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A practical approach for assessing the effect of grouping in hierarchical spatio-temporal models

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Abstract

Hierarchical spatio-temporal models allow for the consideration and estimation of many sources of variability. A general spatio-temporal model can be written as the sum of a spatio-temporal trend and a spatio-temporal random effect. When spatial locations are considered to be homogeneous with respect to some exogenous features, the groups of locations may share a common spatial domain. Differences between groups can be highlighted both in the large-scale, spatio-temporal component and in the spatio-temporal dependence structure. When these differences are not included in the model specification, model performance and spatio-temporal predictions may be weak. This paper proposes a method for evaluating and comparing models that progressively include group differences. Hierarchical modeling under a Bayesian perspective is followed, allowing flexible models and the statistical assessment of results based on posterior predictive distributions. This procedure is applied to tropospheric ozone data in the Italian Emilia–Romagna region for 2001, where 30 monitoring sites are classified according to environmental laws into two groups by their relative position with respect to traffic emissions.

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References

  • Banerjee, S., Carlin, B.P., Gelfand, A.E.: Hierarchical Modeling and Analysis for Spatial Data. Chapman and Hall/CRC Press, Boca Raton (2004)

    MATH  Google Scholar 

  • Bruno, F., Cocchi, D.: Seasonal spatio-temporal non-separability: the case of ozone in Emilia Romagna. In: Cafarelli, B., Jona Lasinio, G., Pollice, A. (eds.) SPATIAL—Spatial Data Methods for Environmental and Ecological Processes, Book of Abstracts. WIP Edizioni, Bari (2006). ISBN 88-8459-078-7

    Google Scholar 

  • Christakos, G.: Modern Spatiotemporal Geostatistics. Oxford University Press, Oxford (2000)

    Google Scholar 

  • Cocchi, D., Bruno, F.: Considering groups in the statistical modeling of spatio-temporal data. Statistica 70(4), 511–527 (2010)

    Google Scholar 

  • Cocchi, D., Greco, F., Trivisano, C.: Displaced calibration of PM10 measurements using spatio-temporal models. Statistica 66, 127–138 (2006)

    MathSciNet  MATH  Google Scholar 

  • Cocchi, D., Greco, F., Trivisano, C.: Hierarchical space-time modelling of PM10 pollution. Atmos. Environ. 41, 532–542 (2007)

    Article  Google Scholar 

  • D.M.A.: Attivazione di un sistema di sorveglianza di inquinamento da Ozono. In Italian (16/05/1996) http://isprambiente.gov.it/site/_files/aria/DM16_maggio1996.pdf

  • EEA: Air pollution by ozone across Europe during summer 2010. EEA Technical report No 6/2011, European Environment Agency (2011). http://www.eea.europa.eu/pubblications/air-pollution-by-ozone-across

  • Finkenstädt, B.F., Held, L., Isham, V.: Statistical Methods for Spatio-Temporal Systems. CRC Press/Chapman and Hall, Boca Raton (2007)

    MATH  Google Scholar 

  • Fotheringham, A.S., Charlton, M., Brunsdon, C.: Geographically weighted regression: a natural evolution of the expansion method for spatial data analysis. Environ. Plan. 30, 1905–1927 (1998)

    Article  Google Scholar 

  • Gelfand, A.E., Ghosh, S.K.: Model Choice: A minimum Posterior Predictive Loss Approach. Biometrika 85, 1–11 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • Gneiting, T., Genton, M.G., Guttorp, P.: Geostatistical space-time models, stationarity, separability and full symmetry. In: Finkenstädt, B.F., Held, L., Isham, V. (eds.) Statistical Methods for Spatio-Temporal Systems, pp. 151–175. CRC Press/Chapman and Hall, Boca Raton (2007)

    Google Scholar 

  • Jona Lasinio, G., Orasi, A., Divino, F., Conti, P.L.: Statistical contributions to the analysis of environmental risks along the coastline. In: Società Italiana di Statistica—rischio e previsione, Venezia, 6–8 June, pp. 255–262 (2007)

    Google Scholar 

  • Laud, P.W., Ibrahim, J.G.: Predictive Model Selection. J. R. Stat. Soc. B 57, 247–262 (1995)

    MathSciNet  MATH  Google Scholar 

  • Lee, D., Shaddick, G.: Time-varying coefficient models for the analysis of air pollution and health outcome data. Biometrics 63, 1253–1261 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Pollice, A., Jona Lasinio, G.: Spatiotemporal analysis of the PM10 concentration over the Taranto area. Environ. Monit. Assess. 162(1–4), 177–190 (2010)

    Article  Google Scholar 

  • Pollice, A., Jona Lasinio, G.: Two approaches to imputation and adjustment of air quality data from a composite monitoring network. J. Data Sci. 7, 43–59 (2009)

    Google Scholar 

  • Regional Environmental Center: The ambient air ozone directive. In: Handbook on the Implementation of EC Environmental Legislation, pp. 67–70 of Sect. 3: Air Quality Legislation. Regional Environmental Center for Central and Eastern Europe and UBA (2008). http://ec.europa.eu/environment/enlarg/handbook/handbook.htm

  • Sahu, S.K., Gelfand, A.E., Holland, D.M.: High resolution space-time ozone modeling for assessing trends. J. Am. Stat. Assoc. 102, 1221–1234 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Sahu, S.K., Nicolis, O.: An evaluation of European air pollution regulations for particulate matter monitored from a heterogeneous network. Environmetrics 20, 943–961 (2009)

    MathSciNet  Google Scholar 

  • Sang, H., Gelfand, A.E.: Hierarchical modeling for extreme values observed over space and time. Environ. Ecol. Stat. 16, 407–426 (2009)

    Article  MathSciNet  Google Scholar 

  • Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Van der Linde, A.: Bayesian measures of model complexity and fit (with discussion). J. R. Stat. Soc., Ser. B, Stat. Methodol. 64, 583–616 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Spiegelhalter, D.J., Thomas, A., Best, N.: WinBugs: Bayesian Inference Using Gibbs Sampler, Manual Version 1.2. Imperial College/Medical Research Council Biostatistics Unit, London/Cambridge (1998)

    Google Scholar 

  • Wang, J., Christakos, G., Hu, M.-G.: Modeling spatial means of surfaces with stratified nonhomogeneity. IEEE Trans. Geosci. Remote Sens. 47, 4167–4174 (2009)

    Article  Google Scholar 

  • Wikle, C.K., Berliner, L.M., Cressie, N.: Hierarchical Bayesian space-time models. Environ. Ecol. Stat. 5, 117–154 (1998)

    Article  Google Scholar 

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Acknowledgements

The research work underlying this paper was funded by a 2008 grant (project no. 2008CEFF37_001, sector: Economics and Statistics) for research projects of national interest provided by the Italian Ministry of Universities and Scientific and Technological Research. We thank two anonymous referees for their useful comments that strongly improved the paper.

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Correspondence to Francesca Bruno.

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Bruno, F., Cocchi, D. & Paci, L. A practical approach for assessing the effect of grouping in hierarchical spatio-temporal models. AStA Adv Stat Anal 97, 93–108 (2013). https://doi.org/10.1007/s10182-012-0193-6

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