Test Efficiency Analysis of Parametric, Nonparametric, Semiparametric Regression in Spatial Data

Regression analysis has three approaches in estimating the regression curve, namely: parametric, nonparametric, and semiparametric approaches. Several studies have discussed modeling with the three approaches in cross-section data, where observations are assumed to be independent of each other. In this study, we propose a new method for estimating parametric, nonparametric, and semiparametric regression curves in spatial data. Spatial data states that at each point of observation has coordinates that indicate the position of the observation, so between observations are assumed to have different variations. The model developed in this research is to accommodate the influence of predictor variables on the response variable globally for all observations, as well as adding coordinates at each observation point locally. Based on the value of Mean Square Error (MSE) as the best model selection criteria, the results are obtained that modeling with a nonparametric approach produces the smallest MSE value. So this application data is more precise if it is modeled by the nonparametric truncated spline approach. There are eight possible models formed in this research, and the nonparametric model is better than the parametric model, because the MSE value in the nonparametric model is smaller. As for the semiparametric regression model that is formed, it is obtained that the variable X2 is a parametric component while X1 and X3 are the nonparametric components (Model 2). The regression curve estimation model with a nonparametric approach tends to be more efficient than Model 2 because the linearity assumption test results show that the relationship of all the predictor variables to the response variable shows a non-linear relationship. So in this study, spatial data that has a non-linear relationship between predictor variables and responses tends to be better modeled with a nonparametric approach.