Automatic selection of a spatial weight matrix in spatial econometrics: Application to a spatial hedonic approach

The recent progress of spatial econometrics has developed a new technique called the “spatial hedonic approach,” which considers the elements of spatial autocorrelation among property values and geographically distributed attributes. The practical difficulties in applying spatial econometric models include the specification of the spatial weight matrix (SWM), which affects the final analysis results. Some simulation studies suggest that information criteria such as AIC are useful for the SWM's selection, but if many model candidates exist (e.g., when the selections of explanatory variables are performed simultaneously), then the computational burden of calculating such criteria for each model is large. The present study develops an automatic model selection algorithm using the technique of reversible jump MCMC combined with simulated annealing; termed trans-dimensional simulated annealing (TDSA). The performance of the TDSA algorithm is verified using the well-known Boston housing dataset, and it is applied empirically to a Japanese real estate dataset. The obtained results suggest a two-step strategy for model selection, with SWM (W) first, followed by the explanatory variables (X and WX), will result in local optima, and therefore these variables should be selected simultaneously. The TDSA algorithm can find the significant variables that are “hidden” because of multicollinearity in the unrestricted model, and can attain the minimum AIC automatically.