Comparison of beta coefficients within the same group

#1
Hello!
I have a question, to which I have found some answers from different sources, but never really applicable to my problem.

So, I have measured how Var1 predicts Var2 (beta = .14)
Then, I have measured how Var1 predicts Var2 while controlling for Var3 (beta = .12).

How can I measure if the beta coefficients (.14 and .12) are statistically different from each other? This is within the same group.

Can I use the graphcial way (Cumming, 2009), where you inspect how much the CI's overlap....? Or is there an easier way?

Thank you in advance!
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
Well I am sure there is an easy way/test, but this is not my expertise area. You could potentially looked at the partial R^2 values with confidence intervals on them. I know there are eta and omega squared values for these estimates and not sure if one does a better job of adjusting for changes in R^2 solely related to the number of terms in the model.

In the field of epidemiology, they typically look for a 10% change in estimates as a sign of confounding. Also, I wonder if you could just create 10,000 bootstrap samples and run the models on each sample and calculate all of the differences, than plot them and find the 95% percentile confidence intervals for differences.
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
A slight point of clarification, sobel examines mediated effects, i was referencing confounding, and you also have backdoor paths from controlling for common effects and interaction issues. It is best to try and draw out the proposed relationships.