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I'm playing with some multiple linear regression models in r. After I run a regression, I use vif() to see if there is multicollinearity between my predictors. For the model with fixed effects for countries (factor(countryname)), vif() gives incredibly high results for some of the predictors. I would like to know why?

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  • $\begingroup$ How many countries do you have exactly? $\endgroup$ May 24 at 18:16
  • $\begingroup$ 149. It's a high number, but it's standard practice in pol sci to include dummy variables for such a large number of countries. $\endgroup$
    – Ken Lee
    May 24 at 18:18
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    $\begingroup$ So you're using vif() from the car package. The answer here should help. $\endgroup$ May 24 at 20:39
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    $\begingroup$ Every field has its standards and routine practices. That's not a defense of practice as usual, but I've found that there is often some methodological lineage within fields that often arose from a specific need but then crept into more and more unhelpful applications. I can't speak for your field, but I know that in psychology it can be hard to find people who actually check the assumptions of regression. We've been taught it's "robust" and seemingly are happy to abuse it. Your description makes me wonder whether mixed models are better with countries as a random factor $\endgroup$
    – Billy
    May 25 at 13:07
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    $\begingroup$ @KenLee In regard to your other concern, it isn't "flawed" to adjust for covariates. So long as GDP and/or population size vary over time, then it is permissible to include them. $\endgroup$ May 25 at 19:23
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In my opinion, I wouldn't concern yourself with the variance inflation factors associated with the country fixed effects. The country-specific effects usually aren't of substantive interest; they're nuisance. In practice, we often have little hope of obtaining precise estimates on the country dummies, and your results may vary depending upon which country is the referent.

Technically, the vif() function in the car package is estimating generalized variance inflation factors (GVIFs). Instead of treating each of the $N - 1$ country effects separately, it estimates a "combined measure" of collinearity. In my experience, it is not uncommon to see wildly inflated GVIFs in settings with 150 countries. I wouldn't even calculate the GVIFs for the country dummies since they're considered as a "group" of predictors and not as separate country-specific intercepts.

The inflated GVIFs appear to be associated with your vector of covariates (e.g., GDP per capita, logged population, etc.), some of which do not appear to be of principal interest. If your set of controls aren't themselves collinear with the primary variable(s) of interest, then I wouldn't concern yourself with their GVIFs. In some scenarios you may find one or more covariates to be perfectly collinear with the country fixed effects. For instance, in shorter panels with smaller time units you may not observe any variation over time for some of your socio-demographic measures. I would imagine the within-country population growth is likely a sluggish variable (i.e., slow-moving), though still a sensible adjustment in my opinion.

I would also examine the standard errors associated with the key variable(s) of interest. Does the estimated uncertainty seem sensible even in the presence of the country fixed effects? So long as the GVIFs on the principal variable(s) of interest remain low, then I would be less concerned about high GVIF predictors, especially when the predictor list includes a full series of country effects.

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I would add that if you include country fixed effects, and you have country-related variables in the data, it is logical that multicollinearity would increase. However, I think this article: https://statisticalhorizons.com/multicollinearity sums up pretty well when multicollinearity is an issue and when it isn't.

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