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Simple Bayesian testing of scientific expectations in linear regression models.

J Mulder1,2, A Olsson-Collentine3

  • 1Department of Methodology and Statistics, Tilburg University, Warrandelaan 1, Tilburg, The Netherlands. j.mulder3@tilburguniversity.edu.

Behavior Research Methods
|March 24, 2019
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Summary

This study introduces a default Bayes factor test for linear regression models with constrained effects. The method, implemented in the R-package 'lmhyp', allows hypothesis testing without prior information.

Keywords:
Bayes factorsBayesian hypothesis testingEquality and order constraintsRegression modeling

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Area of Science:

  • Statistics
  • Econometrics
  • Psychometrics

Background:

  • Scientific theories frequently involve hypotheses about the relative magnitudes of effects in linear regression models.
  • Testing these constrained hypotheses is crucial for validating scientific expectations.
  • Existing methods may require subjective prior information or lack flexibility.

Purpose of the Study:

  • To propose a simple default Bayes factor test for hypotheses with equality and order constraints on regression effects.
  • To provide a method that does not require external prior information.
  • To implement the method in an accessible R package for practical use.

Main Methods:

  • A default Bayes factor test is developed for multiple hypotheses involving equality and order constraints.
  • The testing criterion is computed directly from the data, avoiding the need for subjective prior specifications.
  • The 'lmhyp' R package is created to facilitate the application of the proposed method.

Main Results:

  • The proposed Bayes factor test effectively compares hypotheses with constrained effects in linear regression.
  • The method is computationally feasible and does not rely on external prior information.
  • Empirical applications demonstrate the utility and ease of use of the 'lmhyp' package.

Conclusions:

  • The developed Bayes factor test offers a straightforward and objective approach for hypothesis testing with constrained effects.
  • The 'lmhyp' R package provides a valuable tool for researchers in social and behavioral sciences.
  • This method enhances the ability to test scientific theories formulated as constraints on regression coefficients.