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RE: st: Test of ordered probit vs ordinary probits


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu, <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Test of ordered probit vs ordinary probits
Date   Wed, 31 Oct 2007 22:52:46 -0400

At 06:48 PM 10/31/2007, Schaffer, Mark E wrote:
Thanks, Richard, that's *really* helpful.  The only thing I would add is
that another reason my test result vs. the test result from -omodel-
differ is that I used -suest-, which means it was a heterosk-robust Wald
test vs. -omodel-'s non-robust approximate LR test.
Sounds good.


Your use of the -coef- option of -test- is very nifty.  If I understand
what you've said and what the manual says about -coef- correctly:

(1) -gologit2- imposes during the estimation the one-step constraints
that the cutoffs are ordered.
If you use gologit2 with the pl option, it will require that the coefficients be equal across equations, which in turn will force the cutoffs to be ordered. Yes, these are one step constraints; internally gologit2 is creating a bunch of constraint commands and then imposing those constraints on the estimates. In an unconstrained gologit, the coefficients can all differ across equations; in a totally constrained gologit the coefficients are all the same across equations and it becomes the ologit model.

To be clear, there is nothing in the code that explicitly says the cutpoints have to be ordered; rather the ordering of the cutpoints is a consequence of the rest of the model's requirements/constraints.


(2) Separate -probit-s followed by -test- with the -coef- option in
effect imposes asymptotically equivalent two-step constraints that the
cutoffs are ordered.
Yes, I believe that is correct, although again I would clarify that the ordering of the cutoffs is a consequence of the constraint that the coefficients be equal; it isn't a separate constraint. i.e. equal coefficients across equations implies/forces ordered cutoff points. (If that isn't clear I can try to elaborate further on why equal coefficients implies ordered cutpoints.)

Weesie's -linest- command (available from his own site; use -findit-) can be another nifty way of doing this sometimes. So, for example, picking up from the last example where the suest command was given,

. suest probit12 probit23 probit34

[ Output deleted]

. constraint 1 [probit12]yr89 = [probit23]yr89

. constraint 2 [probit23]yr89 = [probit34]yr89

. linest, c(1 2) modify

Two-step constrained suest
Dim unrestricted model = 6
Dim restricted model = 4
# restrictions = 2
Wald X2 for restrictions = 13.1530
Prob > chi2(2) = 0.0014
( 1) [probit12]yr89 - [probit23]yr89 = 0
( 2) [probit23]yr89 - [probit34]yr89 = 0
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
probit12 |
yr89 | .363189 .045948 7.90 0.000 .2731326 .4532454
_cons | .9988136 .037007 26.99 0.000 .9262812 1.071346
-------------+----------------------------------------------------------------
probit23 |
yr89 | .363189 .045948 7.90 0.000 .2731326 .4532454
_cons | -.0067555 .0321153 -0.21 0.833 -.0697003 .0561892
-------------+----------------------------------------------------------------
probit34 |
yr89 | .363189 .045948 7.90 0.000 .2731326 .4532454
_cons | -1.063885 .0365802 -29.08 0.000 -1.135581 -.9921892
------------------------------------------------------------------------------

We modified the stored results of suest.
Post-estimation commands use the constrained model!
Beware (see online help!)

One nice (dangerous?) thing about -linest- is that, with the -modify- option, the constrained estimates replace the unconstrained estimates. So, any post-estimation command is now going to use the results you see above. If you have a command that does not support the -constraints- option, linest may be the next best thing. Early versions of gologit2 used linest until I figured out how to do 1 step estimation.


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