Common Variance as a Separate Variable

#1
Hi all, I have a regression model exhibiting significant multicollinearity and am trying to figure out how to correct for it, or at least to minimize the effect. I found a suggestion for the following:

Treat the common variance as a separate variable and decontaminate each covariate by regressing them on the others and using the residuals. That is, analyze the common variance as a separate variable.​

I'm not familiar with this procedure, but it makes conceptual sense to me. My question is, if I have 50 IVs, do I need to run 50 separate regressions and save the residuals? Also, an example of how you would actually operationalize this (say in a two-factor model) would be extremely helpful, as this is brand new to me.

Thanks!
 

Lazar

Phineas Packard
#3
It is simpler in structural equation modelling. Look up bi-factor SEM models where the bi-factor is a global method factor.