In generalized linear mixed model approach, as an alternative, the use of negative binomial distribution instead of Poisson distribution or adding the random effects under Poisson distribution assumption in model algorithms occurred presents the effective alternative solutions to overcome the overdispersion case. © 2016, Centenary University. All rights reserved.