Analyzing a categorical variable with 'Only A', 'Only B', and 'Both A and B' I may not be searching the correct terms to get an education on this seemingly simple question:
I am analyzing the correlation between two categorical variables with Pearson's chi-square test and its residuals (http://v8doc.sas.com/sashtml/insight/chap39/sect56.htm). One categorical variable has three possible values 'Only A', 'Only B' and 'Both A and B'. A reviewer of the analysis suggested that the 'Both A and B' category be removed and instead absorbed into 'Only A' and 'Only B'.
I wonder if this is commonly done and if so I'm hoping to find a 'textbook' example of such. My concern is if a subject is counted twice under both 'Only A' and 'Only B' then the total number of subjects will not be consistent with the population N.
Edit: I realized my question may be described as a problem of 'categorical variables with overlapping values'. Common solutions include one-hot encoding and have '1' under both 'A' and 'B' for ML models, and perhaps add an interaction term for statistical regression. But I still am not sure how to handle it for simple count-based statistic tests such as chi-square and fisher's exact. Is this possible?
Thank you so much.
 A: I'd suspect that the reviewer rather means (or should have meant) to replace the one categorical variable that you use by two binary variable A vs. not A and B vs. not B (apparently this is what you mean by "one hot encoding"; never heard that term). Using just one variable but counting individuals twice in A and B is clearly inappropriate as you state. On the other hand, having one variable with categories none, A, B, and "A and B" loses the information that "A and B" is more connected to A and B than A and B are to each other.
You can then analyse the then three variables that you have by a log-linear model, see https://en.wikipedia.org/wiki/Log-linear_analysis
I should add that if for some reason the "A and B" category is something essentially different than simply aggregating effects of A and B (for example because A changes its character in presence of B), I can imagine using the original categorical variable with levels none, A, B, and "A and B" if the research question is simple enough that messing around with log-linear models and interactions seems too complex.
