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Re: st: Testing the extent of difference between two coefficients in the same model


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: Testing the extent of difference between two coefficients in the same model
Date   Tue, 31 Jan 2012 11:19:22 -0500

At 06:34 AM 1/31/2012, Maarten Buis wrote:
On Mon, Jan 30, 2012 at 11:12 PM, David Hoaglin wrote:
>  A model in
> which the two coefficients are equal is the same as the model in which
> the predictor associated with that coefficient is the sum of "old" and
> "new."

This is a trick that is often forgotten (at least in my discipline),
but can have surprisingly useful applications beyond adding linear
constraints to models that do not allow the -constraint- option. I
submitted a Stata tip on this topic a couple of days ago.
<http://www.maartenbuis.nl/wp/sumconstr.html>

-- Maarten

As Maarten's tip shows, this approach lets you do likelihood ratio tests of the constraint, whereas the -test- command does a Wald test. Starting with Stata 11, the -logit- and -ologit- commands allowed the use of the -constraint- option, so the tip isn't quite as necessary as it used to be, although I think it may be just as easy if not easier to compute the sum as it is to specify the constraints. For teaching purposes I like to write out the equations and illustrate approaches like this just so my students understand the constraints being imposed and why this works.


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Richard Williams, Notre Dame Dept of Sociology
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