How to interpret VIF and Condition Index for the purpose of assessing reliability of formative measures?

Question

I am testing the reliability of my formative measurement model and I am using Variance Inflation Factor (VIF) and Condition Index (CI) (see this earlier question asking whether to and how to do this). I am using SPSS.

All my scores for VIF are less than 5.00 and all except one for CI is less than 10.00 (i.e. it is 22.379).

1. Is VIF and CI appropriate in this case?
2. How do I interpret this result?
3. Is there any generally accepted thresholds for VIF and CI scores?

As far as I understand, multicollinearity is NOT good for a formative measurement model (i.e. where the arrow goes from the indicators to the construct).

Also, any measure of internal consistency such as Cronbach Alpha or Split Half Reliability are not appropriate in this case.

I am told that a VIF score of 10 or less and CI score of 30 or less are acceptable.

Answer 1

First, rules of thumb should not be mistaken for rules per se. It is doubtful that anyone except you could provide a satisfactory answer to the question of how much collinearity is too much. If you look in different regression texts you'll find various rules of thumb about the VIF and indeed various degrees of willingness to put forth a rule of thumb at all.

Why should you believe me (or anyone else) if I were to say, "tripling the uncertainty around a regression coefficient is fine, but quadrupling it is out of the question"? The important thing is to know what the collinearity's consequences are for your parameter estimates and, once you settle on a regression solution, to be honest about reporting those consequences with your other model information.

Having said all that, I can think of few situations in which a VIF of 4 or 5 would not make me search for a less collinear solution! The reciprocal of VIF is tolerance; think carefully about whether a predictor is effective if all but 20% of its information content can be accounted for by the other predictors. In such a situation, attempts to assess the relative contributions of the predictors will be seriously hampered. You'll want to consider whether that matters to you in this current project.