st: RE: Standard error for correlation coefficient in "biprobit"

[Nick Cox <n.j.cox@durham.ac.uk>]

This won't help at all, but I am going to point out that the inverse hyperbolic functions such as atanh are not properly described as arc-hyperbolic functions. That common misconception, or misuse of terminology, is based on a false analogy with inverse trigonometric functions such as arcsine which can be thought of as yielding arcs as result. Hyperbolic functions are not periodic and their inverses do not yield (lengths of) arcs. 

The problem can also be blamed on the English language which means that "a" or "ar" can be read as abbreviations for "arc", "area" and "argument"; however, in this case the first interpretation is incorrect. 

Nick 
n.j.cox@durham.ac.uk 

kubo kensuke

I am using the "biprobit" command for bivariate probit regression, and
would like to know how Stata computes the standard error for the
correlation coefficient ("rho") between the two error terms.

I have read the manual and understand that Stata indirectly estimates
"rho", by estimating its arc-hyperbolic tangent ("\athrho"), and
transforming it back to the original parameter using the inverse
function.  I also understand how the confidence interval of "rho" is
calculated from the confidence interval of "\athrho".  However,
nowhere can I find any explanation on how the reported standard error
of "rho" is calculated.  I tried a delta-method calculation to obtain
the standard error of "rho" from the standard error of "\athrho" and
the analytical derivative of the hyperbolic tangent function, but the
result was clearly different from what was reported by Stata.

Hoping for an explanation, I purchased Professor Cox's Stata Journal
article ("Speaking Stata: Correlation with confidence, or Fisher's z
revisited", 2008), but could not find a direct answer to this specific
question.

All I need is the formula that Stata uses to obtain the standard error
of "rho", based on its direct estimation of the arc-hyperbolic
tangent.   Any suggestions on this topic would be greatly appreciated.


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