Bayes factors for testing order-constrained hypotheses on correlations

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Correlation coefficients play a key role in the social and behavioral Sciences for quantifying the degree of linear association between variables. A Bayes factor is proposed that allows researchers to test hypotheses with order constraints on correlation coefficients in a direct manner. This Bayes factor balances between fit and complexity of order-constrained hypotheses in a natural way. A diffuse prior on the correlation matrix is used that minimizes prior shrinkage and results in most evidence for an order-constrained hypothesis that is supported by the data. An efficient method is proposed for the computation of the Bayes factor. A key aspect in the computation is a Fisher Z transformation on the posterior distribution of the correlations such that an approximately normal distribution is obtained. The methodology is implemented in a freely downloadable software program called "BOCOR". The methods are applied to a multitrait multimethod analysis, a repeated measures study, and a study on directed moderator effects. (C) 2014 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)104-115
Number of pages12
JournalJournal of Mathematical Psychology
Volume72
DOIs
Publication statusPublished - 2016

Keywords

  • Bayes factor
  • Bivariate correlations
  • Order constraints
  • MCMC computation
  • CORRELATION-MATRICES
  • MODELS
  • SAMPLE

Cite this

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title = "Bayes factors for testing order-constrained hypotheses on correlations",
abstract = "Correlation coefficients play a key role in the social and behavioral Sciences for quantifying the degree of linear association between variables. A Bayes factor is proposed that allows researchers to test hypotheses with order constraints on correlation coefficients in a direct manner. This Bayes factor balances between fit and complexity of order-constrained hypotheses in a natural way. A diffuse prior on the correlation matrix is used that minimizes prior shrinkage and results in most evidence for an order-constrained hypothesis that is supported by the data. An efficient method is proposed for the computation of the Bayes factor. A key aspect in the computation is a Fisher Z transformation on the posterior distribution of the correlations such that an approximately normal distribution is obtained. The methodology is implemented in a freely downloadable software program called {"}BOCOR{"}. The methods are applied to a multitrait multimethod analysis, a repeated measures study, and a study on directed moderator effects. (C) 2014 Elsevier Inc. All rights reserved.",
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Bayes factors for testing order-constrained hypotheses on correlations. / Mulder, J.

In: Journal of Mathematical Psychology, Vol. 72, 2016, p. 104-115.

Research output: Contribution to journalArticleScientificpeer-review

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AB - Correlation coefficients play a key role in the social and behavioral Sciences for quantifying the degree of linear association between variables. A Bayes factor is proposed that allows researchers to test hypotheses with order constraints on correlation coefficients in a direct manner. This Bayes factor balances between fit and complexity of order-constrained hypotheses in a natural way. A diffuse prior on the correlation matrix is used that minimizes prior shrinkage and results in most evidence for an order-constrained hypothesis that is supported by the data. An efficient method is proposed for the computation of the Bayes factor. A key aspect in the computation is a Fisher Z transformation on the posterior distribution of the correlations such that an approximately normal distribution is obtained. The methodology is implemented in a freely downloadable software program called "BOCOR". The methods are applied to a multitrait multimethod analysis, a repeated measures study, and a study on directed moderator effects. (C) 2014 Elsevier Inc. All rights reserved.

KW - Bayes factor

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KW - Order constraints

KW - MCMC computation

KW - CORRELATION-MATRICES

KW - MODELS

KW - SAMPLE

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