# st: asmprobit

 From Alexander Cavallo To statalist@hsphsun2.harvard.edu Subject st: asmprobit Date Wed, 1 Nov 2006 01:15:59 -0600

Stata experts,

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.

. which asmprobit
*! version 2.0.3  18aug2006
. which asmprobit_p
*! version 2.0.1  25apr2006
. which asmprobit_estat
*! version 2.0.2  25apr2006
. query born
06 Oct 2006
. webuse travel
. asmprobit choice travelcost termtime , casevars(income) case(id) alternative(mode) corr(unstructured) stdd
> ev(heteroskedastic)
Iteration 0:   log simulated-likelihood = -201.33896
[output deleted]
Iteration 26:  log simulated-likelihood = -190.09419
Alternative-specific multinomial probit        Number of obs      =        840
Case variable: id                              Number of cases    =        210
Alternative variable: mode                     Alts per case: min =          4

avg =        4.0
max =          4
Integration sequence:      Hammersley
Integration points:               200             Wald chi2(5)    =      32.06
Log simulated-likelihood = -190.09419             Prob > chi2     =     0.0000
------------------------------------------------------------------------------
choice |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
mode         |
travelcost |  -.0097707   .0027835    -3.51   0.000    -.0152261   -.0043152
termtime |  -.0377034   .0094046    -4.01   0.000    -.0561361   -.0192708
-------------+----------------------------------------------------------------
air          |  (base alternative)
-------------+----------------------------------------------------------------
train        |
income |  -.0291886   .0089232    -3.27   0.001    -.0466778   -.0116995
_cons |   .5615485    .394619     1.42   0.155    -.2118906    1.334988
-------------+----------------------------------------------------------------
bus          |
income |  -.0127473   .0079269    -1.61   0.108    -.0282839    .0027892
_cons |  -.0572738   .4791635    -0.12   0.905    -.9964169    .8818693
-------------+----------------------------------------------------------------
car          |
income |  -.0049067   .0077481    -0.63   0.527    -.0200927    .0102792
_cons |  -1.833159     .81842    -2.24   0.025    -3.437233   -.2290856
-------------+----------------------------------------------------------------
/lnl2_2 |  -.5499745   .3903368    -1.41   0.159    -1.315021    .2150717
/lnl3_3 |  -.6008993   .3354232    -1.79   0.073    -1.258317     .056518
-------------+----------------------------------------------------------------
/l2_1 |   1.131589   .2125186     5.32   0.000     .7150604    1.548118
/l3_1 |   .9720683   .2352248     4.13   0.000     .5110362      1.4331
/l3_2 |   .5196988   .2860692     1.82   0.069    -.0409865    1.080384
------------------------------------------------------------------------------
(mode=air is the alternative normalizing location)
(mode=train 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
. di exp(-.5499745)
.57696452
. di exp(-.6008993)
.54831831

I don't understand how to convert the /lnl2_2 and /lnl3_3 parameters into the reported variances of (1.61 and 1.51).  Also, why is the variance of train=2 - I had expected it to be 1.00 since train is the scale normalization.
Finally, I don't quite understand how to compare /l2_1 /l3_1 and /l3_2 to the reported correlations of 0.891 0.790 and 0.895.