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

 From Scott Merryman To statalist@hsphsun2.harvard.edu Subject Re: st: Standard error for correlation coefficient in "biprobit" Date Mon, 18 Oct 2010 04:41:08 -0500

```. local est = (exp([athrho]_cons)-exp(-[athrho]_cons))/(exp([athrho]_cons)+exp(-[athrho]_cons))

. local se = (1 - (`est')^2)*[athrho]_se[_cons]

Scott

On Sun, Oct 17, 2010 at 9:03 PM, kubo kensuke <kuboken@gmail.com> wrote:
> 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.
>
> With thanks,
> Ken Kubo
> Institute of Developing Economies, Japan

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