Estimating spatial regression models with sample data-points: A Gibbs sampler solution

The individual observations used to estimate spatial regression models often constitute only a sample of the theoretically observable data points. In many cases, such a sample does not obey a specific design and it is collected only with convenience criteria as it happens, e.g. when data are web scraped or crowdsourced. Thus, we expect to observe possible biases and inefficiencies while estimating the spatial regression parameters. In this paper, we present the results of various Monte Carlo experiments conducted to assess the extent of this problem in the estimation of a spatial econometric model. This assessment is done by isolating the effects because of the sample size, the pattern of the point distribution and sample criterion used in the data collection process. Furthermore, we suggest an approach based on Gibbs sampler that can be used to replace the unsampled data points. Our simulations and a real data case study confirm that our proposed strategy reduces the distorting effects produced by the sample observation, thus providing more reliable parameters’ estimations.