Parameter estimation and hypothesis testing of multivariate adaptive bivariate Generalized Poisson Regression spline

Abstract

Poisson regression is a regression method used to model the count data. The response variable of Poisson regression has a Poisson distribution. Poisson regression assumes that the response variable average value is equal to the response variable variance value, called the equidispersion condition. Generalized Poisson Regression (GPR) is used to overcome that if the equidispersion assumption cannot be fulfilled. If there are two correlated responses variable, the modeling used Bivariate Generalized Poisson Regression (BGPR). Multivariate Adaptive Regression Spline (MARS) is a nonparametric regression method with flexibility in high-dimensional data. Multivariate Adaptive Bivariate Generalized Poisson Regression Spline (MABGPRS) is a development of the MARS method and BGPR method. This study will discuss parameter estimation and test statistics for the MABGPRS model. The estimation of the MABGPRS model parameters was carried out using Weighted Least Square (WLS) method and the Maximum Likelihood Estimation (MLE) method. MLE was not found analytical solution, so the estimation uses the Berndt-Hall-Hall-Hausman (BHHH) iteration method to solve it. The test statistics for simultaneous and using Maximum Likelihood Ratio Test (MLRT).