An introduction to Bayesian model selection for evaluating informative hypotheses
Most researchers have specific expectations concerning their research questions. These may be derived from theory, empirical evidence, or both. Yet despite these expectations, most investigators still use null hypothesis testing to evaluate their data, that is, when analysing their data they ignore the expectations they have. In the present article, Bayesian model selection is presented as a means to evaluate the expectations researchers have, that is, to evaluate so called informative hypotheses. Although the methodology to do this has been described in previous articles, these are rather technical and havemainly been published in statistical journals. The main objective of thepresent article is to provide a basic introduction to the evaluation of informative hypotheses using Bayesian model selection. Moreover, what is new in comparison to previous publications on this topic is that we provide guidelines on how to interpret the results. Bayesian evaluation of informative hypotheses is illustrated using an example concerning psychosocial functioning and the interplay between personality and support from family.
Van de Schoot, R., Mulder, J., Hoijtink, H., Van Aken, M. A. G., Dubas, J. S., Orobio de Castro, B., Meeus, W., & Romeijn, J.-W. (2011). An introduction to Bayesian model selection for evaluating informative hypotheses. European Journal of Developmental Psychology, 8(6), 713–729.
As correctly noted by Anouk van Dijk, there is a mistake in Equation 3 (p.719).
The value of the marginal likelihood for Model A should be 2.83e-67 instead of 5.71e-67. The resulting Bayes Factor is 0.064 instead of 0.031. In Equation 3, 0.064 should be used for BF_ba resulting in a Bayes Factor of 31.25 instead of 64.51. We regret that this mistake was made, but fortunately the overall conclusion was not affected.