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Bayesian estimation of order-restricted and unrestricted association models

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  • Demirhan, Haydar

Abstract

Association models include score parameters to multiplicatively represent the hierarchy between the levels of the considered ordinal factor. If order restrictions are placed on the scores, an estimation problem becomes a non-linear and restricted estimation, which is somewhat problematic with respect to the classical approaches. In this article, we consider the Bayesian estimation of the scores and other parameters of an association model both with and without order restrictions. We propose the use of a previously introduced multivariate prior in the unrestricted case and an order statistics approach in the order-restricted case. The advantages of using these prior structures are that we are able to consider the correlation patterns arising from the hierarchy between the levels of ordinal factors, there is no violation of the exchangeability assumption, the approaches are general for any size of contingency table, and the posterior inferences are easily derived. The proposed approaches are applied to both a previously analyzed popular two-way contingency table and a three-way contingency table. Smaller standard deviations than those of previous analyses are obtained, and a new best-fitting model is identified for the two-way table.

Suggested Citation

  • Demirhan, Haydar, 2013. "Bayesian estimation of order-restricted and unrestricted association models," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 109-126.
    • Handle: RePEc:eee:jmvana:v:121:y:2013:i:c:p:109-126
    DOI: 10.1016/j.jmva.2013.06.008
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    References listed on IDEAS

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    1. Francisca Galindo-Garre & Jeroen Vermunt, 2004. "The order-restricted association model: Two estimation algorithms and issues in testing," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 641-654, December.
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    3. Michael J. Daniels, 2002. "Bayesian analysis of covariance matrices and dynamic models for longitudinal data," Biometrika, Biometrika Trust, vol. 89(3), pages 553-566, August.
    4. Haydar Demirhan & Canan Hamurkaroglu, 2008. "Bayesian estimation of log odds ratios from R × C and 2 × 2 × K contingency tables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(4), pages 405-424, November.
    5. G. Iliopoulos & M. Kateri & I. Ntzoufras, 2009. "Bayesian Model Comparison for the Order Restricted RC Association Model," Psychometrika, Springer;The Psychometric Society, vol. 74(4), pages 561-587, December.
    6. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
    7. Zhen Chen & David B. Dunson, 2003. "Random Effects Selection in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 59(4), pages 762-769, December.
    8. Lawrence Hubert, 1974. "A note on Freeman's measure of association for relating an ordered to an unordered factor," Psychometrika, Springer;The Psychometric Society, vol. 39(4), pages 517-520, December.
    9. Iliopoulos, G. & Kateri, M. & Ntzoufras, I., 2007. "Bayesian estimation of unrestricted and order-restricted association models for a two-way contingency table," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4643-4655, May.
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    Cited by:

    1. Mani Suleiman & Haydar Demirhan & Leanne Boyd & Federico Girosi & Vural Aksakalli, 2019. "Bayesian logistic regression approaches to predict incorrect DRG assignment," Health Care Management Science, Springer, vol. 22(2), pages 364-375, June.
    2. Berthold-Georg Englert & Michael Evans & Gun Ho Jang & Hui Khoon Ng & David Nott & Yi-Lin Seah, 2021. "Checking for model failure and for prior-data conflict with the constrained multinomial model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1141-1168, November.
    3. Haydar Demirhan & Kamil Demirhan, 2016. "A Bayesian approach for the estimation of probability distributions under finite sample space," Statistical Papers, Springer, vol. 57(3), pages 589-603, September.

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