Hello Pascal,

for me, the most important issue first would be to be clear what you want to achieve and it boils down to the prediction vs. explanation dichotomy. Your post seems to signal a kind of both--for instance you talk about the r-square and how your new variable can increase prediction. If this is your goal I would not worry at all about multicolinearity (as it does not affect rsquare). If you have many predictors, perhaps applying a LASSO model with crossvalidation would do the job. And of course, you can combine highly colinear predicators if this helps (and its effect could be evaluated).

If you want to interpret the (causal) role of your new variables, than this approach will probably not get you what you want and other strategies (e.g., running an exploratory TETRAD model would be an avenue. In any case, if you have a theoretical basis for including variables due to substantive reasons than, yes, multicolinearity may hurt by reducing power. However, 1) you say you have a large sample and this would help and 2) one should not simply add colinear predictors when their (separate) inclusion was theory-based in the first place. This mixes explanatory approaches with predictive approaches.

In this regard, I stumbled about a passage in Wooldriges econometrics textbook that I will massage every reviewer in his/her face in the future :)

"If we think certain explanatory variables need to be included in a regression to infer causality of xj, then we are hesitant to drop them, and whether we think VIFj is “too high” cannot really affect that decision. If, say, our main interest is in the causal effect of x1 on y, then we should ignore entirely the VIFs of other coefficients. Finally, setting a cutoff value for VIF above which we conclude multicollinearity is a “problem” is arbitrary and not especially helpful." (p. 98)

Wooldridge, J. M. (2012). Introductory econometrics. Cengage Learning.

Hello Pascal.

Since you are working with perceptions related to clients, have you considered the possibility of working with a model based on structural equation modeling (SEM)?

It sounds like you don' really care about estimating the separate coefficients for the 4 traditional variables, which is the problem that you would have multi-collinearity among them. If so, then I would recommend a hierarchical regression where you first enter the 4 re-determined variables, and then enter your "new" variables and examine the overall increment to R-sq as well as the significance of each new predictor.

To check for severe multicollinearity in OLS variables, you can follow these steps:

In summary, to check for severe multicollinearity in OLS variables, you can open the Eviews program, load the data you want to use for your analysis, click on the “Quick” menu and select “Estimate Equation”, select the variables you want to include in your model, click on the “Options” button, select the “Collinearity Diagnostics” tab, check the “Variance Inflation Factor (VIF)” option, click on the “OK” button to close the Options window, and click on the “OK” button to run the analysis.