Re: st: Multivariate logistic regression (and -not- just multilevel logistic)

[Phil Schumm <pschumm@uchicago.edu>]

On Aug 29, 2013, at 4:13 PM, Maria Ana Vitorino <vitorino@umn.edu> wrote:
> From what I understand there is no official command in stata for performing bivariate or multivariate logistic regression. 
> I was able to find only a command for performing bivariate probit ("biprobit").
> Is there a user-written command that would allow me to estimate a bivariate (or preferably multivariate) logistic regression? Note that I'm not talking about the much simpler multilevel logistic regression. The idea is to have separate equations, each with a different 0/1 dependent variable (Y) but with the same independent variables (Xs) while allowing for correlations among the unobservables for the different equations.

On Aug 29, 2013, at 4:51 PM, Maria Ana Vitorino <vitorino@umn.edu> wrote:
> We wish to model the bivariate outcomes of whether children attend private school and whether the head of the household voted for an increase in property tax based on the other covariates.


To add to what Stas has already said, understand that unlike the case of a multivariate probit model, there is no single multivariate logistic distribution (as there is with the multivariate Normal).  Thus, to say that you want to fit a multivariate logistic regression model is, by itself, somewhat ambiguous.

Previous approaches to this problem have included:

1) Marginal logistic regression via GEE (e.g., Carey and Zeger 1993)

2) Mixed effects logistic regression

3) Use of a multivariate distribution with logistic univariate marginals (e.g., O'Brien and Dunson 2004)

In the case of (1) you get logistic marginals and, in the case of Carey and Zeger's alternating logistic regression, you also get to parameterize the pairwise association between outcomes in terms of odds ratios.  Unfortunately, I am not currently aware of an implementation of this in Stata (though there is in R).  In contrast, you can perform (2) in Stata easily, but after integrating out the random effect(s) you no longer have logistic marginals.  Finally, approaches based on a full distributional specification like (3) have yet to become available in Stata (in fact, I'm not aware of any frequentist implementation of these, though there may be in R).

So, the question becomes, what is/are your primary reasons for wanting to use a logistic model instead of, say, a multivariate probit model?  There are, of course, good reasons to prefer a logistic model (these are what motivates (1) and (3) above), but if those don't apply in your case, you can probably get by with a multivariate probit model pretty well (i.e., similar substantive conclusions and similar predicted values, at least over much of the range).


-- Phil

Carey, V and Zeger, SL. 1993. Modelling multivariate binary data with alternating logistic regressions. Biometrika 80, 517-526.

O'Brien, SM and Dunson, DB. 2004. Bayesian Multivariate Logistic Regression. Biometrics 60, 739-746.


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