Bayes factor testing of multiple intraclass correlations

Joris Mulder, Jean Paul Fox

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

The intraclass correlation plays a central role in modeling hierarchically structured data, such as educational data, panel data, or group-randomized trial data. It represents relevant information concerning the between-group and within-group variation. Methods for Bayesian hypothesis tests concerning the intraclass correlation are proposed to improve decision making in hierarchical data analysis and to assess the grouping effect across different group categories. Estimation and testing methods for the intraclass correlation coefficient are proposed under a marginal modeling framework where the random effects are integrated out. A class of stretched beta priors is proposed on the intraclass correlations, which is equivalent to shifted F priors for the between groups variances. Through a parameter expansion it is shown that this prior is conditionally conjugate under the marginal model yielding efficient posterior computation. A special improper case results in accurate coverage rates of the credible intervals even for minimal sample size and when the true intraclass correlation equals zero. Bayes factor tests are proposed for testing multiple precise and order hypotheses on intraclass correlations. These tests can be used when prior information about the intraclass correlations is available or absent. For the noninformative case, a generalized fractional Bayes approach is developed. The method enables testing the presence and strength of grouped data structures without introducing random effects. The methodology is applied to a large-scale survey study on international mathematics achievement at fourth grade to test the heterogeneity in the clustering of students in schools across countries and assessment cycles.

Original languageEnglish
Pages (from-to)521-552
Number of pages32
JournalBayesian Analysis
Volume14
Issue number2
Early online date10 Aug 2018
DOIs
Publication statusPublished - 1 Jan 2019

Fingerprint

Multiple Correlation
Intraclass Correlation
Bayes Factor
Testing
Random Effects
Data structures
Decision making
Intraclass Correlation Coefficient
Students
Credible Interval
Grouped Data
Marginal Model
Hierarchical Data
Randomized Trial
Multiple Testing
Hypothesis Test
Panel Data
Prior Information
Bayes
Modeling

Keywords

  • Bayes factors
  • Hierarchical models
  • Intraclass correlations
  • Shifted F priors
  • Stretched beta priors

Cite this

Mulder, Joris ; Fox, Jean Paul. / Bayes factor testing of multiple intraclass correlations. In: Bayesian Analysis. 2019 ; Vol. 14, No. 2. pp. 521-552.
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Bayes factor testing of multiple intraclass correlations. / Mulder, Joris; Fox, Jean Paul.

In: Bayesian Analysis, Vol. 14, No. 2, 01.01.2019, p. 521-552.

Research output: Contribution to journalArticleAcademicpeer-review

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