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st: asmprobit
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
C:\Program Files\Stata9\ado\updates\a\asmprobit.ado
*! version 2.0.3 18aug2006
. which asmprobit_p
C:\Program Files\Stata9\ado\updates\a\asmprobit_p.ado
*! version 2.0.1 25apr2006
. which asmprobit_estat
C:\Program Files\Stata9\ado\updates\a\asmprobit_estat.ado
*! 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
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.
Thanks for your help!
--Alex Cavallo
Managing Consultant
Navigant Consulting, Inc.
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