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When using multiple dummies for a categorical variable: what happens if a few of your observations can check off "1" in more than one of the dummies? Does it matter? Does it only matter dependent on what proportion of observations fit that category (i.e., 5% vs. 50%)? How might it affect results?

Example: comparing medical costs for different diseases off of patient records. Patient A has cancer, Patient B has diabetes, Patient C has both. How does that affect interpretation (or does it)? Another example would be race: A marks white, B marks black, C marks both. Do Persons C just get lumped in with the A group and the B group both in calculations against the reference group (we'll say Persons D)? Is it dropped?

One solution I've thought of is to create a dummy specifically for those with multiple answers (i.e., "multiple diagnoses" or "multiracial") and leave the individual boxes unchecked, as a way to both statistically and conceptually deal with those. (Arguably, someone with more than one serious illness or who identifies with more than one race may well be a different category than those of one illness or one race for some research questions.) But sometimes datasets make this computation difficult, or things can be missed, and I'm wondering about the ultimate impact of having a few of these within a dataset. I've always treated these types of variables with the idea that they absolutely must be mutually exclusive categories, but now I'm curious. I hadn't really considered it before--I've always just used the above solution, but I can now see some cases where it might be difficult to do so.

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  • $\begingroup$ Are all of the categorical variables you are thinking about independent / predictor variables? Also / if so, are you thinking about including those variables in interactions? $\endgroup$ – gung Sep 4 '14 at 16:28
  • $\begingroup$ Yes, all independent. I was not planning on interaction terms, although it is a possibility. $\endgroup$ – ShannonC Sep 4 '14 at 17:23
  • $\begingroup$ Results or interpretation of what? What specific analyses do you have in mind? $\endgroup$ – Nick Stauner Sep 4 '14 at 18:30
  • $\begingroup$ Thinking through it, perhaps I've been going about this wrong. I've been thinking of it as a single variable broken down into dummies for each category, using n-1 in the regression. Perhaps I should consider each possible outcome as its own variable, so that it's interpreted relative to everyone else (those with cancer versus everyone without), not just to an omitted reference group (those with cancer versus those with diabetes, when someone could have both and then be in both reference group and measured variable). Does that make sense? Is that a better way to approach it? $\endgroup$ – ShannonC Sep 4 '14 at 22:22
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    $\begingroup$ Sounds like you'd be better off treating them as separate independent variables as in your second comment. Is there any advantage that you're aware of so far in treating them as one variable? Some specific ways of framing your question might benefit from it, but unless you're already planning to address the general problem in some such way, I guess I wouldn't go there, because you'd then have to iron out the issue you raise in this question...whereas otherwise it shouldn't be a problem to just treat them as separate variables. $\endgroup$ – Nick Stauner Sep 4 '14 at 22:48
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There shouldn't be a problem with checking both. If you believe there is interaction then you could do hasCancer + hasDiabetes + (hasCancer)(hasDiabetes). As for the racial issue one then I don't think interaction would be correct. I think you would create a third variable as people who mark both would be identifying as part of both groups. Someone identifying as part of both groups may be influenced by both group or they might act as a group of their own - so this really depends on type of survey being done.

But to your original question, there should not be any problems having both variables as an option.

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