Linear vs Bayesian regression anomalies

DrMark

Morning all
I have been dipping my toes into Bayesian statistics and have seen some strange anomalies between the normal and Bayesian regression coefficients (see attached file). This is a very simple regression to predict kicking distance with right leg strength- both methods show that the model is good but the coefficients are in an order of magnitude different.
Linear regression intercept = 57.1 Bayesian intercept = 486.1 (same as the mean of the outcome variable!)
Linear regression R_strength = 6.425 Bayesian = 5.497

Using these in a simple linear prediction equation y = b0 + b1*x the normal coefficients are fine but are way out using the Bayesian coefficients.

Am I interpreting this incorrectly?
Cheers
Mark

vandenman

Hi Mark,

Thanks for your interest in JASP!

What you're observing might be an effect of the prior which shrinks parameters to 0. If the sample is large
(N = 100) the shrinkage will be minimal, but since your dataset consists of 13 observations there might be some effect. If possible, could you perhaps send us the raw data so we can further investigate this?

Cheers,
Don

EJ

Don, the data set is from "punting", available under "Regression" at the JASP generic workshop materials on the OSF: https://osf.io/r73y9/

DrMark

Thanks - thats where I adapted it from.
My colleague has suggested that the coefficients are used in a different way to the intercept and gradient given by the linear regression coefficients. In this case the outcome (y)is predicted where y = ({x - mean x} *b1)+ intercept (mean of y). I guess this makes sense but is not intuitive in the output.

DrMark

BTW - we have just moved all our undergraduate and postgraduate teaching from SPSS (where students have to be dragged screaming by wild horses to lectures) to the much more intuitive JASP. The software is now available to all students through our University software centre. Well done chaps and look forward to seeing some of you in Amsterdam in August.

EJ

That is great to hear! And our upcoming version will offer a lot more. We are testing it out now.
@Don: it is good to attend people to the interpretation of the coefficients (also for the paper you are writing).
E.J.