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Re: st: RE: MLOGIT versus a set of LOGIT models [re-posting]

From   "Michael I. Lichter" <>
Subject   Re: st: RE: MLOGIT versus a set of LOGIT models [re-posting]
Date   Wed, 19 Aug 2009 11:14:45 -0400

According to Long and Freese (2003), the reason that a set of binary logits do not produce the same results as a single mlogit is because mlogit places constraints on the coefficients that the set binary logits does not (pp. 190-192). As you know, for a nominal variable Y with J categories, mlogit only estimates J-1 equations. The parameter estimates are constrained so that the third set of parameters are a simple linear combination of the other estimates, which is why they don't need to be shown. Without the constraints, binary logistic will generally produce different results.

Long JS, Freese J. Regression models for categorical dependent variables using Stata. Revised ed. College Station, Tex.: Stata Press; 2003.

Jon Heron wrote:
 Thanks Kieran,

 I was beginning to think that the difference lay between continuous
 and categorical predictors - i had shown that a model with a 4-level
 categorical predictor could be factored into logits, whilst treating
 the same variable as continuous meant that this was not possible.

 I now see that including *two* categorical predictors also results in
 the logits giving a different answer.  Hence it does appear to be
 model complexity rather than variable type.

 I have a Kleinbaum paper in front of me (IJE 26(6), pp1323-1333)
 but I will attempt to track down the book you mention.

 In the meantime I think I have learned enough to drop this from
 from my lecture as it is nothing more than a distraction.

 all the best, Jon

On Tue, August 18, 2009 7:47 pm, Kieran McCaul wrote:
Hi Jon,

I think your belief may be wrong.
I think that when you only have one binary predictor then the results
from a multinomial logistic regression will agree with the results of a
series of logistic regressions, but in more complex models this is not

From memory (I haven't got the book with me) Kleinbaum & Klein discuss

Kleinbaum DG and Klein M (2005). Logistic Regression: A Self-Learning
Text. 2nd Ed.  Springer.

Kieran McCaul MPH PhD
WA Centre for Health & Ageing (M573)
University of Western Australia
Level 6, Ainslie House
48 Murray St
Perth 6000
Phone: (08) 9224-2701
Fax: (08) 9224 8009
If you live to be one hundred, you've got it made.
Very few people die past that age - George Burns

-----Original Message-----
[] On Behalf Of Jon Heron
Sent: Wednesday, 19 August 2009 1:31 AM
Subject: st: MLOGIT versus a set of LOGIT models [re-posting]

 Re-posted following a reading of the relevant FAQ

 Dear Statalisters,

  (I am using Stata/MP v10.1, born 02 Feb 2009)

 It was my belief that the regression estimates from a multinomial
 regression model -mlogit- could be replicated through a set of simple
 models with the appropriately derived binary outcomes.

 Whilst attempting to demonstrate this fact for some teaching material
 polytomous IRT that i am writing, I moved from my usual categorical
 predictors to a continuous covariate + discovered that the above
 no longer held.

 for instance, with a 4-level outcome (ghq1)  and either a binary
 (ghq3_bin) or a 4-level predictor treated as a continuous variable
 I fitted models with the two commands

 mlogit ghq1 ghq3_bin, baseoutcome(0)
 mlogit ghq1 ghq3, baseoutcome(0)

 the former can be replicated using logits, whilst the latter cannot.
 I am struggling to understand why this should be.

 I would very much appreciate any advice you can give,

Dr Jon Heron
ALSPAC Stats Team Leader
Department of Social Medicine
University of Bristol
Oakfield House
Oakfield Grove

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Michael I. Lichter, Ph.D. <>
Research Assistant Professor & NRSA Fellow
UB Department of Family Medicine / Primary Care Research Institute
UB Clinical Center, 462 Grider Street, Buffalo, NY 14215
Office: CC 126 / Phone: 716-898-4751 / FAX: 716-898-3536

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