IDEAS home Printed from https://ideas.repec.org/p/ipe/ipetds/0116.html
   My bibliography  Save this paper

Multivariate Spatial Regression Models

Author

Listed:
  • Dani Gamerman
  • Ajax R. B. Moreira

Abstract

This paper describes the inference procedures required to perform Bayesian inference to some multivariate econometric models. These models have a spatial component built into commonly used multivariate models. In particular, the seemingly unrelated regression and vector autoregressive models are addressed and extended to accommodate for spatial dependence. Inference procedures are based on a variety of simulation-based schemes designed to obtain samples from the posterior distribution of model parameters. They are also used to provide a basis to forecast new observations. Este artigo descreve os procedimentos para a inferência bayesiana de modelos multivariados. Esses modelos incluem uma componente espacial que é comumente utilizada em modelos econômicos. Em particular, os modelos de regressões aparentemente não-relacionadas Sure e vetores auto-regressivos são estendidos para acomodar a dependência espacial. Os procedimentos de inferência são baseados em uma variedade de esquemas de simulação desenhados para obter amostras da distribuição a posteriori dos parâmetros do modelo. Estes podem ser utilizados para prover também estimativas da previsão de novas observações.

Suggested Citation

  • Dani Gamerman & Ajax R. B. Moreira, 2015. "Multivariate Spatial Regression Models," Discussion Papers 0116, Instituto de Pesquisa Econômica Aplicada - IPEA.
  • Handle: RePEc:ipe:ipetds:0116
    as

    Download full text from publisher

    File URL: http://www.ipea.gov.br/portal/images/stories/PDFs/TDs/ingles/dp_116.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pace, R. Kelley & Barry, Ronald & Gilley, Otis W. & Sirmans, C. F., 2000. "A method for spatial-temporal forecasting with an application to real estate prices," International Journal of Forecasting, Elsevier, vol. 16(2), pages 229-246.
    2. Mardia, K. V., 1988. "Multi-dimensional multivariate Gaussian Markov random fields with application to image processing," Journal of Multivariate Analysis, Elsevier, vol. 24(2), pages 265-284, February.
    3. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    4. Gamerman, Dani & Moreira, Ajax R. B. & Rue, Havard, 2003. "Space-varying regression models: specifications and simulation," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 513-533, March.
    5. Andersen, Lykke E. & Granger, Clive W.J. & Reis, Eustáquio J., 1997. "A Random Coefficient Var Transition Model of the Changes in Land Use in the Brazilian Amazon," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 17(1), May.
    6. P. Damlen & J. Wakefield & S. Walker, 1999. "Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 331-344, April.
    7. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gamerman, Dani & Moreira, Ajax R. B., 2004. "Multivariate spatial regression models," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 262-281, November.
    2. Håvard Rue & Ingelin Steinsland & Sveinung Erland, 2004. "Approximating hidden Gaussian Markov random fields," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 877-892, November.
    3. Gamerman, Dani & Moreira, Ajax R. B. & Rue, Havard, 2003. "Space-varying regression models: specifications and simulation," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 513-533, March.
    4. Hernández-Mireles, C., 2010. "Finding the Influentials that Drive the Diffusion of New Technologies," ERIM Report Series Research in Management ERS-2010-023-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    5. Ying C. MacNab, 2018. "Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 497-541, September.
    6. Alexandra Schmidt & Ajax Moreira & Steven Helfand & Thais Fonseca, 2009. "Spatial stochastic frontier models: accounting for unobserved local determinants of inefficiency," Journal of Productivity Analysis, Springer, vol. 31(2), pages 101-112, April.
    7. Ferreira, Marco A.R. & De Oliveira, Victor, 2007. "Bayesian reference analysis for Gaussian Markov random fields," Journal of Multivariate Analysis, Elsevier, vol. 98(4), pages 789-812, April.
    8. Bolin, David & Lindström, Johan & Eklundh, Lars & Lindgren, Finn, 2009. "Fast estimation of spatially dependent temporal vegetation trends using Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2885-2896, June.
    9. Peter Congdon, 2010. "A Multilevel Model for Comorbid Outcomes: Obesity and Diabetes in the US," IJERPH, MDPI, vol. 7(2), pages 1-20, January.
    10. Areti Boulieri & Silvia Liverani & Kees Hoogh & Marta Blangiardo, 2017. "A space–time multivariate Bayesian model to analyse road traffic accidents by severity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(1), pages 119-139, January.
    11. Xiaoping Jin & Bradley P. Carlin & Sudipto Banerjee, 2005. "Generalized Hierarchical Multivariate CAR Models for Areal Data," Biometrics, The International Biometric Society, vol. 61(4), pages 950-961, December.
    12. Peter Congdon, 2014. "Estimating life expectancies for US small areas: a regression framework," Journal of Geographical Systems, Springer, vol. 16(1), pages 1-18, January.
    13. Ying C. MacNab, 2018. "Rejoinder on: Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 554-569, September.
    14. Vinicius Mayrink & Dani Gamerman, 2009. "On computational aspects of Bayesian spatial models: influence of the neighboring structure in the efficiency of MCMC algorithms," Computational Statistics, Springer, vol. 24(4), pages 641-669, December.
    15. Congdon, P., 2007. "Bayesian modelling strategies for spatially varying regression coefficients: A multivariate perspective for multiple outcomes," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2586-2601, February.
    16. Xiaoping Jin & Sudipto Banerjee & Bradley P. Carlin, 2007. "Order‐free co‐regionalized areal data models with application to multiple‐disease mapping," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 817-838, November.
    17. Ying C. MacNab, 2023. "On coregionalized multivariate Gaussian Markov random fields: construction, parameterization, and Bayesian estimation and inference," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 263-293, March.
    18. Wheeler, David C. & Hickson, DeMarc A. & Waller, Lance A., 2010. "Assessing local model adequacy in Bayesian hierarchical models using the partitioned deviance information criterion," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1657-1671, June.
    19. F. S. Nathoo & C. B. Dean, 2008. "Spatial Multistate Transitional Models for Longitudinal Event Data," Biometrics, The International Biometric Society, vol. 64(1), pages 271-279, March.
    20. Stefan Lang & Samson B. Adebayo & Ludwig Fahrmeir & Winfried J. Steiner, 2003. "Bayesian Geoadditive Seemingly Unrelated Regression," Computational Statistics, Springer, vol. 18(2), pages 263-292, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ipe:ipetds:0116. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Fabio Schiavinatto (email available below). General contact details of provider: https://edirc.repec.org/data/ipeaabr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.