Estimation Parameter of Generalized Poisson Regression Model Using Generalized Method of Moments and Its Application

Poisson Regression is a standard model for data counts that can be used to determine the relationship between the response variable and predictors variables. Equidispersion is assumptions that must be met in Poisson Regression. Equidispersion is a condition that the variance of the response variable is equal with the average of the response variable. In real cases, these assumptions are often not meet. In real cases, there are overdispersion and underdispersion cases. Generalized Poisson Regression (GPR) is one method that can handle cases of overdispersion and underdispersion. The GPR model is used to estimate regression parameters. Many articles proposed to use only Maximum Likelihood Estimation (MLE) to estimate the parameters of GPR. This article will develop the parameter estimation method of the GPR model, which is using the Generalized Method of Moments (GMM). GPR model is applied in the case of diarrhea in infants in Pasuruan Regency, East Java. The best model is chosen by the value of AICc. The smaller the value of AICc, the better the model. The best model is a model that includes exclusive breastfeeding, complete basic immunization, and healthy living behavior in the model.