Spatial Econometric Approaches for Count Data: An Overview and New Directions
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.
[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.
[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.
@article{"International Journal of Business, Human and Social Sciences:72226", author = "Paula Simões and Isabel Natário", title = "Spatial Econometric Approaches for Count Data: An Overview and New Directions", 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.", volume = "10", number = "1", pages = "348-10", }
