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:
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.
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
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.