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

From   kubo kensuke <[email protected]>
To   [email protected]
Subject   Re: st: RE: Standard error for correlation coefficient in "biprobit"
Date   Mon, 18 Oct 2010 20:26:45 +0900

Dear Professor Cox,
Thank you for correcting me on the terminology.  I forgot to mention
in my post that I found your paper to be extremely illuminating,
especially the comparison against bootstrap results.
With best regards,

On Mon, Oct 18, 2010 at 18:33, Nick Cox <[email protected]> wrote:
> 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
> [email protected]
> 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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