Bayesian Analysis of Spatial Econometrics Regression Models

Document Type : Original Paper


Semnan University, Department of Statistics


Spatial regression models are often used for modeling spatial economic data. The main purpose of studying these models is to obtain parameter estimates and then predict at new locations. For this purpose, the maximum likelihood approach is first investigated and in order to increase the accuracy of parameter estimation and reduce the computation time, the conventional Bayesian approach and an approximate Bayesian approach are examined for three regression models, spatial Lag model, spatial Durbin model and spatial error model. Finally, in a simulation study and a real example of housing data in Tehran, the performance of models and approaches are compared. The existence of a spatial effect and a direct relationship between housing price and area in the data is accepted. Using the Relative Root Mean Square Error for these two data sets, it was concluded that the approximate Bayesian approach for spatial econometric models has a better performance than the maximum likelihood and the conventional Bayesian approaches. In addition, it was found that the computational time of the Bayesian approach is about twice as long as the approximate Bayesian approach.


Main Subjects

[1] L. Anselin, Spatial Econometrics: Method and Models In: Studies in Operational Regional Science, Springer, 1988.
[2] L. Anselin, Thirty Years of Spatial Econometrics, Papers in Regional Science, 89 (2010) 3-25.
[3] G. Arbia, Spatial Econometrics: A Broad View, Foundations and Trends in Econometrics, (8:3-4) (2016) 145-265.
[4] R. P. Barry, R. K. Pace, Kriging with Large Data Sets using Sparse Matrix Techniques, Communication Statistics: Computation and Simulation, 26 (1997) 619-629.
[5] R.s. Bivand, V. Gómez-Rubiob, H. Rue, Approximate Bayesian Inference for Spatial Econometrics Models, Spatial Statistics, 9 (2014) 146–165.
[6] S. P. Brooks. and A. Gelman, General Methods for Monitoring Convergence of Iterative Simulations, Journal of Computational and Graphical Statistics, 7 (1998) 434-455.
[7] R. Davidson, J. G. Mackinnon, Estimation and Inference in Econometrics, Oxford University, New York, 1993.
[8] J. Eidsvik, A. O. Finley, S. Banerjee, H. Rue, Approximate Bayesian Inference for Large Spatial Datasets Using Predictive Process Models, Computational Statistics and Data Analysis. 56 (2012) 1362-1380.
[9] H. Kelejian, G. Piras, Spatial Econometrics. London, England: Academic Press, 2017.
[10] J. LeSage, Spatial Econometrics, Department of Economics University of Toledo, 1999.
[11] J. LeSage, R. K. Pace, Introduction to Spatial Econometrics, Chapman and Hall/CRC, 2009.
[12] J. Lesage, M. Ficher, Spatial Growth Regression : Model Specification , Estimation and Interpretation, Spatial Economic Analysis , 3 (2008) 275–304 .
[13] H. Rue, L. Held, Gaussian Markov Random Fields. Theory and Applications, Chapman and Hall, London, 2005.
[14] H. Rue, S. Martino, N. Chopin, Approximate Bayesian Inference for Latent Gaussian Model by Using Integrated Nested Laplace Approximations (with discussion), Journal of the Royal Statistical Society. 71 (2009) 319–392.
[15] F. Hosseini, J. Eidsvik, M. Mohammadzadeh, Approximate Bayesian inference in spatial GLMM with skew normal latent variables, Computational Statistics & Data Analysis 55 (4) (2011) 1791-1806.
[16] F. Hosseini, M. Mohammadzadeh, Bayesian Prediction for Spatial Generalized Linear Mixed Models with Closed Skew Normal Latent Variables, Australian & New Zealand Journal of Statistics 54 (1) (2012) 43-62.
[17] F. Hosseini, O. Karimi, Approximate composite marginal likelihood inference in spatial generalized linear mixed models, Journal of Applied Statistics 46 (3) (2020) 542-558.