# st: -_diparm- (and its tanh option)

 From "Stephen P. Jenkins" To statalist@hsphsun2.harvard.edu Subject st: -_diparm- (and its tanh option) Date Thu, 24 Oct 2002 17:00:27 +0100 (GMT Daylight Time)

```-_diparm-  is a very useful utility for displaying ancillary
parameters. These parameters are often estimated in a transformed
metric, but we are interested in the estimate in the original metric.
Handily, -_diparm- includes several standard transformations as options.
My questions are:
1. In the example below, why does the value for the standard error
of the ancillary parameter "rho" that gets pumped out by -_diparm- with
the tanh option differ from the value that I calculated by hand.
2. More generally, why does -_diparm- /not/ produce the "z" and "P > z"
values?  ... and yet it produces a c.i.?  [I, for one, would like to
see "z" and "P > z" reported as well.]

Motivation:
In a model with a correlation ("rho") as ancillary parameter,
a model is typically estimated in terms of
t = atanh(rho) = .5*ln((1+rho)/(1-rho)),
to ensure that rho lies in the range (-1,1). A bivariate
probit (-biprobit-) is an example of such a model.

The following output illustrates the basis of my questions:

. * Use same data set as for -biprobit- in Ref [A-G], p. 142

. use http://www.stata-press.com/data/r7/school.dta, clear

Seemingly unrelated bivariate probit              Number of obs   =         95
Wald chi2(6)    =       9.59
Log likelihood = -89.254028                       Prob > chi2     =     0.1431

------------------------------------------------------------------------------
|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
private      |
years |  -.0118884   .0256778    -0.46   0.643    -.0622159    .0384391
logptax |  -.1066962   .6669782    -0.16   0.873    -1.413949    1.200557
loginc |   .3762037   .5306484     0.71   0.478     -.663848    1.416255
_cons |  -4.184694   4.837817    -0.86   0.387    -13.66664    5.297253
-------------+----------------------------------------------------------------
vote         |
years |  -.0168561   .0147834    -1.14   0.254    -.0458309    .0121188
logptax |  -1.288707   .5752266    -2.24   0.025    -2.416131   -.1612839
loginc |    .998286   .4403565     2.27   0.023     .1352031    1.861369
_cons |  -.5360573   4.068509    -0.13   0.895    -8.510188    7.438073
-------------+----------------------------------------------------------------
/athrho |  -.2764525   .2412099    -1.15   0.252    -.7492153    .1963102
-------------+----------------------------------------------------------------
rho |  -.2696186   .2236753                     -.6346806    .1938267
------------------------------------------------------------------------------
Likelihood ratio test of rho=0:     chi2(1) =  1.38444    Prob > chi2 = 0.2393

. local t = [athrho]_b[_cons]

. local set =  [athrho]_se[_cons]

. /* rho = (exp(2*t)-1) / (exp(2*t)+1)  = g(t), where t = [athrho]_b[_cons]
>  By delta method:
>    std error of rho = g'(t)*(std. error of t) where ( ... I think that ...)
>                 g'(t) = 2*sqrt(exp(2*t))/((exp(2*t)+1)
>
> -biprobit- produces rho and se(rho) using the "tanh" option in a call to _diparm
> */
.
. di "rho = " (exp(2*`t')-1) / (exp(2*`t')+1)
rho = -.26961864

. di " std error of rho = "  `set'*2*sqrt(exp(2*`t'))/(exp(2*`t')+1)
std error of rho = .23227723

Observe that
(1) the hand-calculated value for s.e.(rho) is close to, but definitely
not the same as, the value printed out in the -biprobit- output. Why?
(2) -_diparm- (called by -biprobit-) did not produce "z" and "P > z"
statistics for rho.

Stephen
----------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research (ISER)
University of Essex, Colchester, CO4 3SQ, UK
Tel: +44 (0)1206 873374. Fax: +44 (0)1206 873151.
http://www.iser.essex.ac.uk

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