Parameter estimation of mixed geographically weighted weibull regression model

Abstract

This study discusses a Mixed Geographically Weighted Weibull Regression (MGWWR) Model. MGWWR is a regression model developed from a Geographically Weighted Weibull Regression (GWWR) model. Parameter estimation of GWWR model is done locally at every observation location using geographical location weighting. Based on parameter identification result in GWWR model, the certain covariates influencing the GWWR model may be global (the same value) in nature, whist others are different. Based on consideration this situation, a MGWWR model is proposed, in which some parameters are assumed to be constant and the others are different for every local model in the study area. The aim of this study is to identify the constant and local parameters in GWWR model, and to estimate the MGWWR model parameters using maximum likelihood estimation (MLE) method. Identification of constant and local parameters in GWWR model is initial step to construct the MGWWR model. The results show that test statistic for hypothesis testing on the constant parameter identification is Wilk's statistic derived from likelihood ratio test (LRT) method, and the maximum likelihood estimator of MGWWR model can be obtained by using the Newton-Raphson iterative method based on the back-fitting procedure.