Interpreting BF10, 95% CI and model comparisons in Bayesian linear regression
Hi,
I'm interested in using Bayesian linear regression and am trying to understand how to interpret correctly BF10, the 95% credible intervals, and the model comparisons when I add the other predictors to the null model. I have been reading Rouder and Morey (2012; as referred to in other posts on this forum), for an example of how to write up a Bayesian linear regression, and testing the covariates as described there.
In the example attached, the best model contains all three predictors, but the 95% credible interval for one of the three, IQ, includes zero. When I compare each of the predictors to a null model which contains the other two, the Bayes Factors indicate that there is very strong evidence for openness as a predictor, but only anecdotal evidence for IQ and leisq1_sumfreq.
I'm not sure how to interpret this, when the best model includes all three predictors. Rouder & Morey say that testing covariates doesn't allow for correlations between them, and there are some significant correlations between the predictors (openness and IQ, Pearson's r = 0.12; openness and leisq1_sumfreq Pearson's r = 0.39). Should I therefore ignore the results of covariate testing, and focus on the main model comparisons? How should I consider a 95% credible interval that includes zero?
Thanks in advance for any help you can give 
Sarah
Comments
Hi Sarah,
Interesting example! Here's my take on what's going on here. Basically, there is no contradiction. Yes, the credible interval just overlaps with zero, but that does not mean that should be strong evidence for excluding that predictor. The Bayes factors suggest that several models remain in contention, and that the data do not strongly confirm or disconfirm the relevance of some of the variables. You definitely have strong evidence for openness; for the other variables, this is a result that is "too close to call".
Cheers,
E.J.