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Bayesian test on equality of score parameters in the order restricted RC association model

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  • Oh, Man-Suk

Abstract

In the RC association model for a two-way contingency table, it is often natural to impose order constraints on the score parameters of the row and column variables. In this article, a simple and efficient Bayesian model selection procedure is proposed that simultaneously compares all possible combinations of (in)equalities of successive score parameters in the order restricted RC association model. The method introduces normal latent variables into the model and uses a simple and accurate approximation to the likelihood function so that the full conditional posterior distributions of elements of the parameter are given as truncated normal distributions. The Gibbs sampling algorithm of Gelfand and Smith (1990) is employed to generate samples from the full model in which all the scores are strictly ordered, and posterior probabilities of all possible models are estimated by using the Gibbs output from the full model. A simulation study shows that the proposed method performs well in detecting the true model. Two real data sets are analyzed using the proposed method.

Suggested Citation

  • Oh, Man-Suk, 2014. "Bayesian test on equality of score parameters in the order restricted RC association model," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 147-157.
    • Handle: RePEc:eee:csdana:v:72:y:2014:i:c:p:147-157
    DOI: 10.1016/j.csda.2013.11.009
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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. Klugkist, Irene & Hoijtink, Herbert, 2007. "The Bayes factor for inequality and about equality constrained models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6367-6379, August.
    4. Francisca Galindo‐Garre & Jeroen K. Vermunt, 2005. "Testing log‐linear models with inequality constraints: a comparison of asymptotic, bootstrap, and posterior predictive p‐values," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 82-94, February.
    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. Man-Suk Oh & Yong Bin Lim, 2001. "Bayesian analysis of time series Poisson data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(2), pages 259-271.
    7. 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.
    8. Yee, Thomas W., 2010. "The VGAM Package for Categorical Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i10).
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