I am running a model in which I want to explain my dependent variable with the racial/ethnic diversity in a person's residential area. Diversity is measured with 4 continuous variables. Each one of these variables gives me the percentage of the total population of a racial/ethnic group in the residential area. That means that putting all of them together is the complete population and I should only include 3 of the variables in my model because of multicollinearity.

Now here is my question: How do I interpret the effect of the other variables that I included in the model? Their effects depend on the variable that I left out. Does the model give me the effect when the left out variable is zero or the mean?

I cannot find anything on this online and would be very happy if someone could help me with this question.

Thanks, Sara


First, having multiple classes that add up together to 100% means you are dealing with compositional data, for which there is a tag on this site with 64 linked questions; this page is a useful example. You can't get information about all 4 of the racial/ethnic categories independently. Exactly how the results of an analysis based on the 3 independent categories are presented can depend on the statistical software that you are using, so I can't give a general answer to that part of your question.

Second, and perhaps more important, you say that you want to investigate "racial/ethnic diversity" as an explanatory variable. It's not clear that simply looking at the individual racial/ethnic categories in the way you propose actually would accomplish that goal. There are several well-documented indices of diversity that have been used in many scientific fields. If your interest is in diversity itself rather than in relations to specific racial/ethnic categories, you should consider using one of those diversity measures instead.

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  • $\begingroup$ Compositional data! Thanks, I didn't know that term, so I guess I searched for the wrong topics. Regarding your second comment: Looking at different diversity measures is part of my project, but I only had problems with this one. $\endgroup$ – Sara Dec 7 '17 at 20:12
  • $\begingroup$ @Sara finding the right statistical terminology for the problem at hand can be quite a problem in itself. $\endgroup$ – EdM Dec 7 '17 at 20:24

I would choose one race to be a baseline category, and express the other races as ratios from that category. Eg: in the 2016 US Census,

  • 61% of people included were Caucasian alone,
  • 18% Hispanic,
  • 13% African-American,
  • 6% Asian, and
  • <2% everyone else.

I would represent this as

  • Hispanic = 18 / 61 = 0.295 times as likely as Caucasian alone,
  • AA = 0.213 times,
  • Asian = 0.098 times, and
  • Everyone else = 0.033 times.

This removes one of the columns, while still preserving the change from baseline (so that you can explain all five groups). This means you are explaining if the different proportions of the races / ethnicities have an effect on the outcome.

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