# Re: st: asmprobit

 From [email protected] (Richard Gates) To [email protected] 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
[email protected]
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```