The modeling of human development index (HDI) in Papua - Indonesia using geographically weighted ridge regression (GWRR)

Abstract

In regression model, there are several assumptions which have to be fulfilled, one of which is the absence of multicollinearity between its independent variables. If multicollinearity occurs, parameter estimation of the model using method of least squares results in unbiased estimators, and even the estimators are likely to have large variance. Such large variance causes hypothesis testing towards estimators of parameter of regression model to tend to accept H0, meaning that the regression coefficient is insignificant. One approach to deal with multicolinearity is biased regression parameter estimator, one of which is ridge regression. Ridge regression is defined as the modification of the method of least squares by adding a small constant c to the diagonal elements of X'X. The value of the constant c reflects the degree of bias towards coefficient of ridge estimators. The application, which is fit for ridge regression model discussed in the article, is Human Development Index (HDI) and its influencing factors. HDI is a standard based on components of human quality of life composed of three aspects including health, education, and living standards. HDI in Indonesia has shown an increase the last few years, except that in Papua. Papua was a province with the lowest HDI with such influencing factors as health care quality, education quality, employment sector, and population condition. The low HDI in Papua with its 29 regencies/ cities is caused by the difference in characteristics and geographical conditions in spatial units known as the effect of spatial heterogeneity. To deal with the spatial heterogeneity, geographically weighted regression (GWR) is applied and to encounter the occurrence of multicollinearity, GWRR model is used. In the research, the GWRR model was applied for data of HDI in Papua province. The predicted value of ridge parameter (c) appropriate for the GWRR model is 0.149. From the model, the distribution of spatial units based on variables which are significant to the HDI for 29 regencies/ cities in Papua can be constructed.