Modelling Over-Dispersion Countable Data with GLMM

This scholarly investigation aims to surmount the predicament of over- dispersion in datasets with Poisson distributed that exhibit a variance larger than the mean. For the aforementioned objective, information regarding the number of beekeeping enterprises at the IBBS-1 level from the years 2004 to 2022, acquired from the TUIK's animal husbandry statistics, has been utilized. To address the issue of overdispersion, four distinct models were developed through the utilization of varied model algorithms within the framework of generalized linear mixed models (GLMM). As the first model in the modeling, overdispersions were checked. Upon identifying the presence of overdispersion, random effects were incorporated into the models with the premise of Poisson and Negative Binomial distribution. In analyzing the data about beekeeping enterprises, it was observed that the fixed effect (year) was found non-significant in the models wherein over-spread was eliminated (Models 2, 3, 4). Conversely, in Model 1 where over-spread was observed, the effect of year was found highly significant (p<0.0001). The models were compared using the "Generalized Chi-Square/Df" fit statistic. The utilization of the Negative Binomial distribution in the GLMM or the incorporation of random effects in the Poisson distribution within the model can effectively address the issue of overdispersion.