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Geostatistical Binary Data: Models, Properties And Connections


  • Victor De Oliveira

    () (UTSA)


This work considers models for geostatistical data for situations in which the region where the phenomenon of interest varies is partitioned into two disjoint subregions, which is called a binary map. The goals of this work are threefold. First, a review is provided of the classes of models that have been proposed so far for geostatistical binary data as well as a description of their main features. Second, a generalization is provided of a spatial multivariate probit model that eases regression function modeling, interpretation of the regression parameters, and establishing connections with other models. The second-order properties of this model are studied in some detail. Finally, connections between the aforementioned classes of models are established, showing that some of these are reformulations (reparametrizations) of the other models.

Suggested Citation

  • Victor De Oliveira, 2017. "Geostatistical Binary Data: Models, Properties And Connections," Working Papers 0151mss, College of Business, University of Texas at San Antonio.
  • Handle: RePEc:tsa:wpaper:0151mss

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    References listed on IDEAS

    1. Zengri Wang, 2003. "Matching conditional and marginal shapes in binary random intercept models using a bridge distribution function," Biometrika, Biometrika Trust, vol. 90(4), pages 765-775, December.
    2. Oliveira, Victor De, 2000. "Bayesian prediction of clipped Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 299-314, September.
    3. Samuel D. Oman & Victoria Landsman & Yohay Carmel & Ronen Kadmon, 2007. "Analyzing Spatially Distributed Binary Data Using Independent-Block Estimating Equations," Biometrics, The International Biometric Society, vol. 63(3), pages 892-900, September.
    4. 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.
    5. Peter Diggle & Rana Moyeed & Barry Rowlingson & Madeleine Thomson, 2002. "Childhood malaria in the Gambia: a case‐study in model‐based geostatistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 51(4), pages 493-506, October.
    6. Brent A. Coull & Alan Agresti, 2000. "Random Effects Modeling of Multiple Binomial Responses Using the Multivariate Binomial Logit-Normal Distribution," Biometrics, The International Biometric Society, vol. 56(1), pages 73-80, March.
    7. Hao Zhang, 2002. "On Estimation and Prediction for Spatial Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 58(1), pages 129-136, March.
    8. Yun Bai & Jian Kang & Peter X.-K. Song, 2014. "Efficient pairwise composite likelihood estimation for spatial-clustered data," Biometrics, The International Biometric Society, vol. 70(3), pages 661-670, September.
    9. Jing, Liang & De Oliveira, Victor, 2015. "geoCount: An R Package for the Analysis of Geostatistical Count Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i11).
    10. Laura Boehm & Brian J. Reich & Dipankar Bandyopadhyay, 2013. "Bridging Conditional and Marginal Inference for Spatially Referenced Binary Data," Biometrics, The International Biometric Society, vol. 69(2), pages 545-554, June.
    11. Ole F. Christensen & Rasmus Waagepetersen, 2002. "Bayesian Prediction of Spatial Count Data Using Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 58(2), pages 280-286, June.
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    More about this item


    Clipped Gaussian random field; Gaussian copula model; Generalized linear mixed model; Indicator kriging; Multivariate probit model.;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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