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Re: st: RE: Adding a -constraints- option

From   Richard Williams <[email protected]>
To   [email protected]
Subject   Re: st: RE: Adding a -constraints- option
Date   Wed, 23 Mar 2005 08:34:30 -0500

At 05:21 PM 3/22/2005 -0600, Scott Merryman wrote:
Possibly, Jeroen Weesie's -linest- maybe of use:

      linest.  Two-stage linear-constrained estimation.

      linest imposed linear constraints on the last estimation
      results. This two-stage estimator is asymptotically equivalent
      to the "true" one-stage constrained estimator.
If anyone else is interested in this neat little command - as far as I can tell, it produces the same coefficients and test statistic that you get from using the -test- command with the -coef- parameter. Its biggest advantage over -test-, at least that I can see, is that it lets you replace the values stored in memory from the unconstrained model with the values from the constrained model. This is very useful for post-estimation commands such as -predict- or -fitstat-.

The "asymptotically equivalent" qualifier is important. Using -linest- is like using a Wald test rather than a likelihood ratio test. I believe what it does is use the parameter estimates from the unconstrained model, along with their variances and covariances, and uses those to compute constrained coefficients. This gives results that tend to be similar, but not identical, to what you would get by computing the estimates in a single step, like you could do when a command supports the -constraints- option. For example, I used -linest- after -gologit-, constraining corresponding coefficients to be equal across equations. This gave results that were very similar, but not exactly identical, to what I got by running -ologit-.

It is a very nice command, especially if, like me, you don't know enough about programming to do anything else. But, when possible, it is better to use the -constraints- option, and to write programs that support the -constraints- option. Only a few Stata commands support the -constraints- option now, but hopefully more will do so in the future.

Richard Williams, Notre Dame Dept of Sociology
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