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

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 18 Oct 2010 20:17:37 +0900 |

Dear Scott, Thank you very much for the formula! I see that the standard error is indeed calculated by the delta method. When I was trying to apply the method earlier, I must have been using an erroneous analytical derivative. Thanks again for your time, Ken On Mon, Oct 18, 2010 at 18:41, Scott Merryman <scott.merryman@gmail.com> wrote: > . 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 > > * > * 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/ > * * 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/

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

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

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