Configuration of sample points for the reduction of multicollinearity in regression models with distance variables

Regression models often suffer from multicollinearity that greatly reduces the reliability of estimated coefficients and hinders an appropriate understanding of the role of independent variables. It occurs in regional science especially when independent variables include the distances from urban facilities. This paper proposes a new method for deriving the configuration of sample points that reduces multicollinearity in regression models with distance variables. Multicollinearity is evaluated by the maximum absolute correlation coefficient between distance variables. A spatial optimization technique is utilized to calculate the optimal configuration of sample points. The method permits us not only to locate sample points appropriately but also to evaluate the location of facilities from which the distance is measured in terms of the correlation between distance variables in a systematic way. Numerical experiments and empirical applications are performed to test the validity of the method. The results support the technical soundness of the proposed method and provided some useful implications for the design of sample location.