Bayes factor testing of equality and order constraints on measures of association in social research

TL;DR

This paper introduces a Bayesian method for testing hypotheses with equality and order constraints on measures of association in social science data, providing a direct way to evaluate competing theories.

Contribution

It proposes a Bayes factor test for hypotheses with constraints on association measures, including software implementation and empirical applications.

Findings

Effective in evaluating social science hypotheses

Supports comparison of multiple constrained hypotheses

Demonstrated with real-world social science data

Abstract

Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses with equality and/or order constraints on these measures of association. In this paper a Bayes factor test is proposed for testing multiple hypotheses with constraints on the measures of association between ordinal and/or continuous variables, possibly after correcting for certain covariates. This test can be used to obtain a direct answer to the research question how much evidence there is in the data for a social science theory relative to competing theories. The accompanying software package `BCT' allows users to apply the methodology in an easy manner. An empirical application from leisure studies about the associations between life, leisure and relationship satisfaction and an application about the differences about egalitarian justice beliefs across countries are used to illustrate the methodology.