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From |
Nick Cox <n.j.cox@durham.ac.uk> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

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

Date |
Mon, 18 Oct 2010 10:33:44 +0100 |

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. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: Standard error for correlation coefficient in "biprobit"***From:*kubo kensuke <kuboken@gmail.com>

**References**:**st: Standard error for correlation coefficient in "biprobit"***From:*kubo kensuke <kuboken@gmail.com>

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