# Variance Inflation Factor for Meta-Analyses

I've conducted a Meta-Regression Analysis for my Masters Thesis. However, my supervisor told me that I should check if the proposed moderating variables highly correlate.

So I thought, that I can assess multicollinearity with the use of the Variance Inflation Factor. There are numerous examples on how to calculate VIF for "normal" Regression Analyses.

This requires the specification of a linear model (see this video as an example https://www.youtube.com/watch?v=pZsOn6wnGSo). However, in Meta-Regression I do not have a dependent variable. It's more that the effect size between the dependent and independent variable is the dependent variable for the meta-regression.

So my question is, how do I correctly calculate the VIF when dealing with Meta-Regression? I did not find any examples out there.

I would especially appreciate if someone could tell me what R-Packages I could use to calculate the VIF (and what I have to consider in order to do it correctly) or how I can calculate it with SPSS.

I hope that my question is clear. Thanks for considering my request.

Greetings!

• Can you clarify what you mean by dependent variable here? Most people do meta-regression by regressing the effect size on the moderators. Is that what you did? If so surely the effect size is what you are calling the dependent variable. – mdewey Feb 16 '17 at 17:12
• Yes this is what I did. However, I dont have an idea on how to calculate the VIFs appropriately. Or do you suggest that I can adopt the procedure from the video, just taking the effect size as dependent varible? – Fealzz Feb 16 '17 at 17:17

If your supervisor insist on VIF then this Q&A shows you how to calculate it from the value of $R^2$ from a multiple regression. Again I can see arguments for doing that regression with weights extracted from the meta-regression.
I do not use SPSS so I have no idea how to do this except that you must not use what are called frequency weights but what are called importance weights. Weighted regression is available in R in lm.
The variance inflation factors (VIFs) are functions of the predictor variables and do not involve the dependent variable. This page provides formulas. Although there are VIF formulas that involve $R^2$, this $R^2$ is for regressing one independent variable against the other independent variables, as shown on the linked page. It doesn't involve the dependent/outcome variable at all.