Modeling the Count Data of Public Health Service Visits with Overdispersion Problem by Using Negative Binomial Regression

Abstract

Abstract The count data of health service visits can be modeled into Poisson regression analysis, where there is no overdispersion assumption by looking at the comparison between mean and variance. The overdispersion test is performed by using the ratio of the sum of Pearson residuals over the number of degrees of freedom that must be less than one. The overdispersion problem can be corrected accurately by building mixture distribution where the parameter of Poisson distribution is made to have Negative Binomial distribution as the theoretical model. The data used in this study are the number of visits to public health service at Padang city as many as 460 data, where the predictor variables are age, gender, education level, occupation, income, home health status, individual health status, health insurance type, distance to health service, and diet type. The best model of negative binomial regression is selected by considering the values of AIC, BIC, Log-likelihood, and overdispersion tests that occur between the resulting models. The final result of this count data model with negative binomial regression fits better and overcomes the overdispersion problem with the significant variable is individual health status for this population, and it can be explained that the more individual has a history of having severe illness the more often the number of visits to the health service, meanwhile the other predictor variables have no effect to the number of visits.