# Multivariate logistic regression vs multinomial logistic regression?

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?

• When you say you would use multinomial--would the outcome be an 8 category variable comprised of the $2^3$ possible combinations of the three binary variables? That would estimate completely different parameters from the based on modeling the joint distribution of three binary variables (the multivariate model). – gammer Jan 15 '17 at 21:32
• If you prefer the multivariate binary model, I'm not sure the multivariate logistic model (specifically, the correlations between variables) is identified. I've never heard of anyone doing multivariate logistic regression and, you're absolutely right that it is hard to tell because so many researchers misuse the term "multivariate" in reference to regression. The multivariate probit model is identified, though, and may suit your purposes. See the wikipedia page for a brief description. en.wikipedia.org/wiki/Multivariate_probit_model – gammer Jan 15 '17 at 21:37
• @gammer, you make a good point, thank you. I think then that the multivariate is more what I am getting at, and the multivariate probit looks promising. Thanks! – kgstat Jan 16 '17 at 14:32