# multiple choice data simple logistic regression or multinomial logistic regression

I have a survey question where the respondent can check one choice or two choice maximum. Question looks like this:

What is the more important characteristic when you buy chocolate?

• Sweetness (characteristic 1)
• Packaging (characteristic 2)
• Price (characteristic 3)
• ... (characteristic 4)
• ... (characteristic 5)
• ... (characteristic 6)

In my data, I have 6 column (1 for each characteristic) with the value 1 if the respondent checked the ad-hoc column and 0 otherwise.

I would like to perform a regression where the outcome is the question and the predictors the socio demographic criteria (some of them are numerical such as the age and other categorical such as the gender).

Now I wonder how I should do. Should I do a simple logistic regression 6 times with same predictors but each time different outcome?

• glm(caracteristic1 ~ age+gender)
• glm(caracteristic2 ~ age+gender)
• glm(caracteristic3 ~ age+gender)
• glm(caracteristic4 ~ age+gender)
• glm(caracteristic5 ~ age+gender)
• glm(caracteristic6 ~ age+gender)

Or is it possible to use another method such as the multinomial logistic regression. If yes which R packages do you recommend me to use?

If the user was allowed to select only one of the characteristics, then multinomial logistic regression would be an acceptable model choice. However, since you allow the user to select possibly two characteristics, you cannot use the multinomial model directly. This is because the multinomial model assumes the responses to follow a multinomial distribution, in which out of say $n$ categories, a single response corresponds to a single category.