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.