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]
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