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Re: st: asmprobit


From   rgates@stata.com (Richard Gates)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: asmprobit
Date   Wed, 01 Nov 2006 07:24:50 -0600

Alex queried:

> I don't understand how -asmprobit- converts from the transformed scale of
> variance and correlation parameters into the actual space.  See this
> example.  I am using Stata 9 which has been updated.
> 
>      /lnl2_2 |  -.5499745  
>      /lnl3_3 |  -.6008993   
> -------------+---------------------------------------------------------=
>        /l2_1 |   1.131589   
>        /l3_1 |   .9720683 
>        /l3_2 |   .5196988  
> 
> (mode=3Dair is the alternative normalizing location)
> (mode=3Dtrain is the alternative normalizing scale)
> . estat cov
>   +------------------------------------------------+
>   |              |     train        bus        car |
>   |--------------+---------------------------------|
>   |        train |         2                       |
>   |          bus |  1.600309   1.613382            |
>   |          car |  1.374712    1.39983   1.515656 |
>   +------------------------------------------------+
> Note: covariances are for alternatives differenced with air
> . estat corr
>   +---------------------------------------+
>   |              |  train     bus     car |
>   |--------------+------------------------|
>   |        train |  1.000                 |
>   |          bus |  0.891   1.000         |
>   |          car |  0.790   0.895   1.000 |
>   +---------------------------------------+
> Note: correlations are for alternatives differenced with air

By default -asmprobit- estimates the Cholesky (square root) matrix of the
differenced variance-covariance using the log transform for the diagonal
elements.  Below shows how to build the Cholesky matrix (L), then the matrix
product L*L' gives you the variance-covariance matrix (V).

. mat L = (sqrt(2),0,0\ 1.131589,exp(-.5499745),0\.9720683,.5196988,exp(-.6008993))

. mat li L

L[3,3]
           c1         c2         c3
r1  1.4142136          0          0
r2   1.131589  .57696452          0
r3   .9720683   .5196988  .54831831

. mat V = L*L'

. mat li V

symmetric V[3,3]
           r1         r2         r3
r1          2
r2  1.6003085  1.6133817
r3  1.3747122  1.3998296  1.5156566

-Rich
rgates@stata.com
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