# Calculating odds ratio in Multiple select choice question analysis

I have a multiple response categorical variable (MRCV) and a single response categorical variable (SRCV). Respondents in my survey were presented with 6 choices (6 barriers to access an application) and were asked to check all that apply. Respondents were healthcare providers so I have physicians, nurses, pharmacists and dentists (4 levels). I wish to answer the following questions:

1. Do the number of barriers selected differ among provider levels? I am thinking about the following procedures:

• calculate the mean number of barriers per provider level and do a one-way ANOVA.
• sum the barriers per subject and do a Poisson regression with provider as predictor.
• consider the 6 choices as 6 questions (dichotomous) and do a generalized linear mixed model with binomial link function and respondent id as random factor.

I am wondering if the above analyses are answering the same question.

1. Do the distribution of barriers differ among the provider levels? I already found an analysis to answer this question. The method is called Test for Marginal Independence and is available in MRCV package in R. https://journal.r-project.org/archive/2014/RJ-2014-014/RJ-2014-014.pdf

2. This is my main question. Can we able to quantify in terms of odds ratio or probability to say a provider group (E.g. physicians) are more likely to have selected a particular barrier compared to another provider (E.g. nurses). I couldn't find any regression model to answer this question. Any help on this is greatly appreciated.

• For Q3 do you want to do each barrier separately? – mdewey Jan 11 '19 at 16:21
• I should have asked that question. Can we do a binomial regression independently for each barrier or does it violate any assumptions given the nature of multi-select question? I am going through the MRCV package and found an example I think that can answer my Q3. If you look at help(MI.TEST) (requires MRCV package) and go to the last example, they used a gee model on data similar to mine. Can you please check it and tell me if I can proceed with this model. – rftw Jan 11 '19 at 16:41
• I see no reason, if they are at liberty to check as many barriers as they please, why you cannot analyse each separately, presumably with logistic regression. – mdewey Jan 11 '19 at 16:45
• Thank you for your suggestion @mdewey. I will go with logistic regression. As for Q1, is there any difference between the three methods? – rftw Jan 11 '19 at 17:00
• I would have thought ordinal logistic regression might be better than either of your first 2 and I do not immediately see what your third one would do. – mdewey Jan 11 '19 at 17:03