Spatial Econometric Approaches for Count Data: An Overview and New Directions

Authors: Paula Simões, Isabel Natário

Abstract:

This paper reviews a number of theoretical aspects for implementing an explicit spatial perspective in econometrics for modelling non-continuous data, in general, and count data, in particular. It provides an overview of the several spatial econometric approaches that are available to model data that are collected with reference to location in space, from the classical spatial econometrics approaches to the recent developments on spatial econometrics to model count data, in a Bayesian hierarchical setting. Considerable attention is paid to the inferential framework, necessary for structural consistent spatial econometric count models, incorporating spatial lag autocorrelation, to the corresponding estimation and testing procedures for different assumptions, to the constrains and implications embedded in the various specifications in the literature. This review combines insights from the classical spatial econometrics literature as well as from hierarchical modeling and analysis of spatial data, in order to look for new possible directions on the processing of count data, in a spatial hierarchical Bayesian econometric context.

Keywords: Spatial data analysis, spatial econometrics, Bayesian hierarchical models, count data.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1111729

References:

[1] L. Anselin, “Thirty years of spatial econometrics,” Papers in Regional Science, vol. 89, pp. 3–25, 2010.
[2] J. LeSage, The theory and Practice of Spatial Econometrics. University of Toledo, 1999.
[3] L. Anselin(a), “Spatial dependence and spatial structural instability in applied regression analysis,” Journal of Regional Science, vol. 30, pp. 185–207, 1990.
[4] L. Anselin(b), Spatial Econometrics: Methods and Models. Kluwer Academic, Dordrecht.
[5] M. Fischer, Spatial Analysis and Geocomputation. Springer, 2006.
[6] G. D. and L. H., Markov Chain Monte Carlo-Stocastic Simulation for Bayesian Inference. Chapman and Hall, CRC, 2006.
[7] D. Lambert et al., “A two-step estimator for a spatial lag model of counts-theory, small sample performance and an application,” Regional Science and Urban Economics, vol. 40, pp. 241–252, 2010.
[8] R. Bivand et al., “Approximate bayesian inference for spatial econometric models,” Spatial Statistics, vol. 9, pp. 146–165, 2014.
[9] J. Wooldrige, Introductory Econometrics, A Modern Approach. Thomson South Western, 2006.
[10] D. Gujarati, Basic Econometrics. McGrawHill, 1995.
[11] J. LeSage and R. Pace, Introduction to Spatial Econometrics. CRC Press, 2009.
[12] G. Arbia, Spatial Econometrics, Statistical Foundations and Aplications to Regional Convergence. Springer, 2006.
[13] N. Cressie, Statistics for Spatial Data. Jonh Wiley & Sons,Inc., 1993.
[14] M. Carvalho and I. Nat´ario, An´alise de Dados Espaciais. Sociedade Portuguesa de Estat´ıstica, 2008.
[15] L. Anselin, Spatial Regression Analysis in R - A Workbook. Center for Spatially Integrated Social Sciences, 2007.
[16] L. Anselin and S. Rey, “Properties of tests for spatial dependency in linear regression models,” Geographical Analysis, vol. 23, pp. 112–131, 1991.
[17] L. Anselin(a) et al., Small sample properties of tests for spatial dependence in regression models: some further results. In:Luc anselin and Raymond Florax (eds.), New Directions in Spatial Econometrics. Geographical Analysis. Berlin:Springer-Verlag, 1995.
[18] L. Anselin(b) et al., “Simple diagnostic tests for spatial dependence,” Regional Science and Urban Economics, vol. 26, pp. 77–104, 1996.
[19] M. Turkman and G. Silva, Modelos Lineares Generalizados- da teoria ´a pr´atica. Sociedade Portuguesa de Estat´ıstica, 2000.
[20] M. Quddus, “Modelling area-wide count outcomes with spatial correlation and heterogeneity -an analysis of london crash data,” Accident Analysis and Prevention, vol. 40, pp. 1486–1497, 2008.
[21] S. Banerjee et al., Hierarchical Modeling and Analysis for Spatial Data. Chapman and Hall/CRC, 2004.
[22] S. Gschl¨oSSl and C. Czado, “Modelling count data with overdispersion and spatial effects,” Statistical Papers, vol. 49, pp. 531–552, 2008.
[23] R. Haining et al., “Modelling small area counts in the presence of overdispersion and spatial autocorrelation,” Computational Statistics and Data Analysis, vol. 53, pp. 2923–2937, 2009.
[24] J. Besag et al., “Bayesian image restoration with two applications in spatial statistics (with discussion),” 2004.
[25] B. Leroux et al., “Estimation of disease rates in small areas: A new mixed model for spatial dependence. in me halloran, d berry (eds.),” Statistical Models in Epidemiology, the Environment, and Clinical Trials, Springer-Verlag, 1999.
[26] H. Stern and N. Cressie, “Inference for extremes in disease mapping, in ab. lawson, a. biggeri, d. b¨ohning, e. lesaffre, jf. viel, r. bertollini (eds.),” Disease Mapping and Risk Assessment for Public Health,John Wiley & Sons, 1999.
[27] S. Dass et al., “Experiences with aproximate bayes inference for the poisson-car model.” Techinal Report RM679 Department of Statistics and Probability, Michigan State University, Tech. Rep., 2010.
[28] D. Lee, “Carbayes: an r package for bayesian spatial modeling with conditional autoregressive priors,” Journal of Statistical Software.
[29] J. Besag, “Spatial interaction and the statistical analysis of lattice systems (with discussion),” Journal of the Royal Statistical Society B, vol. 36, No.2, pp. 192–236, 1974.
[30] A. Doucet et al., Sequential Monte Carlo Methods in Practice. Springer, 2001.
[31] A. Bhati, “A generalized cross-entropy approach for modeling spatially correlated counts,” Econometric Reviews, vol. 27, pp. 574–595, 2008.
[32] R. H., “Approximate bayesian inference for latent gaussian models using integrated nested laplace approximations (with discussion),” Journal of the Royal Statistical Society, Series B, vol. 71, pp. 319–392, 2009.