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2021 | OriginalPaper | Buchkapitel

15. Spatial Statistics, or How to Extract Knowledge from Data

verfasst von : Anna Antoniuk, Miryam S. Merk, Philipp Otto

Erschienen in: Handbook of Big Geospatial Data

Verlag: Springer International Publishing

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Abstract

In this paper, we give an overview of selected statistical models to draw (statistically significant) conclusions from data. This is particularly important to prove theoretical/physical models. For this reason, we initially describe classical modeling approaches in geostatistics and spatial econometrics. Moreover, we show how large spatial and spatiotemporal data can be modeled by these approaches. Therefore, we sketch selected suitable methods and their computational implementation. Thus, the paper should give a general guideline to analyze big geospatial data, where “big data” refers to the total number of spatially dependent observations, and to draw conclusions from these data. Finally, we compare two of these approaches by applying them to an empirical data set. To be precise, we model the particulate matter concentration (PM2.5) in Colorado.

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Literatur
Zurück zum Zitat Ahrens A, Bhattacharjee A (2015) Two-step lasso estimation of the spatial weights matrix. Econometrics 3(1):128–155CrossRef Ahrens A, Bhattacharjee A (2015) Two-step lasso estimation of the spatial weights matrix. Econometrics 3(1):128–155CrossRef
Zurück zum Zitat Anselin L (1988) Spatial econometrics: methods and models, vol 1. Kluwer Academic Publishers, DodrechtCrossRefMATH Anselin L (1988) Spatial econometrics: methods and models, vol 1. Kluwer Academic Publishers, DodrechtCrossRefMATH
Zurück zum Zitat Anselin L (2003) Spatial externalities, spatial multipliers, and spatial econometrics. Int Reg Sci Rev 26(2):153–166CrossRef Anselin L (2003) Spatial externalities, spatial multipliers, and spatial econometrics. Int Reg Sci Rev 26(2):153–166CrossRef
Zurück zum Zitat Anselin L, Bera AK, Florax R, Yoon MJ (1996) Simple diagnostic tests for spatial dependence. Reg Sci Urban Econ 26(1):77–104CrossRef Anselin L, Bera AK, Florax R, Yoon MJ (1996) Simple diagnostic tests for spatial dependence. Reg Sci Urban Econ 26(1):77–104CrossRef
Zurück zum Zitat Apanasovich TV, Genton MG (2010) Cross-covariance functions for multivariate random fields based on latent dimensions. Biometrika 97(1):15–30MathSciNetCrossRefMATH Apanasovich TV, Genton MG (2010) Cross-covariance functions for multivariate random fields based on latent dimensions. Biometrika 97(1):15–30MathSciNetCrossRefMATH
Zurück zum Zitat Bailey N, Holly S, Pesaran MH (2016) A two-stage approach to spatio-temporal analysis with strong and weak cross-sectional dependence. J Appl Econ 31(1):249–280MathSciNetCrossRef Bailey N, Holly S, Pesaran MH (2016) A two-stage approach to spatio-temporal analysis with strong and weak cross-sectional dependence. J Appl Econ 31(1):249–280MathSciNetCrossRef
Zurück zum Zitat Banerjee S, Gelfand AE, Finley AO, Sang H (2008) Gaussian predictive process models for large spatial data sets. J R Stat Soc Series B Stat Methodol 70(4):825–848MathSciNetCrossRefMATH Banerjee S, Gelfand AE, Finley AO, Sang H (2008) Gaussian predictive process models for large spatial data sets. J R Stat Soc Series B Stat Methodol 70(4):825–848MathSciNetCrossRefMATH
Zurück zum Zitat Banerjee S, Carlin BP, Gelfand AE (2014) Hierarchical modeling and analysis for spatial data. CRC Press, Boca RatonCrossRefMATH Banerjee S, Carlin BP, Gelfand AE (2014) Hierarchical modeling and analysis for spatial data. CRC Press, Boca RatonCrossRefMATH
Zurück zum Zitat Barry RP, Pace RK (1999) Monte Carlo estimates of the log determinant of large sparse matrices. Linear Algebra Appl 289(1–3):41–54MathSciNetCrossRefMATH Barry RP, Pace RK (1999) Monte Carlo estimates of the log determinant of large sparse matrices. Linear Algebra Appl 289(1–3):41–54MathSciNetCrossRefMATH
Zurück zum Zitat Bhattacharjee A, Jensen-Butler C (2013) Estimation of the spatial weights matrix under structural constraints. Reg Sci Urban Econ 43(4):617–634CrossRef Bhattacharjee A, Jensen-Butler C (2013) Estimation of the spatial weights matrix under structural constraints. Reg Sci Urban Econ 43(4):617–634CrossRef
Zurück zum Zitat Billé AG, Blasques F, Catania L (2019) Dynamic spatial autoregressive models with time-varying spatial weighting matrices. Available at SSRN 3241470 Billé AG, Blasques F, Catania L (2019) Dynamic spatial autoregressive models with time-varying spatial weighting matrices. Available at SSRN 3241470
Zurück zum Zitat Bivand R, Piras G (2015) Comparing implementations of estimation methods for spatial econometrics. J Stat Softw 63(18):1–36CrossRef Bivand R, Piras G (2015) Comparing implementations of estimation methods for spatial econometrics. J Stat Softw 63(18):1–36CrossRef
Zurück zum Zitat Bivand RS, Pebesma E, Gomez-Rubio V (2013) Applied spatial data analysis with R, 2nd edn. Springer, New YorkCrossRefMATH Bivand RS, Pebesma E, Gomez-Rubio V (2013) Applied spatial data analysis with R, 2nd edn. Springer, New YorkCrossRefMATH
Zurück zum Zitat Bivand RS, Gómez-Rubio V, Rue H (2014) Approximate bayesian inference for spatial econometrics models. Spat Stat 9:146–165MathSciNetCrossRef Bivand RS, Gómez-Rubio V, Rue H (2014) Approximate bayesian inference for spatial econometrics models. Spat Stat 9:146–165MathSciNetCrossRef
Zurück zum Zitat Blangiardo M, Cameletti M (2015) Spatial and spatio-temporal bayesian models with R-INLA. Wiley, ChichesterCrossRefMATH Blangiardo M, Cameletti M (2015) Spatial and spatio-temporal bayesian models with R-INLA. Wiley, ChichesterCrossRefMATH
Zurück zum Zitat Blangiardo M, Cameletti M, Baio G, Rue H (2013) Spatial and spatio-temporal models with R-INLA. Spat Spatio-temporal Epidemiol 4:33–49CrossRef Blangiardo M, Cameletti M, Baio G, Rue H (2013) Spatial and spatio-temporal models with R-INLA. Spat Spatio-temporal Epidemiol 4:33–49CrossRef
Zurück zum Zitat Burrough PA, McDonnell R, McDonnell RA, Lloyd CD (2015) Principles of geographical information systems. Oxford University Press, Oxford Burrough PA, McDonnell R, McDonnell RA, Lloyd CD (2015) Principles of geographical information systems. Oxford University Press, Oxford
Zurück zum Zitat Cameletti M (2015) Stem: spatio-temporal EM. R package version 1.0 Cameletti M (2015) Stem: spatio-temporal EM. R package version 1.0
Zurück zum Zitat Cameletti M, Lindgren F, Simpson D, Rue H (2013) Spatio-temporal modeling of particulate matter concentration through the spde approach. AStA Adv Stat Anal 97(2):109–131MathSciNetCrossRefMATH Cameletti M, Lindgren F, Simpson D, Rue H (2013) Spatio-temporal modeling of particulate matter concentration through the spde approach. AStA Adv Stat Anal 97(2):109–131MathSciNetCrossRefMATH
Zurück zum Zitat Center for International Earth Science Information Network (2005) Poverty mapping project: global subnational prevalence of child malnutrition Center for International Earth Science Information Network (2005) Poverty mapping project: global subnational prevalence of child malnutrition
Zurück zum Zitat Corrado L, Fingleton B (2012) Where is the economics in spatial econometrics? J Reg Sci 52(2):210–239CrossRef Corrado L, Fingleton B (2012) Where is the economics in spatial econometrics? J Reg Sci 52(2):210–239CrossRef
Zurück zum Zitat Cressie N, Huang HC (1999) Classes of nonseparable, spatio-temporal stationary covariance functions. J Am Stat Assoc 94(448):1330–1339MathSciNetCrossRefMATH Cressie N, Huang HC (1999) Classes of nonseparable, spatio-temporal stationary covariance functions. J Am Stat Assoc 94(448):1330–1339MathSciNetCrossRefMATH
Zurück zum Zitat Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, New YorkMATH Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, New YorkMATH
Zurück zum Zitat Elhorst JP (2001) Dynamic models in space and time. Geograph Anal 33(2):119–140CrossRef Elhorst JP (2001) Dynamic models in space and time. Geograph Anal 33(2):119–140CrossRef
Zurück zum Zitat Elhorst JP (2010) Applied spatial econometrics: raising the bar. Spat Econ Anal 5(1):9–28CrossRef Elhorst JP (2010) Applied spatial econometrics: raising the bar. Spat Econ Anal 5(1):9–28CrossRef
Zurück zum Zitat Finazzi F, Fasso A (2014) D-STEM: a software for the analysis and mapping of environmental space-time variables. J Stat Softw 62(6):1–29CrossRef Finazzi F, Fasso A (2014) D-STEM: a software for the analysis and mapping of environmental space-time variables. J Stat Softw 62(6):1–29CrossRef
Zurück zum Zitat Furrer R, Genton MG, Nychka D (2006) Covariance tapering for interpolation of large spatial datasets. J Comput Graph Stat 15(3):502–523MathSciNetCrossRef Furrer R, Genton MG, Nychka D (2006) Covariance tapering for interpolation of large spatial datasets. J Comput Graph Stat 15(3):502–523MathSciNetCrossRef
Zurück zum Zitat Gomez-Rubio V, Bivand RS, Rue H (2017) Estimating spatial econometrics models with integrated nested laplace approximation. arXiv preprint arXiv:170301273 Gomez-Rubio V, Bivand RS, Rue H (2017) Estimating spatial econometrics models with integrated nested laplace approximation. arXiv preprint arXiv:170301273
Zurück zum Zitat Hansen LP (1982) Large sample properties of generalized method of moments estimators. Econ J Econ Soc 50:1029–1054MathSciNetMATH Hansen LP (1982) Large sample properties of generalized method of moments estimators. Econ J Econ Soc 50:1029–1054MathSciNetMATH
Zurück zum Zitat Kelejian HH, Prucha IR (1998) A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autorgegressive disturbance. J Real Estate Fin Econ 17(1):99–121CrossRef Kelejian HH, Prucha IR (1998) A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autorgegressive disturbance. J Real Estate Fin Econ 17(1):99–121CrossRef
Zurück zum Zitat Kelejian HH, Prucha IR (1999) A generalized moments estimator for the autoregressive parameter in a spatial model. Int Econ Rev 40:509–533MathSciNetCrossRef Kelejian HH, Prucha IR (1999) A generalized moments estimator for the autoregressive parameter in a spatial model. Int Econ Rev 40:509–533MathSciNetCrossRef
Zurück zum Zitat Kelejian HH, Prucha IR (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. J Econ 157(1):53–67MathSciNetCrossRefMATH Kelejian HH, Prucha IR (2010) Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. J Econ 157(1):53–67MathSciNetCrossRefMATH
Zurück zum Zitat Lee LF (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72(6):1899–1925MathSciNetCrossRefMATH Lee LF (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72(6):1899–1925MathSciNetCrossRefMATH
Zurück zum Zitat Lee LF, Yu J (2012) QML estimation of spatial dynamic panel data models with time varying spatial weights matrices. Spat Econ Anal 7(1):31–74MathSciNetCrossRef Lee LF, Yu J (2012) QML estimation of spatial dynamic panel data models with time varying spatial weights matrices. Spat Econ Anal 7(1):31–74MathSciNetCrossRef
Zurück zum Zitat LeSage JP (1997) Bayesian estimation of spatial autoregressive models. Int Reg Sci Rev 20(1–2):113–129CrossRef LeSage JP (1997) Bayesian estimation of spatial autoregressive models. Int Reg Sci Rev 20(1–2):113–129CrossRef
Zurück zum Zitat LeSage JP (2008) An introduction to spatial econometrics. Revue d’économie industrielle (3):19–44CrossRef LeSage JP (2008) An introduction to spatial econometrics. Revue d’économie industrielle (3):19–44CrossRef
Zurück zum Zitat LeSage J, Pace RK (2009) Introduction to spatial econometrics. Chapman &Hall/CRC, Boca Raton LeSage J, Pace RK (2009) Introduction to spatial econometrics. Chapman &Hall/CRC, Boca Raton
Zurück zum Zitat Lindgren F, Rue H, Lindström J (2011) An explicit link between gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. J R Stat Soc Series B Stat Methodol 73(4):423–498MathSciNetCrossRefMATH Lindgren F, Rue H, Lindström J (2011) An explicit link between gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. J R Stat Soc Series B Stat Methodol 73(4):423–498MathSciNetCrossRefMATH
Zurück zum Zitat Lindgren F, Rue H et al (2015) Bayesian spatial modelling with R-INLA. J Stat Softw 63(19):1–25CrossRef Lindgren F, Rue H et al (2015) Bayesian spatial modelling with R-INLA. J Stat Softw 63(19):1–25CrossRef
Zurück zum Zitat Martin RJ (1993) Approximations to the determinant term in Gaussian maximum likelihood estimation of some spatial models. Commun Stat Theory Methods 22(1):189–205CrossRefMATH Martin RJ (1993) Approximations to the determinant term in Gaussian maximum likelihood estimation of some spatial models. Commun Stat Theory Methods 22(1):189–205CrossRefMATH
Zurück zum Zitat Matérn B (1960) Spatial variation: meddelanden fran statens skogsforskningsinstitut. Lect Notes Stat 36:21 Matérn B (1960) Spatial variation: meddelanden fran statens skogsforskningsinstitut. Lect Notes Stat 36:21
Zurück zum Zitat Merk MS, Otto P (2019) Estimation of anisotropic, time-varying spatial spillovers of fine particulate matter due to wind direction. Geograph Anal Merk MS, Otto P (2019) Estimation of anisotropic, time-varying spatial spillovers of fine particulate matter due to wind direction. Geograph Anal
Zurück zum Zitat Merk MS, Otto P (2020) Estimation of the spatial weighting matrix for regular lattice data–an adaptive lasso approach with cross-sectional resampling. arXiv:200101532 Merk MS, Otto P (2020) Estimation of the spatial weighting matrix for regular lattice data–an adaptive lasso approach with cross-sectional resampling. arXiv:200101532
Zurück zum Zitat Otto P (2019) spGARCH: an R-package for spatial and spatiotemporal ARCH models. R J 11(2):401–420CrossRef Otto P (2019) spGARCH: an R-package for spatial and spatiotemporal ARCH models. R J 11(2):401–420CrossRef
Zurück zum Zitat Otto P, Steinert R (2018) Estimation of the spatial weighting matrix for spatiotemporal data under the presence of structural breaks. arXiv:181006940 Otto P, Steinert R (2018) Estimation of the spatial weighting matrix for spatiotemporal data under the presence of structural breaks. arXiv:181006940
Zurück zum Zitat Otto P, Schmid W, Garthoff R (2018) Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity. Spat Stat 26:125–145MathSciNetCrossRef Otto P, Schmid W, Garthoff R (2018) Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity. Spat Stat 26:125–145MathSciNetCrossRef
Zurück zum Zitat Pace RK, Barry R (1997) Quick computation of spatial autoregressive estimators. Geograph Anal 29(3):232–247CrossRef Pace RK, Barry R (1997) Quick computation of spatial autoregressive estimators. Geograph Anal 29(3):232–247CrossRef
Zurück zum Zitat Pace RK, LeSage JP (2004) Chebyshev approximation of log-determinants of spatial weight matrices. Comput Stat Data Anal 45(2):179–196MathSciNetCrossRefMATH Pace RK, LeSage JP (2004) Chebyshev approximation of log-determinants of spatial weight matrices. Comput Stat Data Anal 45(2):179–196MathSciNetCrossRefMATH
Zurück zum Zitat Pebesma EJ (2004) Multivariable geostatistics in S: the gstat package. Comput Geosci 30:683–691CrossRef Pebesma EJ (2004) Multivariable geostatistics in S: the gstat package. Comput Geosci 30:683–691CrossRef
Zurück zum Zitat Porcu E, Bevilacqua M, Genton MG (2016) Spatio-temporal covariance and cross-covariance functions of the great circle distance on a sphere. J Am Stat Assoc 111(514):888–898MathSciNetCrossRef Porcu E, Bevilacqua M, Genton MG (2016) Spatio-temporal covariance and cross-covariance functions of the great circle distance on a sphere. J Am Stat Assoc 111(514):888–898MathSciNetCrossRef
Zurück zum Zitat Qu X, Lee Lf, Yu J (2017) QML estimation of spatial dynamic panel data models with endogenous time varying spatial weights matrices. J Econ 197(2):173–201MathSciNetCrossRefMATH Qu X, Lee Lf, Yu J (2017) QML estimation of spatial dynamic panel data models with endogenous time varying spatial weights matrices. J Econ 197(2):173–201MathSciNetCrossRefMATH
Zurück zum Zitat Rue H, Martino S, Chopin N (2009) Approximate bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J R Stat Soc Ser B 71(2):319–392MathSciNetCrossRefMATH Rue H, Martino S, Chopin N (2009) Approximate bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. J R Stat Soc Ser B 71(2):319–392MathSciNetCrossRefMATH
Zurück zum Zitat Smirnov O, Anselin L (2001) Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach. Comput Stat Data Anal 35(3):301–319MathSciNetCrossRefMATH Smirnov O, Anselin L (2001) Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach. Comput Stat Data Anal 35(3):301–319MathSciNetCrossRefMATH
Zurück zum Zitat Smith TE (2009) Estimation bias in spatial models with strongly connected weight matrices. Geograph Anal 41(3):307–332CrossRef Smith TE (2009) Estimation bias in spatial models with strongly connected weight matrices. Geograph Anal 41(3):307–332CrossRef
Zurück zum Zitat Stakhovych S, Bijmolt TH (2009) Specification of spatial models: a simulation study on weights matrices. Papers Reg Sci 88(2):389–408CrossRef Stakhovych S, Bijmolt TH (2009) Specification of spatial models: a simulation study on weights matrices. Papers Reg Sci 88(2):389–408CrossRef
Zurück zum Zitat Tobler WR (1970) A computer movie simulating urban growth in the detroit region. Econ Geograph 46(sup1):234–240 Tobler WR (1970) A computer movie simulating urban growth in the detroit region. Econ Geograph 46(sup1):234–240
Zurück zum Zitat Vetter P, Schmid W, Schwarze R (2014) Efficient approximation of the spatial covariance function for large datasets – analysis of atmospheric CO2 concentrations. J Environ Stat 6(3):1–36 Vetter P, Schmid W, Schwarze R (2014) Efficient approximation of the spatial covariance function for large datasets – analysis of atmospheric CO2 concentrations. J Environ Stat 6(3):1–36
Zurück zum Zitat Zhu J, Huang HC, Reyes PE (2010) On selection of spatial linear models for lattice data. J R Stat Soc Series B Stat Methodol 72(3):389–402MathSciNetCrossRefMATH Zhu J, Huang HC, Reyes PE (2010) On selection of spatial linear models for lattice data. J R Stat Soc Series B Stat Methodol 72(3):389–402MathSciNetCrossRefMATH
Metadaten
Titel
Spatial Statistics, or How to Extract Knowledge from Data
verfasst von
Anna Antoniuk
Miryam S. Merk
Philipp Otto
Copyright-Jahr
2021
DOI
https://doi.org/10.1007/978-3-030-55462-0_15

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