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A clipped latent variable model for spatially correlated ordered categorical data

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  • Higgs, Megan Dailey
  • Hoeting, Jennifer A.
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    Abstract

    We propose a model for a point-referenced spatially correlated ordered categorical response and methodology for inference. Models and methods for spatially correlated continuous response data are widespread, but models for spatially correlated categorical data, and especially ordered multi-category data, are less developed. Bayesian models and methodology have been proposed for the analysis of independent and clustered ordered categorical data, and also for binary and count point-referenced spatial data. We combine and extend these methods to describe a Bayesian model for point-referenced (as opposed to lattice) spatially correlated ordered categorical data. We include simulation results and show that our model offers superior predictive performance as compared to a non-spatial cumulative probit model and a more standard Bayesian generalized linear spatial model. We demonstrate the usefulness of our model in a real-world example to predict ordered categories describing stream health within the state of Maryland.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-4YJ4N4C-3/2/a8f83c2bc094ab183fb974e759741145
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 54 (2010)
    Issue (Month): 8 (August)
    Pages: 1999-2011

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    Handle: RePEc:eee:csdana:v:54:y:2010:i:8:p:1999-2011

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Bayesian Ordinal Benthic IBI Generalized linear mixed models;

    References

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    1. Vivekananda Roy & James P. Hobert, 2007. "Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 607-623.
    2. Jo Eidsvik & Sara Martino & H�Vard Rue, 2009. "Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 36(1), pages 1-22.
    3. Li, Yonghai & Schafer, Daniel W., 2008. "Likelihood analysis of the multivariate ordinal probit regression model for repeated ordinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3474-3492, March.
    4. Oliveira, Victor De, 2000. "Bayesian prediction of clipped Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 299-314, September.
    5. Ole Olesen & N. Petersen, 2003. "Introduction," Journal of Productivity Analysis, Springer, vol. 20(3), pages 237-241, November.
    6. E. E. Kammann & M. P. Wand, 2003. "Geoadditive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 1-18.
    7. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(1), pages 11-30, March.
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