Testing for variable independence with count data and assumption violations

Question

I used a survey to collect information about injuries suffered while practicing and competing in gymnastics. I have count data on the injuries that looks something like this:

           Floor   Vault   Rings ...
Head         33      45      7
Neck         43      19      17
Shoulder     21      39      25
...         ...     ...     ...
Toes         16      9       3

I wanted to see if there was a relationship between the body part injured and the equipment being used. I thought that using a chi square test of independence would work but I've hit a snag, I think.

When the participants filled out the survey, they were able to check multiple responses. For example, if someone was injured while performing the vault, they could have injured both their head and neck and both would show up in the injury count. Thus one injury contributed to two cells.

I've considered running separate analyses for each body part but I don't think that exactly answers my question. Is there another way to tackle this problem or a different statistical test that might work?

Answer 1

There are at least a couple options with "check all that apply" data.

First, you could analyze each body part as a separate dependent (in this case) possibly logistic regression (injured that part vs. did not) or possibly some form of count regression (number of times that part was injured). I suspect a zero-inflated negative binomial regression would be best here. The equipment would be the independent variable.

Second you could analyze combinations of body parts as the dependent variable. This would depend on having a large enough N to make various combinations common enough to analyze, and it would require some judgement in picking combinations. You don't say how many body parts you list, but it looks like it would be at least 10. That makes for a LOT of potential combinations. You might wind up with things like "Head and something else" but you'd have to be careful to make the categories exhaustive and exclusive.