I am trying to analyse data from a survey examining what variables affect teachers perceived barriers to incorporating technology into their classroom. I have 5 predictor variables however my DV (perceived barriers) is nominal, and answers are not mutually exclusive as participants were allowed to select all options that applied to them. I was hoping to do a multinomial regression but as the DV is not mutually exclusive this is not possible. I am wondering if there is a similar analysis that allows for a non-mutually exclusive DV.
There is, you could try multivariate logistic regression (a bunch of logistic regressions, one for each possible barrier), or even multivariate probit regression, but check if your barriers correlate strongly, if they are highly correlated latent class analysis could be more appropriate
In that kind of case, the dependent variable is usually viewed as multiple binary variables. That is, Barrier A is it's own yes/no question. Barrier B is it's own yes/no question.
The easiest thing, then, is just to analyze them with separate models.
It would be worthwhile to start, as Marius Ole Johansen suggests, by becoming curious about the structure of the DV. Do the categories in the variable represent a smaller number of underlying dimensions? Do they form a scale or several scales? You can work on this from the bottom up, using exploratory statistical methods, but also from the top down by using what you know of the situation to identify likely barrier "clusters" that might be treated together.
But I'd explore the DV before you start modelling it, for sure.
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