In this study, the hypothesis testing of geographically weighted bivariate logistic regression (GWBLR) procedure is proposed. The GWBLR model is a bivariate logistic regression (BLR) model which all of the regression parameters depend on the geographical location in the study area. The geographical location is expressed as a point coordinate in two-dimensional geographic space (longitude and latitude). The response variables of BLR model are constructed from a (2 × 2) contingency table and it follows the multinomial distribution. The purpose of this study is to test the GWBLR model parameters. There are three hypothesis tests. The first is a parameters similarity test using the Vuong test method. The test is to obtain a significant difference between GWBLR and BLR. The second is a simultaneous test using the likelihood ratio test method. The simultaneous test is to obtain the simultaneous significance of the regression parameters. The last is a partial test using Wald test method. The result showed that the Vuong statistic and Wald statistic have an asymptotic standard normal distribution, whereas the likelihood ratio statistic has an asymptotic chi-squared distribution.
The Public Health Development Index (PHDI) is a composite indicator that describes the progress of health development and is useful for ranking provinces and districts/cities in achieving successful community health development. In addition, the PHDIM can also be used to determine regional priorities that require assistance in improving health development. Based on the publication of the PHDI ranking by the Health Research and Development Agency of the Ministry of Health in 2013, the PHDI ranking for 55 districts/cities in Kalimantan Island varied greatly. So it needs to be studied, examined the factors that influence it. The purpose of this study was to examine the modeling of the factors that influence the PHDI of districts/cities in Kalimantan Island in 2013 using the probit regression approach. The results of this study indicate that the factors that significantly influence the PHDI of districts/cities in Kalimantan Island in 2013 are the human development index and the labor force participation rate.
This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 × 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt–Hall–Hall–Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.
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.
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