Parameter estimation and hypothesis testing the second order of bivariate binary logistic regression (S-BBLR) model with Berndt Hall-Hall-Hausman (BHHH) iterations

Abstract

Bivariate Binary Logistic Regression (BBLR) is a logistic model that has two response variables where each variable depends on two categories with the response variables being correlated with each other. In this research, a development study will be conducted on a Bivariate Binary Logistic Regression model using the second order (S-BBLR). Furthermore, the S-BBLR will be applied to the problem of Sustainable Development Goals (SDGs) related to the Human Development Index (HDI) and Public Health Development Index (PHDI) data in East Java, Indonesia. The parameter estimation process uses the Maximum Likelihood Estimator (MLE) method. The problem in estimate the parameters of this model is that MLE cannot find an implicit analytical solution, so an iteration method will be used in the form of Berndt Hall-Hall-Hausman (BHHH) in the iteration process. Hypothesis test for the S-BBLR model include simultaneous and partial tests performed using the Maximum Likelihood Ratio (MLRT) and the Wald method. Based on the analysis, it was found that the percentage of poor people, the pure participation rate (APM), and the number of public health centers had a significant impact on PHI and PHDI with a classification accuracy of 86.84%.