Three-parameter bivariate gamma regression model for analyzing under-five mortality rate and maternal mortality rate

Abstract

Gamma regression is often used to model continuous, right-skewed and strictly positive data. This paper discusses three-parameter gamma regression, namely scale, shape, and location parameter, with two correlated response variables. The purpose of this study is to determine the estimator parameters, perform the testing for the parameters using Maximum Likelihood Ratio Test (MLRT) and its application in the cases of the Under-five Mortality Rate (U5MR) and the Maternal Mortality Rate (MMR) in North Sulawesi, Gorontalo, Central Sulawesi Provinces in 2016. The parameter estimation in this global model obtained through MLE. Nevertheless, the results showed an unsolvable equation in closed-form, then we used numerical optimization. In this study, we were using the Berndt-Hall-Hall-Hausman optimization method. After the estimation results are obtained, the estimation parameters need to be tested with a simultaneous test with the MLRT,while for test partially, we used the Z test. Moreover, the factors that influence U5MR and MMR are the poor population, the obstetric complications handled, the mothers received Fe3 during pregnancy, the teenage pregnancy,the children under-five received vitamin A and the households with clean and healthy life behavior.