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I'm working with a data set with 2-3 response variables and 7 predictor variables. All the variables are categorical. If there were just one response variable, I think a multinomial logit would be the right model, but there are 2 or 3. So my question is - is there a multivariate version of the multinomial logit?

I've looked at several books on categorical data, but haven't seen anything like this (mainly using Agresti 2002).

I have about 2000 observations, though I'll probably need to split it up into 2 or 3 data subsets to really see what's going on. One thing I was thinking about is converting it to counts and use a model for count data. I could also combine the 2-3 response vars into 1 categorical with a lot of categories, but I think that will lower the chances of anything showing up for any of the categories. I could also do 2-3 separate models, one for each variable, which is obviously not as good.

I might also be able to get rid of some of the predictors (I think 3 of the 7 have the most explanatory power). I'm not opposed to using machine learning methods, I've found some interesting stuff already with decision trees.

thanks,

-paul

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    $\begingroup$ in multivariate regression if you estimate each equation separately you lose out only in efficiency, the estimates of the coefficients and their standard errors are estimated correctly. I suspect that the same should hold for multivariate multinomial logit. $\endgroup$ – mpiktas Apr 1 '11 at 6:05
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    $\begingroup$ Mpiktas' hunch is right. There exists multivariate multinomial logit models and I have seen it in Agresti 2002. I will get back with the exact page numbers as I dont have the book on me. But I have seen the theory being developed in the same chapter in which they introduce Mutivariate logit; I think immediately after the horse-shoe crabs or crocodile examples. $\endgroup$ – suncoolsu Apr 1 '11 at 7:17
  • $\begingroup$ May not be what you're looking for, but it might be worth considering mixed effects multinomial logit models. Yet another approach would be to look at package drm in R, which claims to do regression for clustered variables using "dependence ratios" to model intra-unit association (helsinki.fi/~jtjokine/drm). $\endgroup$ – lockedoff Apr 1 '11 at 15:57
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Agresti 2007 discusses them. They're in chapter 9 and 10. The 2002 edition probably discusses them too, as @suncoolsu mentioned.

Agresti refers to the group of response variables as a cluster and discusses according analysis with marginal models, conditional models and generalized estimating equations.

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    $\begingroup$ Ok, thanks. It was the terminology that got me - I didn't realize clustered/repeated response data meant basically the same thing as mutlivariate in regression, but it seems that's the case. In Agresti 2002 I think it's Ch. 11 & 12. 2007 and 2002 cover most of the same stuff, but '02 is a little more in depth. Time to read those chapters. $\endgroup$ – paul Apr 1 '11 at 21:30

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