IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v27y2018i1d10.1007_s10260-017-0391-1.html
   My bibliography  Save this article

Two-scale spatial models for binary data

Author

Listed:
  • Cécile Hardouin

    (MODAL’X, Université Paris Nanterre)

  • Noel Cressie

    (University of Wollongong)

Abstract

A spatial lattice model for binary data is constructed from two spatial scales linked through conditional probabilities. A coarse grid of lattice locations is specified, and all remaining locations (which we call the background) capture fine-scale spatial dependence. Binary data on the coarse grid are modelled with an autologistic distribution, conditional on the binary process on the background. The background behaviour is captured through a hidden Gaussian process after a logit transformation on its Bernoulli success probabilities. The likelihood is then the product of the (conditional) autologistic probability distribution and the hidden Gaussian–Bernoulli process. The parameters of the new model come from both spatial scales. A series of simulations illustrates the spatial-dependence properties of the model and likelihood-based methods are used to estimate its parameters. Presence–absence data of corn borers in the roots of corn plants are used to illustrate how the model is fitted.

Suggested Citation

  • Cécile Hardouin & Noel Cressie, 2018. "Two-scale spatial models for binary data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 1-24, March.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:1:d:10.1007_s10260-017-0391-1
    DOI: 10.1007/s10260-017-0391-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-017-0391-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-017-0391-1?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. Kang, Emily L. & Cressie, Noel, 2011. "Bayesian Inference for the Spatial Random Effects Model," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 972-983.
    2. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
    3. Wenceslao González‐Manteiga & Rosa M. Crujeiras & Matthias Katzfuss & Noel Cressie, 2012. "Bayesian hierarchical spatio‐temporal smoothing for very large datasets," Environmetrics, John Wiley & Sons, Ltd., vol. 23(1), pages 94-107, February.
    4. Sangkil Moon & Gary J. Russell, 2008. "Predicting Product Purchase from Inferred Customer Similarity: An Autologistic Model Approach," Management Science, INFORMS, vol. 54(1), pages 71-82, January.
    5. Raffaella Calabrese & Johan A. Elkink, 2016. "Estimating Binary Spatial Autoregressive Models for Rare Events," Advances in Econometrics, in: Spatial Econometrics: Qualitative and Limited Dependent Variables, volume 37, pages 145-166, Emerald Group Publishing Limited.
    6. Vivekananda Roy & Evangelos Evangelou & Zhengyuan Zhu, 2016. "Efficient estimation and prediction for the Bayesian binary spatial model with flexible link functions," Biometrics, The International Biometric Society, vol. 72(1), pages 289-298, March.
    7. James P. LeSage & R. Kelley Pace & Nina Lam & Richard Campanella & Xingjian Liu, 2011. "New Orleans business recovery in the aftermath of Hurricane Katrina," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(4), pages 1007-1027, October.
    8. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    9. Christopher Wikle & Mevin Hooten, 2010. "A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 417-451, November.
    10. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    11. Christopher Wikle & Mevin Hooten, 2010. "Rejoinder on: A general science-based framework for dynamical spatio-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 466-468, November.
    12. Lee, Jaehyung & Kaiser, Mark S. & Cressie, Noel, 2001. "Multiway Dependence in Exponential Family Conditional Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(2), pages 171-190, November.
    13. Schlather, Martin & Malinowski, Alexander & Menck, Peter J. & Oesting, Marco & Strokorb, Kirstin, 2015. "Analysis, Simulation and Prediction of Multivariate Random Fields with Package RandomFields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i08).
    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. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    2. Matthias Katzfuss, 2017. "A Multi-Resolution Approximation for Massive Spatial Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 201-214, January.
    3. K. Shuvo Bakar & Nicholas Biddle & Philip Kokic & Huidong Jin, 2020. "A Bayesian spatial categorical model for prediction to overlapping geographical areas in sample surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 535-563, February.
    4. Ephraim M. Hanks, 2017. "Modeling Spatial Covariance Using the Limiting Distribution of Spatio-Temporal Random Walks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 497-507, April.
    5. Sameh Abdulah & Yuxiao Li & Jian Cao & Hatem Ltaief & David E. Keyes & Marc G. Genton & Ying Sun, 2023. "Large‐scale environmental data science with ExaGeoStatR," Environmetrics, John Wiley & Sons, Ltd., vol. 34(1), February.
    6. Huang Huang & Stefano Castruccio & Marc G. Genton, 2022. "Forecasting high‐frequency spatio‐temporal wind power with dimensionally reduced echo state networks," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(2), pages 449-466, March.
    7. Philip A. White & Durban G. Keeler & Daniel Sheanshang & Summer Rupper, 2022. "Improving piecewise linear snow density models through hierarchical spatial and orthogonal functional smoothing," Environmetrics, John Wiley & Sons, Ltd., vol. 33(5), August.
    8. Esmail Yarali & Firoozeh Rivaz, 2020. "Incorporating covariate information in the covariance structure of misaligned spatial data," Environmetrics, John Wiley & Sons, Ltd., vol. 31(6), September.
    9. Margaret R Donald & Kerrie L Mengersen & Rick R Young, 2015. "A Four Dimensional Spatio-Temporal Analysis of an Agricultural Dataset," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-22, October.
    10. Wilson J. Wright & Peter N. Neitlich & Alyssa E. Shiel & Mevin B. Hooten, 2022. "Mechanistic spatial models for heavy metal pollution," Environmetrics, John Wiley & Sons, Ltd., vol. 33(8), December.
    11. Matthias Katzfuss & Joseph Guinness & Wenlong Gong & Daniel Zilber, 2020. "Vecchia Approximations of Gaussian-Process Predictions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 383-414, September.
    12. Zammit-Mangion, Andrew & Rougier, Jonathan, 2018. "A sparse linear algebra algorithm for fast computation of prediction variances with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 116-130.
    13. Marchetti, Yuliya & Nguyen, Hai & Braverman, Amy & Cressie, Noel, 2018. "Spatial data compression via adaptive dispersion clustering," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 138-153.
    14. Aaron Osgood‐Zimmerman & Jon Wakefield, 2023. "A Statistical Review of Template Model Builder: A Flexible Tool for Spatial Modelling," International Statistical Review, International Statistical Institute, vol. 91(2), pages 318-342, August.
    15. Jonathan Bradley & Noel Cressie & Tao Shi, 2015. "Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 1-28, March.
    16. Hang Zhang & Yong Liu & Dongyang Yang & Guanpeng Dong, 2022. "PM 2.5 Concentrations Variability in North China Explored with a Multi-Scale Spatial Random Effect Model," IJERPH, MDPI, vol. 19(17), pages 1-14, August.
    17. Matthew J. Heaton & Abhirup Datta & Andrew O. Finley & Reinhard Furrer & Joseph Guinness & Rajarshi Guhaniyogi & Florian Gerber & Robert B. Gramacy & Dorit Hammerling & Matthias Katzfuss & Finn Lindgr, 2019. "A Case Study Competition Among Methods for Analyzing Large Spatial Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 398-425, September.
    18. Matthew Bonas & Christopher K. Wikle & Stefano Castruccio, 2024. "Calibrated forecasts of quasi‐periodic climate processes with deep echo state networks and penalized quantile regression," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    19. Furrer, Reinhard & Bachoc, François & Du, Juan, 2016. "Asymptotic properties of multivariate tapering for estimation and prediction," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 177-191.
    20. Morales-Oñate, Víctor & Crudu, Federico & Bevilacqua, Moreno, 2021. "Blockwise Euclidean likelihood for spatio-temporal covariance models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 176-201.

    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:spr:stmapp:v:27:y:2018:i:1:d:10.1007_s10260-017-0391-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.