I'm quite familiar with traditional dummy variable coding - code 1 for presence of the attribute and 0 for absence. A multi-category variable is then represented by a series of dummy variables while omitting 1 category as the reference, so for a variable with n categories I would include n-1 dummy variables.
But what happens if I have overlap in my categories?
Here's a simple (slightly contrived) example to illustrate.
Let's say I'm looking at the effect of different sports on injury (a dichotomous outcome). There are 6 sports - football, baseball, basketball, soccer, lacrosse, and hockey.
Now, I know what you're thinking, these ARE mutually exclusive, there is no overlap. True, I could represent these sports with 5 dummy variables and use one, say football, as the reference.
But instead I want to look at some facet of the sport that is related to injury. Put differently, it's not the 'sport' per se, but the actions involved in playing each sport. Some sports involve the same actions, so there is overlap.
I would like to have dummies such as the following:
- 'ball' is hard (baseball, hockey, lacrosse)
- all players wear helmets (lacrosse, hockey, football)
- floor/ground is hard (hockey, basketball)
Now, I think I can do this so long as the dummy variables are not highly collinear. That would be tantamount to the so called 'dummy variable trap'. Right? How would I check this? VIFs for the dummies? Condition number?
Is there anything else I need to look out for? Anything I'm missing?
In my actual application I'm thinking of around 5 'facets' and there are well over 50 different categories. I can collapse these categories down into 5 or so catchall categories but I'd rather not do that for theoretical reasons that we don't need to get into at this point.
I could let the machine chose the 'dimensions' or 'facets' via exploratory factor analysis, but I have a very specific set of theoretical 'facets' that I wish to test, hence the preference for dummy variables of my choosing.