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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.

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.

Suggested Citation

  • Higgs, Megan Dailey & Hoeting, Jennifer A., 2010. "A clipped latent variable model for spatially correlated ordered categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1999-2011, August.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:8:p:1999-2011
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    References listed on IDEAS

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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, September.
    2. Jo Eidsvik & Sara Martino & Håvard 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, March.
    3. Oliveira, Victor De, 2000. "Bayesian prediction of clipped Gaussian random fields," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 299-314, September.
    4. 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.
    5. N. G. Best & D. J. Spiegelhalter & A. Thomas & C. E. G. Brayne, 1996. "Bayesian Analysis of Realistically Complex Models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(2), pages 323-342, March.
    6. J. Zhu & J. C. Eickhoff & P. Yan, 2005. "Generalized Linear Latent Variable Models for Repeated Measures of Spatially Correlated Multivariate Data," Biometrics, The International Biometric Society, vol. 61(3), pages 674-683, September.
    7. 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.
    8. 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, January.
    9. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 11-30, March.
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    Cited by:

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    2. Lynsie R. Warr & Matthew J. Heaton & William F. Christensen & Philip A. White & Summer B. Rupper, 2023. "Distributional Validation of Precipitation Data Products with Spatially Varying Mixture Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 99-116, March.
    3. Berrett, Candace & Calder, Catherine A., 2012. "Data augmentation strategies for the Bayesian spatial probit regression model," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 478-490.
    4. Schliep Erin M. & Schafer Toryn L. J. & Hawkey Matthew, 2021. "Distributed lag models to identify the cumulative effects of training and recovery in athletes using multivariate ordinal wellness data," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(3), pages 241-254, September.
    5. Megan D. Higgs & Jay M. Ver Hoef, 2012. "Discretized and Aggregated: Modeling Dive Depth of Harbor Seals from Ordered Categorical Data with Temporal Autocorrelation," Biometrics, The International Biometric Society, vol. 68(3), pages 965-974, September.
    6. Matthew Heiner & Matthew J. Heaton & Benjamin Abbott & Philip White & Camille Minaudo & Rémi Dupas, 2023. "Model-Based Clustering of Trends and Cycles of Nitrate Concentrations in Rivers Across France," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 74-98, March.
    7. L. L. Henn, 2022. "Limitations and performance of three approaches to Bayesian inference for Gaussian copula regression models of discrete data," Computational Statistics, Springer, vol. 37(2), pages 909-946, April.

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