Re: st: address standard error of rho in bivariate probit

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: address standard error of rho in bivariate probit Date Sun, 13 Aug 2006 09:10:13 +0100 (BST)

```--- Bernhard Ganglmair <bganglma@uni-bonn.de> wrote:
> version 8
>
> 1) I estimate two bivariate probit models (bivar1, bivar2) using two
> different samples and would like to test for equality of the
> correlation coefficient rho that I get for each sample. rho I
> address with e(rho), but how do I address the standard error of rho
> that is reported in the output table? ereturn list gives me p-values
> and chi-squared for the null, but no standard errors directly.

The correlation is stored as one of the "b" parameters, only in the
form of a Fisher's Z transformed correlation. It is stored as
_b[athrho:_cons]. _b[variable name] usually gives you the regression
coefficient of that variable. _b[equation name:variable name] gives you
the regression coefficient of that variable in that equation. You can
get the constant by typing _b[equation name:_cons]. Fisher's Z
transformation also happens to be the arc-hyperbolic tangent of rho,
which explains the weird equation name. You can transform the variable
back to the correlation metric by taking the hyperbolic tangent. See
the example below:

*-----begin example----
version 8.2
sysuse auto, clear
gen rep2 = rep78 <=3
biprobit rep2 foreign mpg price
matrix list e(b)
nlcom rho: tanh(_b[athrho:_cons])
*-----end example------

> 2) To test for equality of rho in the two samples I thought of
> running a suest on bivar1 and bivar2 and then conduct a simple Wald
> test using test, but suest seems to have lost the results for rho
> in bivar1 and bivar2. Anybody some suggestions how such a test could
> be run?

I would perform the test on the transformed correlations since a) it is
easier to perform because you can use the already available
_b[athrho:_cons], and b) the sampling distribution of the transformed
correlation is more likely to be normally distributed than that of the
correlation coefficient itself.

HTH,
Maarten

-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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