Why multicollinearity increases with country fixed effects in a linear model in r

Question

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?

I don’t disagree with your choice, but shouldn’t we see the country effects? Unless you omitted them. — Thomas Bilach, May 24 '21 at 18:27
@ThomasBilach At the very bottom, you can see the following: factor(countryname) 101363392.344484 58 1.172239. Factor(countryname) is fixed effects for countries. This is what I get when I use vif() for a model with fixed effects. — Ken Lee, May 24 '21 at 18:39
So you're using vif() from the car package. The answer here should help. — Thomas Bilach, May 24 '21 at 20:39
Your code executes ordinary least squares regression. What makes it an "MLR model"? — whuber, May 25 '21 at 11:28
@whuber MLR stands for multiple linear regression. My model is MLR in that it includes more than one independent variable. And yes, the method of estimation is OLS, as you've mentioned. — Ken Lee, May 25 '21 at 12:45
Can you give more details about the variables you're looking at? Just from the names, I'm assuming that these are variables describing various aspects of the countries (e.g., their annual GDP, population size, etc). If that's the case, then including indicators for each country is going to increase multicollinearity because each country already has data that is unique to it entered in the model — Billy, May 25 '21 at 12:51
Yes, you have a correct impression about these variables, @Billy. That's what I've thought as well. But this makes me wonder then: other scholars have included fixed effects for countries, even though their models also include variables like GDP, population, etc. Does this mean that their analyses were flawed because there was multicolinearity between their predictors? I should still look into the post suggested by Thomas---perhaps the answer is there. — Ken Lee, May 25 '21 at 13:01
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 — Billy, May 25 '21 at 13:07
@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. — Thomas Bilach, May 25 '21 at 19:23
@ThomasBilach Even if this results in high multicolinearity as shown in my post? E.g. see population taking the value of 50 for GVIF^(1/(2*Df)). — Ken Lee, May 25 '21 at 19:57
@ThomasBilach, I'm not sure that I agree with the requirement that those variable vary over time unless the model is longitudinal in nature. Cross-sectionally, the worst case scenario is that including countries results in complete redundancy since each country corresponds to a unique vector of predictor values. The model doesn't know that the variables are changing over time unless its specified to know that. If this is a longitudinal model, then I think the case for multilevel modeling is even stronger since you'd likely want to account for the non-independence of your observations — Billy, May 25 '21 at 20:11
@Billy Yes. I was assuming the OP is working with panel or repeated cross-sectional data. — Thomas Bilach, May 25 '21 at 21:02
@ThomasBilach, @Billy. Indeed, I am working with panel data. Sorry, but I am getting a little lost in this discussion. Thomas, do you think that I can use country fixed effects together with my population variable (which indeed varies over time) in my model? The worry that I have is that vif() shows extremely high values for population when I include it, as you can see in my example. Hence, I'm afraid that I can't include population due to multicolinearity, even though I've seen papers in political science/economics including both population variable and country fixed effects. — Ken Lee, May 25 '21 at 21:08
The question of multicollinearity as an issue comes down to what you're analyzing. Mutlicollinearity typically impacts primarily the coefficient in question, so if need to interpret a variable with high VIF, then multicollinearity is definitely an issue. Seems to me like countries is a reasonable random effect and is the intended reason for including it in the regression in the first place. A multilevel model also addresses the dependency in your data — Billy, May 25 '21 at 23:00

score 5 · Answer 1 · answered May 27 '21 at 02:12

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.

score 1 · Answer 2 · answered May 28 '21 at 08:45

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.

Why multicollinearity increases with country fixed effects in a linear model in r

2 Answers2