Automatic Bayes factors for testing equality- and inequality-constrained hypotheses on variances

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In comparing characteristics of independent populations, researchers frequently expect a certain structure of the population variances. These expectations can be formulated as hypotheses with equality and/or inequality constraints on the variances. In this article, we consider the Bayes factor for testing such (in)equality-constrained hypotheses on variances. Application of Bayes factors requires specification of a prior under every hypothesis to be tested. However, specifying subjective priors for variances based on prior information is a difficult task. We therefore consider so-called automatic or default Bayes factors. These methods avoid the need for the user to specify priors by using information from the sample data. We present three automatic Bayes factors for testing variances. The first is a Bayes factor with equal priors on all variances, where the priors are specified automatically using a small share of the information in the sample data. The second is the fractional Bayes factor, where a fraction of the likelihood is used for automatic prior specification. The third is an adjustment of the fractional Bayes factor such that the parsimony of inequality-constrained hypotheses is properly taken into account. The Bayes factors are evaluated by investigating different properties such as information consistency and large sample consistency. Based on this evaluation, it is concluded that the adjusted fractional Bayes factor is generally recommendable for testing equality- and inequality-constrained hypotheses on variances.
Original languageEnglish
Pages (from-to)586-617
JournalPsychometrika
Volume83
Issue number3
DOIs
Publication statusPublished - 2018

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Bayes Factor
Equality
Fractional Bayes Factor
Testing
Specifications
Specification
Parsimony
Prior Information
Inequality Constraints
Likelihood
Adjustment
Evaluation

Keywords

  • VARIABILITY
  • default Bayes factor
  • fractional Bayes factor
  • heterogeneity
  • heteroscedasticity
  • homogeneity of variance
  • inequality constraint

Cite this

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title = "Automatic Bayes factors for testing equality- and inequality-constrained hypotheses on variances",
abstract = "In comparing characteristics of independent populations, researchers frequently expect a certain structure of the population variances. These expectations can be formulated as hypotheses with equality and/or inequality constraints on the variances. In this article, we consider the Bayes factor for testing such (in)equality-constrained hypotheses on variances. Application of Bayes factors requires specification of a prior under every hypothesis to be tested. However, specifying subjective priors for variances based on prior information is a difficult task. We therefore consider so-called automatic or default Bayes factors. These methods avoid the need for the user to specify priors by using information from the sample data. We present three automatic Bayes factors for testing variances. The first is a Bayes factor with equal priors on all variances, where the priors are specified automatically using a small share of the information in the sample data. The second is the fractional Bayes factor, where a fraction of the likelihood is used for automatic prior specification. The third is an adjustment of the fractional Bayes factor such that the parsimony of inequality-constrained hypotheses is properly taken into account. The Bayes factors are evaluated by investigating different properties such as information consistency and large sample consistency. Based on this evaluation, it is concluded that the adjusted fractional Bayes factor is generally recommendable for testing equality- and inequality-constrained hypotheses on variances.",
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Automatic Bayes factors for testing equality- and inequality-constrained hypotheses on variances. / Böing-Messing, F.; Mulder, J.

In: Psychometrika, Vol. 83, No. 3, 2018, p. 586-617.

Research output: Contribution to journalArticleScientificpeer-review

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