# Bayes Test for Partial Correlations

Dear Professor Wagenmakers,

We are writing with a question concerning Bayesian tests for correlations in JASP.

Is there a possibility to calculate Bayesian Factors for partial correlations in JASP?

We are interested in the association between (a) intelligence and (b) brain network efficiency and would like to control for three other variables when testing their association.

We realized that it makes a difference, whether we test the simple association of the two variables of interest with the Bayesian Test for Correlated Pairs or Linear Regression. We tried to get to the bottom of it by comparing prior values. While we understand that Correlated Pairs uses a default beta prior with width 1, we did not find information on the default prior for Linear Regression.

You would very much help us, if you could answer the following questions.

a) Is there an option to directly calculate BF for partial correlations?

b) If not, is there some workaround by using Linear Regression or something similar?

c) Can we see the default priors for Linear Regression in the programme?

d) If there is some other solution to our problem that is not covered by our questions, we are of course grateful for a hint! ☺

We find your programme very helpful and would be happy, if we could use JASP for our purpose.

Best,

Ulrike & Kirsten

## Comments

Hi Ulrike & Kirsten,

Together with Ruud Wetzels I once wrote something about partial correlations (http://www.ejwagenmakers.com/2012/WetzelsWagenmakers2012.pdf). This is not in JASP right now and we are exploring alternatives.

Yes, the correlation test in JASP is based on the framework by Jeffreys. The correlation test that is based on linear regression is outlined in the above paper by Wetzels, but the priors are also discussed in the regression paper by Rouder and Morey (http://pcl.missouri.edu/node/133). The tests will give different results but you should not find a serious difference (at least that would surprise me).

So to address your questions directly:

(a) Is there an option to directly calculate BF for partial correlations?

Not in JASP right now. Jeffreys proposed something incomprehensible :-) but we might have good alternatives.

(b) If not, is there some workaround by using Linear Regression or something similar?

You could try the logic from Wetzels as a workaround. It makes sense and answers the question but I recall that strictly speaking it isn't a partial correlation.

c) Can we see the default priors for Linear Regression in the programme?

Not yet, but we use the defaults from the BayesFactor package, and the defaults should be mentioned in the documentation there.

d) If there is some other solution to our problem that is not covered by our questions, we are of course grateful for a hint!

Hope the above helps.

Cheers,

E.J.

Dear E.J.,

thank you very much for your helpful answer.

We now think about using linear Regression instead of partial correlation to compute the Bayes Factors. Also, we found the prior used for linear regression in the documentation of the BayesFactor package.

Cheers, Kirsten