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

From   Maarten buis <>
Subject   Re: st: address standard error of rho in bivariate probit
Date   Sun, 13 Aug 2006 09:10:13 +0100 (BST)

--- Bernhard Ganglmair <> 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. 


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

visiting adress:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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