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st: RE: Polytomous vs "regular" unconditional logistic regression

From   "Jann, Ben" <>
To   <>
Subject   st: RE: Polytomous vs "regular" unconditional logistic regression
Date   Fri, 28 Nov 2003 10:11:34 +0100

Roger Milne wrote:

> I don't understand why I get different estimates (ignoring 
> standard errors) from the following two models:
> 1. Multivariate polytomous logistic regression, with outcome 
> categories 0, 1 and 2 (with ", basecategory(0)")
> 2. Two separate multivariate (same covariates) "regular" logistic 
> regression models:
>          (i)  with ", if outcome~=2"
>          (ii) with ", if outcome~=1"
> For the univariate case, I get the same estimates from 1 and 
> 2, but they 
> start to "diverge" as soon as I add an additional covariate.

Kieran McCaul answered:

> I haven't used polytomous regression, but was under the impression
> that the same results would be obtained from both approaches.

Wrong. The point estimates are different because -mlogit- (I guess, this
is what Roger used in approach 1) ensures that the probabilities of the
three categories always sum up to one, whereas separate estimation using
-logit- (Roger's approach 2) will yield consitent results (i.e. sum of
probabilities always equal 1) only in certain cases (e.g., in a model
without covariates). Thus, approach 2 only provides approximations of
the -mlogit- estimates (approximation will be poor if group sizes are
small; the most frequent group should be chosen as base category). See
Begg and Gray, 1984: Calculation of Polychotomous Logistic Regression
Parameters Using Individualized Regressions. Biometrika 71: 11-18.


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