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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

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