Mixed Geographically Weighted Regression-Kriging Model for Small Area Estimation, 111-129
Sarpono Dimulyo and Satoshi Aoki
The average of household expenditure per capita, which is usually used as a main indicator of poverty, is commonly explained as a function of some variables in a global regression framework. In the global regression framework, the coefficients in the model are assumed to be equal for all national spatial units. Naturally, however, the average of household expenditure per capita is not equally distributed across the national territory. In fact, the expenditure covariates do not have the same influence on per capita expenditure all over a country or region. The geographically weighted regression (GWR) analysis could be a solution to capture spatial variations and to solve the spatial non-stationarity. Because in GWR models, the spatial relationships are modeled by introducing distance-based weights and the estimates are provided for each variable k and each geographical region i. We have explored the possibility of combining census and survey data in order to construct a GWR model for the average of household expenditure. In view of the predictions, GWR cannot be used to interpolate to other regions without estimating a local parameter, whereas the global regression model allows one to make prediction in other geographical region. To handle this limitation, we propose spatial kriging predictor for estimation of locally parameter in other regions. By this approach, we classified all the villages in Jawa Tengah into poor or disadvantaged villages and non-poor villages. To classify villages into poor or disadvantaged villages and non-poor villages, we compare the estimates of the average of household expenditure with the poverty line, which have been defined in another survey by BPS Statistics Indonesia.