Estimation of Zero-Inflated Negative Binomial Regression Parameters Using the Maximum Likelihood Method (Case Study: Factors Affecting Infant Mortality in Wonogiri in 2015)

Abstract

The relationship between the response variable (Y) with one or several predictor variables (X) can be determined by using regression analysis. In a simple linear regression model there is an assumption that the response variable follows the normal distribution, but in reality it is often found that the response variable does not follow the normal distribution. If a response variable has a Poisson distribution then it can be analyzed with a Poisson regression model. There is an assumption that must be fulfilled in poisson regression that is equidispersion (the variance value must be equal to the average value), so this model is not suitable for use in data that is overdispersed (the variance value is greater than the average value). Poisson regression is a general model used to analyze discrete data where discrete data is often found to be of zero value with an excessive proportion of response variables (zero inflation). An alternative model for dealing with overdispersion and zero inflation is the Zero Inflated Negative Binomial (ZINB) model. This research aims to estimate the Zero-Inflated Negative Binomial (ZINB) regression parameters using the maximum likelihood method. The zero inflated negative binomial model (ZINB) was applied to the case of infant mortality in Wonogiri Regency in 2015. The results showed an independent variable that affected the infant mortality rate was the percentage of pregnant women (X_4) with an AIC value of 113.1961.