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I have been examining high school graduation rates, and wanted to include race/ethnicity as a control. The only data available is % of students identifying as one of 7 race/ethnicity categories. My concern is that these percentages are inherently dependent upon each other.

Is it appropriate to include each of those percentages as independent variables in the regression? If not, is there a method for handling such dependent variables?

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  • $\begingroup$ Your unit of analysis is high school? If I understand things correctly, each high school would give rise to 7 race/ethnicity percentages and the 7 percentages would add up to 100%. So you can't add all 7 percentages as control variables in your model, as you would have perfect multicollinearity between them. You could add just 6 of them perhaps and leave one out of the model entirely. $\endgroup$ – Isabella Ghement Mar 4 at 16:38
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    $\begingroup$ The other thing you could do is to identify a subset of race/ethnicity categories you are most interested in (e.g., white and hispanic ) and define a percentage that reflects that subset (e.g., 60% white + 20% hispanic = 80% white or hispanic). Then you can include that percentage in the model. Or you could use a mixture of percentages: 60% white and 10% black or hispanic (as long as they don't add up to 100%). $\endgroup$ – Isabella Ghement Mar 4 at 16:40
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    $\begingroup$ @IsabellaGhement that's a good answer, and I'd encourage you to post it as one. $\endgroup$ – Weiwen Ng Mar 4 at 17:16
  • $\begingroup$ Thank you, @WeiwenNg! I posted the comments as an answer. $\endgroup$ – Isabella Ghement Mar 4 at 18:22
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@IsabellaGhement provided one reasonable way to handle this in comments. If your substantive interest is the degree of racial segregation between high schools, I'd encourage you to read up on entropy indexes, which quantify the degree of segregation. If you're familiar with the Hirschman-Herfindahl index in economics, they essentially get at the same concept.

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  • $\begingroup$ Thank you for the response! Looking within each high school, would it be appropriate to "quantify" racial diversity using the entropy score (I hate that phrasing, but can't think of a better way to say it)? $\endgroup$ – Ryan Senkpeil Mar 5 at 14:02
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Encouraged by Weiwen, I am posting my comments as an answer.

Your unit of analysis is high school? If I understand things correctly, each high school would give rise to 7 race/ethnicity percentages and the 7 percentages would add up to 100%. So you can't add all 7 percentages as control variables in your model, as you would have perfect multicollinearity between them. You could add just 6 of them perhaps and leave one out of the model entirely. Which one you leave out depends on what you are most interested in.

The other thing you could do is to identify a subset of race/ethnicity categories you are most interested in (e.g., white and hispanic ) and define a percentage that reflects that subset (e.g., 60% white + 20% hispanic = 80% white or hispanic). Then you can include that percentage in the model. In that case, you'll be able to control for the combined percentage of white and hispanic students in your modelling.

Or you could use a mixture of percentages: "60% white" and "10% black or hispanic" (as long as they don't add up to 100%). In that case, you'll be able to control for both the percentage of white and the combined percentage of black or hispanic students in your modelling.

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