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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?

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    $\begingroup$ 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). $\endgroup$
    – gammer
    Commented Jan 15, 2017 at 21:32
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    $\begingroup$ 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 $\endgroup$
    – gammer
    Commented Jan 15, 2017 at 21:37
  • $\begingroup$ @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! $\endgroup$
    – kgstat
    Commented Jan 16, 2017 at 14:32

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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.

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