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From |
kubo kensuke <kuboken@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 18 Oct 2010 11:03:36 +0900 |

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 * * 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: Standard error for correlation coefficient in "biprobit"***From:*Scott Merryman <scott.merryman@gmail.com>

**st: RE: Standard error for correlation coefficient in "biprobit"***From:*Nick Cox <n.j.cox@durham.ac.uk>

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