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Data augmentation and parameter expansion for independent or spatially correlated ordinal data

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  • Schliep, Erin M.
  • Hoeting, Jennifer A.

Abstract

Data augmentation and parameter expansion can lead to improved iterative sampling algorithms for Markov chain Monte Carlo (MCMC). Data augmentation allows for simpler and more feasible simulation from a posterior distribution. Parameter expansion accelerates convergence of iterative sampling algorithms by increasing the parameter space. Data augmentation and parameter-expanded data augmentation MCMC algorithms are proposed for fitting probit models for independent ordinal response data. The algorithms are extended for fitting probit linear mixed models for spatially correlated ordinal data. The effectiveness of data augmentation and parameter-expanded data augmentation is illustrated using the probit model and ordinal response data, however, the approach can be used broadly across model and data types.

Suggested Citation

  • Schliep, Erin M. & Hoeting, Jennifer A., 2015. "Data augmentation and parameter expansion for independent or spatially correlated ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 1-14.
    • Handle: RePEc:eee:csdana:v:90:y:2015:i:c:p:1-14
    DOI: 10.1016/j.csda.2015.03.020
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    References listed on IDEAS

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    1. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    2. Imai, Kosuke & van Dyk, David A., 2005. "A Bayesian analysis of the multinomial probit model using marginal data augmentation," Journal of Econometrics, Elsevier, vol. 124(2), pages 311-334, February.
    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.
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    Cited by:

    1. Walder, Adam & Hanks, Ephraim M., 2020. "Bayesian analysis of spatial generalized linear mixed models with Laplace moving average random fields," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    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. Sahar Zarmehri & Ephraim M. Hanks & Lin Lin, 2021. "A Sample Covariance-Based Approach For Spatial Binary Data," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(2), pages 220-249, June.

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