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My data is cross-sectional macroeconomics data. I have six independent variables (x1,x2,x3,x4,x5,x6) plus 2 dummies (d1,d2) plus 2 interactions terms (d1*x1,d2*x1).I am testing my data for multicollinearity using VIF and condition indices(CI)

The t-test : seven statistical significant variables F: statistical significant overall

VIF&CI

Mean VIF : 10.63 (with very high R-square (>85%) in all dummies and interaction terms) CI : 48.3

When I remove dummies and interactions from the model the results are much more better (Mean VIF : 1.62 , CI: 19.34 R-square <50%).

I am expecting -due to the nature of dummies and interaction terms- that my results would present multicollinearity.

Are the above results serious evidence for multicollinearity in my model?

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  • $\begingroup$ Multicollinearity may or may not be a problem, depending on the objective of your study. Can you describe a bit more about the objectives of your data analysis? Are you simply trying to predict the outcome variable or you concerned with the parameter estimates themselves? $\endgroup$ – StatsStudent Mar 10 '15 at 14:59
  • $\begingroup$ hi, thank you for your answer. My data in cross-sectional, my dependent variable is the average growth rate per capita gdp, the x1 is the average ratio of public debt to gdp, the d1 is a dummy variable which describes high-income countries and d2 is dummy on high debt countries. The object is: does high-income countries has higher growth rate than other countries? does high-debt countries have higher growth rate of gdp than other countries? also the interactions of them. $\endgroup$ – Antonis Mar 10 '15 at 16:20
  • $\begingroup$ Then yes, you'll need to address the issue. Take a look at this article, which should help you. blog.minitab.com/blog/adventures-in-statistics/… $\endgroup$ – StatsStudent Mar 10 '15 at 16:24
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It really depends on the specifics of your study. But generally, you're right that dummy variables can lead to higher VIF as can the inclusion of interaction terms.

The p-value for the interaction term will not be affected by multicollinearity. You might lower the VIF by centering x1 and re-fitting your model. This should not change the p-values but might reduce the VIF for the interaction terms.

For the dummy variables: If your reference category has far fewer cases in it, then this will yield a high VIF. If this is the case, you can just switch your reference category to the one with the greatest number of cases.

Rather than looking at the mean VIF alone, you should also consider the VIF for each individual predictor. If the VIF for the dummy variables and the interaction terms are contributing to a higher mean VIF, then there might be nothing to worry about.

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  • $\begingroup$ Thank you for your comment. What is your opinion about condition indeces for detecting multicollinearity? some people believe that it is a better measure than VIF $\endgroup$ – Antonis Mar 10 '15 at 16:23
  • $\begingroup$ I'd say that you shouldn't depend on any one measure. The wikipedia entry gives some useful things to do to check for multicollinearity: en.wikipedia.org/wiki/… $\endgroup$ – Jordan Collins Mar 11 '15 at 17:17

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