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For the purpose of model selection, I am using the Bayes' factor to compare different combinations of predictors in a linear regression model.

I have used the function regressionBF() from the library(BayesFactor), and I got the following results:

# > regressionBF(return ~ FSCR + VAL, data = dataf)

# Bayes factor analysis
# --------------
#[1] FSCR       : 65.17482  ±0%
#[2] VAL        : 0.1979875 ±0.02%
#[3] FSCR + VAL : 23.58704  ±0%

#Against denominator:
#  Intercept only 

I am not sure how to interpret these results. What do the percentage numbers next to the Bayes' factors mean? Also, 65 and 23 seem pretty high for a Bayes' factor. How can I interpret that?

Any help would be appreciated. Thanks!

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    $\begingroup$ In the rest of the package, the BF is followed by the proportional error estimate on the Bayes factor, that's probably the 2nd number. A BF of 65 against the null doesn't seem implausible. $\endgroup$ – jona Sep 12 '13 at 14:18
  • $\begingroup$ Thanks for your comment. Would a BF = 65 be a "strong/decisive" evidence for the alternative? Also, I am not sure what you mean by proportional error estimate... $\endgroup$ – Mayou Sep 12 '13 at 14:19
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If you do not have a book or reference on how to interpret the Bayes factors check out http://en.wikipedia.org/wiki/Bayes_factor. In your example, your Bayes factors are comparing the model with those covariates against the model with only the intercept. For example, a Bayes Factor of 65/17482 would suggest that the model with FSCR a a covariate is more appropriate than the model with intercept alone with "very strong" evidence.

Now, to clarify what @jona was explaining to you the percentages that displayed can be thought of as standard errors for the estimate of the Bayes factors. Since most Bayes factors are approximated through simulation we can give an estimate of what the Bayes factor should be plus or minus how much we expect to be off by (basically like a confidence interval).

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