GEOGRAPHICALLY WEIGHTED BIVARIATE ZERO INFLATED POISSON REGRESSION (GWBZIPR) MODELLING WITH ADAPTIVE GAUSSIAN KERNEL WEIGHT FUNCTION

Siti Masliyah Lubis., Henny Pramoedyo., and Suci Astutik

Abstract:

Bivariate Poisson regression is a method used to model a pair of data counts with a Poisson distribution that has a correlation. This model has specific assumptions, namely similarities between averages and variance (equilibrium). Violations of this assumption cause the parameters produced from bivariate Poisson regression to be less accurate. Violations of these assumptions can occur because of the count data on the response variable with a zero value (Zero-Inflated) which results in overdispersion or a variance value greater than the average. In a pair of data counts that have correlations between response variables and having data with excessive zero values, they can be modelled with Bivariate Zero-Inflated Poisson Regression (BZIPR). The development of the BZIPR regression which has considered spatial factors is called Geographically Weighted Bivariate Zero-Inflated Poisson Regression (GWBZIPR). The weighting function used is the weighting of the Adaptive Gaussian Kernel and the estimation of the parameters of the GWBZIPR model is done using the Maximum Likelihood Estimation (MLE) method. This research was conducted on the number of cases of PB and MB leprosy in North Sumatra Province in 2017. Based on the results of the modelling that the variable that affects the number of cases of PB and MB leprosy in North Sumatra province is the percentage of poor people, the percentage of households with clean and healthy behavior, ratio of medical personnel and percentage of healthy houses.

 

Keywords: Geographically Weighted Bivariate Zero Inflated Poisson Regression (GWBZIPR), Adaptive Gaussian Kernel, and Leprosy

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