I have 15 independent variables and 3 correlated, binary, dependent variables. It seems like for predicting correlated dependent variables the general recommendation is multivariate regression. One recommendation was to use a multivariate GLM with a log link.
However, since my dependent variables are binary, it also seems like a multinomial logistic regression might fit the bill. However, I am not sure if it is as well-suited for correlated dependent variables as the multivariate approach – or, even, if the two are more or less the same thing.
It's hard to determine how equivalent these two approaches are (especially since there are so many articles that say "Multivariate" when they mean "Multiple/Multivariable")
Is one better than the other for correlated dependent variables, or are they essentially the same?
Best Answer
Multinomial logistic regression would be for predicting something like the animal in a photograph: dog, cat, horse, or alligator.
A multivariate logistic regression would be to predict if the photograph contains a dog or a cat AND if the photo is in the daytime or at night. Notice that that there are two distinct variables to predict: the animal and the time of day.
(Time of day could be argued not to be binary, but let’s say it is.)
It sounds like you are in a situation like the latter.