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ST: st: Logistic regression & standardized coefficients; Multinomial GOF test


From   Ronald McDowell <McDowell-R3@email.ulster.ac.uk>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   ST: st: Logistic regression & standardized coefficients; Multinomial GOF test
Date   Thu, 8 Dec 2011 16:10:08 +0000

I see from the literature (eg Long and Freese' STATA regression book and as used by fitstat), one approach to logistic regression models is the latent variable model, where y*, the extent/propensity to which one
favours one option as opposed to the other, can be written as a linear combination of predictors plus an error term, the latter which has a standard logistic distribution with variance pi-squared/3. By definition
this is the result for a multinomial (logit) model with 2 classes. Is anyone aware of any references which allow this to be generalised to 3 or more classes, for example, so that y* can be calculated
at each of the different levels (relative to the baseline), as a linear combination plus an error term whose distribution is known and hence can be computed?

Many thanks (again)

Ron


------------------------------

Date: Wed, 7 Dec 2011 14:31:45 +0000
From: Ronald McDowell <McDowell-R3@email.ulster.ac.uk>
Subject: st: Re: St: Logistic regression & standardized coefficients; Multinomial GOF test

Richard

Thanks for the excellent references (below). A follow-up question is whether there is such a thing as standardized coefficients in multinomial logistic regression models,
and if so if there are any parallel references.

Many thanks

Ron McDowell
- -----------------------------------------
Ron McDowell
Institute of Nursing Research
University of Ulster, Coleraine
McDowell-R3@email.ulster.ac.uk


Date: Tue, 06 Dec 2011 12:14:22 -0500
From: Richard Williams <richardwilliams.ndu@gmail.com>
Subject: Re: st: St: Logistic regression & standardized coefficients; Multinomial GOF test

At 11:55 AM 12/6/2011, Ronald McDowell wrote:
>Hi all
>
>1. I've been looking at some materials online about standardized
>coefficients in logistic regression eg.
>
>
>http://www.nd.edu/~rwilliam/stats3/L06.pdf
>
>Full standardization includes dividing the estimated coefficients by
>the standard deviation of Y*. Can someone clarify for me what
>exactly Y* is ? I'm aware it is a function of the fitted values. I
>have used listcoef and fitstat to obtain sd(Y*) so far, but
>  would like to be able to manually compute it.

See Long & Freese's book for a detailed explanation:

http://www.stata.com/bookstore/regmodcdvs.html

For a mini-explanation, including how to compute manually, see

http://www.nd.edu/~rwilliam/xsoc73994/L03.pdf

For more advanced discussions, see the first 19 slides of

http://www.nd.edu/~rwilliam/stats/Oglm.pdf

Also take a look at the -khb- command on SSC and the papers
associated with it. The relevant papers may still be forthcoming so
you may need to write the authors if you want them.

Finally, I don't have the full citation handy, but Scott Menard
offered an alternative approach to Y-standardization in a 2010 issue
of Social Forces.

- - -------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
WWW:    http://www.nd.edu/~rwilliam

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