Bayesian Model Comparison for the Order Restricted RC Association Model

Iliopoulos, George; Kateri, Maria; Ntzoufras, Ioannis

doi:10.1007/s11336-009-9117-0

Cited by 10 publications

(10 citation statements)

References 34 publications

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“…Additionally, the last level of the disturbance is homogeneous with respect to the second and third levels in the RC5 model. These inferences are in accordance with those given by Iliopoulos et al [20,21] and maximum likelihood estimates (MLEs) given by the other authors mentioned. However, we identify the unrestricted RC model as the best one among all of the models, whereas Iliopoulos et al [20] identified the RC4 model as the best based on a criterion-based comparison.…”

Section: An Illustrative Examplesupporting

confidence: 92%

“…Therefore, we assume the independence of scores while imposing order restrictions on scores, following the work of Iliopoulos et al [20,21]. We use order statistics to represent order restrictions.…”

Section: Prior Distributions For Unrestricted and Order-restricted Casesmentioning

confidence: 99%

“…The order-restricted version of the log-gamma distribution is preferable to the uniform prior used by Iliopoulos et al [21], because we are able to define simultaneously an informative prior for some of the scores and a non-informative prior for the others in the ordered log-gamma prior setting. Additionally, the posterior computations in the ordered log-gamma prior setting are as easy to perform as those in the ordered uniform prior setting.…”

Section: Prior Distributions For Unrestricted and Order-restricted Casesmentioning

confidence: 99%

“…The analysis is presented in Appendix B. We present a non-informative analysis for the dreams data set to make our approaches comparable to those of Iliopoulos et al [20,21] and the other authors, and conduct a slightly informative analysis for the breathing test results data set to illustrate the use of our approach in an informative setting.…”

Section: An Illustrative Examplementioning

confidence: 99%

“…Their parameterization makes it possible to run Metropolis-within-Gibbs sampling. Iliopoulos et al [21] propose an alternative parameterization and give an approach for the model selection of the order-restricted RC association model.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian estimation of order-restricted and unrestricted association models

Demirhan

2013

Journal of Multivariate Analysis

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a b s t r a c tAssociation 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 threeway 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.

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Section: An Illustrative Examplesupporting

confidence: 92%

Section: Prior Distributions For Unrestricted and Order-restricted Casesmentioning

confidence: 99%

Section: Prior Distributions For Unrestricted and Order-restricted Casesmentioning

confidence: 99%

Section: An Illustrative Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian estimation of order-restricted and unrestricted association models

Demirhan

2013

Journal of Multivariate Analysis

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2010

Analysis of Ordinal Categorical Data

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Bayesian inference about odds ratio structure in ordinal contingency tables

Kateri

Agresti

2013

Environmetrics

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When the goal of a study is to compare two groups on an ordinal categorical scale, a large number of inferential methods are available. Most methods are designed to detect a location effect, such as by focusing a single‐degree‐of‐freedom test on an effect parameter. Often, rather than merely summarizing by a P‐value to describe the evidence against a null hypothesis, it is of interest to consider whether a stronger conclusion can be made. For example, can we conclude that the population distributions are stochastically ordered? For parameter space regions described by order restrictions, frequentist methods are not well designed for significance testing. For example, a frequentist P‐value for testing identical distributions against an alternative of stochastically ordered distributions can be very small even when the sample distributions give clear evidence that the distributions do not have the ordering property. The Bayesian approach seems better equipped to handle such questions. We discuss this in the context of stochastic ordering and other types of ordinal odds ratio structure, for the two‐group comparison and for more general contexts. For Dirichlet priors, simple simulations provide posterior probabilities of particular ordinal odds ratio structures. Copyright © 2013 John Wiley & Sons, Ltd.

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Bayesian Model Comparison for the Order Restricted RC Association Model

Abstract: contingency tables, ordinal variables, reversible jump MCMC algorithm, equality of odds, Bayesian model averaging,

Cited by 10 publications

References 34 publications

Bayesian estimation of order-restricted and unrestricted association models

Bayesian estimation of order-restricted and unrestricted association models

Bibliography

Bayesian inference about odds ratio structure in ordinal contingency tables

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