Geographically Weighted Poisson Regression (GWPR) for Analyzing The Malnutrition Data (Case Study: Java Island in 2008

Abstract

Poisson regression, namely global model is a statistical method used to analyze the relationship between the dependent variable and the explanatory variables, where the dependent variable is a counted data and has a Poisson distribution. The result of its parameter estimation is homogeneous for all of the observations. However, especially in spatial data, its estimation will produce biased estimation. The parameter estimates in each location will vary among regions as it is influenced by territorial or geographical factors, which is known as spatial variability or spatial non-stationarity. Therefore the appropriate analysis for this data is Geographically Weighted Poisson Regression (GWPR) model. GWPR parameter estimation used a weighting matrix which depends on the proximity between the locations. Fisher scoring iteration is used for solving the iteratively parameter estimation. In this research, GWPR will be used in malnutrition data because malnutrition is counted data which is assumed to have a Poisson distribution and the indirect factors of differences in the number of malnourished patients in every region is possible due to spatial factors. The results showed that GWPR model has better performance than global model based on AICc difference. Poverty aspect was the most influencing factor to the number of malnourished patients in a region compared to health, education, and food aspect. The spatial variability map is created for eight variables used in selected global model where every map showed the variability of local parameter estimates. There were five groups of the local parameter estimates in each map based on percentiles grouping which showed the low until hight relation of the parameter estimates groups to the number of malnourished patients. This research also created a significant variables map which detects the variables that were significant in each region.