Geographically Weighted Multivariate Logistic Regression Model and Its Application

M Fathurahman,Vita Ratnasari,Purhadi Purhadi,Sutikno Sutikno

doi:10.1155/2020/8353481

Abstract

This study investigates the geographically weighted multivariate logistic regression (GWMLR) model, parameter estimation, and hypothesis testing procedures. The GWMLR model is an extension to the multivariate logistic regression (MLR) model, which has dependent variables that follow a multinomial distribution along with parameters associated with the spatial weighting at each location in the study area. The parameter estimation was done using the maximum likelihood estimation and Newton-Raphson methods, and the maximum likelihood ratio test was used for hypothesis testing of the parameters. The performance of the GWMLR model was evaluated using a real dataset and it was found to perform better than the MLR model.

Highlights

Over the past decade, most research on geographically weighted regression (GWR) models has been focused on applications that contain two or more correlated responses
ΓT3 ðui, viÞ ÃT is a vector of the geographically weighted multivariate logistic regression (GWMLR) model parameters
The GWMLR model is capable of evaluating the relationships between two correlated categorical dependent variables with one or more independent variables that depend on the spatial weighting function at each location in the study area

Summary

Introduction

Most research on geographically weighted regression (GWR) models has been focused on applications that contain two or more correlated responses (multivariate). Harini et al [1, 2] introduced the multivariate GWR (MGWR) model and demonstrated the parameter estimation and hypothesis test procedures using the restricted maximum likelihood estimation (RMLE) and maximum likelihood ratio test (MLRT) methods, respectively. Triyanto et al [4, 5] introduced the geographically weighted multivariate Poisson regression (GWMPR) model. The estimator of the GWMPR model parameters was obtained through the MLE with the Newton-Raphson iterative method, and the test statistic for hypothesis tests was determined by the MLRT method. Suyitno et al [6] discussed the estimation of the geographically weighted trivariate Weibull regression (GWTWR) model using the MLE and Newton-Raphson methods. The geographically weighted multivariate t regression (GWMtR) model was introduced by Sugiarti et al [7]. In [8], a new method to determine model conformity between the multivariate nonparametric truncated spline GWR model and the multivariate nonparametric truncated spline (global regression) was employed

Methods

Results

Conclusion