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RE: st: Test of ordered probit vs ordinary probits


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Test of ordered probit vs ordinary probits
Date   Thu, 1 Nov 2007 11:14:59 -0000

Thanks, Richard (and thanks, Partha), for the very helpful discussion
and examples.  I have one last question.

The examples we've been going through have focused on the constraint
that the slope coeffs are the same across equations.  The key point is
that imposing this constraint also implies that the cutoffs satisfy the
ordering constraint.

Say that I don't impose the constraint that the slope coeffs are the
same.  Say also that I have some doubts about whether my outcome
variable is genuinely order-able.  I know that outcome A is different
from B, and B is different from C, and I hypothesize that C>B>A but I
have some doubts about it.  (Silly example: in terms of education, PhD >
BA > high school, but maybe spending so much time getting the PhD means
you forget a lot of the useful stuff you learned in high school and
university.  Hmmm, maybe not so silly.)

This takes me back to my original example of a bunch of separate
probits, but this time contrasted with, e.g., the default behavior of
-gologit2- (with link(pr) to make it a generalized ordered probit).  The
latter imposes only the constraint that the cutoffs are ordered,
corresponding to order-ability of the outcome variable.  How would you
test this constraint?

I looked through the mass of very useful refs and packages Richard
suggested yesterday, but didn't see this.  Apologies in advance if it's
there and I didn't spot it.

Cheers,
Mark

Prof. Mark Schaffer
Director, CERT
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS
tel +44-131-451-3494 / fax +44-131-451-3296
email: m.e.schaffer@hw.ac.uk
web: http://www.sml.hw.ac.uk/ecomes
 

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Richard Williams
> Sent: 01 November 2007 02:53
> To: statalist@hsphsun2.harvard.edu; statalist@hsphsun2.harvard.edu
> Subject: RE: st: Test of ordered probit vs ordinary probits
> 
> 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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