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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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    Cited by:

    1. 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.
    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. Kathryn M. Irvine & T. J. Rodhouse & Ilai N. Keren, 2016. "Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 619-640, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

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