Calculating a Bayes Factor for a Regression Coefficient

akinney9797

Hello,

I'd like to conduct a Bayesian re-analysis of regression coefficients using only summary statistics. I know that JASP/Bayes Factor allows you to obtain a Bayes factor for the R^2 using summary statistics, but I have a few questions regarding a method for obtaining a Bayes factor for the regression coefficients themselves:

1) Is it valid to obtain the t-statistic used to evaluate the statistical significance of a particular regression coefficient, and use that to obtain a corresponding Bayes factor by using the JASP summary statistics module for a one-sample t-test (while subtracting the number of predictors from the degrees of freedom)?

2) If this approach is not valid, is there an alternative way to obtain a Bayes factor for a regression coefficient using only summary statistics?

Thanks in advance,

Adam

EJ

Hi Adam,

1. No I don't think that this is valid in general, although I would not be surprised if it is a fairly good approximation under many circumstances. This would be an interesting topic for a statistical study.
2. Well you'd need an interval or SE on the coefficients as well, and also their covariance I think. So it's not straightforward I believe.
3. What we did once (http://www.ejwagenmakers.com/2015/AndraszewiczEtAl2015.pdf) is to simulate data so that we got the same summary stats on the regression coefficients, and then we analyzed that synthetic data set.

Cheers,

E.J.