IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i12p4421-4432.html
   My bibliography  Save this article

Parameter estimation in the spatial auto-logistic model with working independent subblocks

Author

Listed:
  • Lim, Johan
  • Lee, Kiseop
  • Yu, Donghyeon
  • Liu, Haiyan
  • Sherman, Michael

Abstract

We propose an approximation to the likelihood function with independent sub-blocks in the spatial auto-logistic model. The entire data is subdivided into many sub-blocks which are treated as independent from each other. The approximate maximum likelihood estimator, called maximum block independent likelihood estimator, is shown to have the same asymptotic distribution as that of the maximum likelihood estimator in the Ising model, a special case of the spatial auto-logistic model. The computational load for the proposed estimator is much lighter than that for the maximum likelihood estimator, and decreases geometrically as the size of a sub-block decreases. Also, limited simulation studies show that, in finite samples, the maximum block independent likelihood estimator performs as well as the maximum likelihood estimator in mean squared error. We apply our procedure to an estimation and a test of spatial dependence in the longleaf pine tree data in Cressie (1993) and the aerial image data in Pyun et al. (2007). Finally, we discuss the extension of the proposed estimator to other spatial auto-regressive models.

Suggested Citation

  • Lim, Johan & Lee, Kiseop & Yu, Donghyeon & Liu, Haiyan & Sherman, Michael, 2012. "Parameter estimation in the spatial auto-logistic model with working independent subblocks," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4421-4432.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4421-4432
    DOI: 10.1016/j.csda.2012.03.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312001399
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.03.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fuchun Huang & Yosihiko Ogata, 2002. "Generalized Pseudo-Likelihood Estimates for Markov Random Fields on Lattice," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 1-18, March.
    2. Caragea, Petruta C. & Smith, Richard L., 2007. "Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1417-1440, August.
    3. Anselin, Luc & Tam Cho, Wendy K., 2002. "Spatial Effects and Ecological Inference," Political Analysis, Cambridge University Press, vol. 10(3), pages 276-297, July.
    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. Lim, Johan & Wang, Xinlei & Sherman, Michael, 2007. "An adjustment for edge effects using an augmented neighborhood model in the spatial auto-logistic model," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3679-3688, May.
    2. Breandán Ó'hUallacháin, 2008. "Regional growth transition clubs in the United States," Papers in Regional Science, Wiley Blackwell, vol. 87(1), pages 33-53, March.
    3. Acosta, Jonathan & Alegría, Alfredo & Osorio, Felipe & Vallejos, Ronny, 2021. "Assessing the effective sample size for large spatial datasets: A block likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    4. Bhat, Chandra R. & Sener, Ipek N. & Eluru, Naveen, 2010. "A flexible spatially dependent discrete choice model: Formulation and application to teenagers' weekday recreational activity participation," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 903-921, September.
    5. Cem Ertur & Julie Le Gallo & Catherine Baumont, 2006. "The European Regional Convergence Process, 1980-1995: Do Spatial Regimes and Spatial Dependence Matter?," International Regional Science Review, , vol. 29(1), pages 3-34, January.
    6. Stanislav Anatolyev & Renat Khabibullin & Artem Prokhorov, 2012. "Reconstructing high dimensional dynamic distributions from distributions of lower dimension," Working Papers 12003, Concordia University, Department of Economics.
    7. Judge, George G. & Miller, Douglas J. & Cho, Wendy K. T., 2003. "An Information Theoretic Approach to Ecological Estimation and Inference," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7h03r00q, Department of Agricultural & Resource Economics, UC Berkeley.
    8. Erhardt, Tobias Michael & Czado, Claudia & Schepsmeier, Ulf, 2015. "Spatial composite likelihood inference using local C-vines," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 74-88.
    9. Zachary Elkins & Beth Simmons, 2005. "On Waves, Clusters, and Diffusion: A Conceptual Framework," The ANNALS of the American Academy of Political and Social Science, , vol. 598(1), pages 33-51, March.
    10. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    11. Judge, George G. & Miller, Douglas J. & Cho, Wendy K. T., 2003. "An Information Theoretic Approach to Ecological Estimation and Inference," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7h03r00q, Department of Agricultural & Resource Economics, UC Berkeley.
    12. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    13. Jinyuan Chang & Wen Zhou & Wen-Xin Zhou & Lan Wang, 2017. "Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering," Biometrics, The International Biometric Society, vol. 73(1), pages 31-41, March.
    14. Baodong Liu, 2007. "EI Extended Model and the Fear of Ecological Fallacy," Sociological Methods & Research, , vol. 36(1), pages 3-25, August.
    15. Longhi, Simonetta & Nijkamp, Peter, 2006. "Forecasting regional labor market developments under spatial heterogeneity and spatial correlation," Serie Research Memoranda 0015, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    16. Jun, Mikyoung, 2014. "Matérn-based nonstationary cross-covariance models for global processes," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 134-146.
    17. Sergio J. Rey & Luc Anselin & David C. Folch & Daniel Arribas-Bel & Myrna L. Sastré Gutiérrez & Lindsey Interlante, 2011. "Measuring Spatial Dynamics in Metropolitan Areas," Economic Development Quarterly, , vol. 25(1), pages 54-64, February.
    18. repec:asg:wpaper:1028 is not listed on IDEAS
    19. Simonetta Longhi & Peter Nijkamp, 2005. "Forecasting Regional Labour Market Developments Under Spatial Heterogeneity and Spatial Autocorrelation," Tinbergen Institute Discussion Papers 05-041/3, Tinbergen Institute.
    20. Anselin, Luc, 2002. "Under the hood : Issues in the specification and interpretation of spatial regression models," Agricultural Economics, Blackwell, vol. 27(3), pages 247-267, November.
    21. Katherine J. Curtis, 2012. "Book Review: Spatial Regression Models," Sociological Methods & Research, , vol. 41(4), pages 671-674, November.

    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:eee:csdana:v:56:y:2012:i:12:p:4421-4432. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.