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From |
rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: correlation estimates in gee |

Date |
Mon, 05 Oct 2009 16:48:24 -0500 |

David Jeffries <djeffries@mrc.gm> asks: > How is the exchangeable correlation parameter (alpha) estimated for a > generalised estimating equation? > For a binomial family with unbalanced panels, it is not as listed (Karim's > implementation) on page 140 of the longitudinal/panel data manual (Stata > 11). It doesn't appear to be Liang and Zeger's 1986 implementation either, > although comments within the xtgee ado code say it is? > Within xtgee it is calculated as scalar `alpha' = `alpha'*`phi'/`cF' > phi is the sum of squared Pearson residuals / total observations cF is > 0.5*sum(ni*(ni-1)), where ni are the panel sizes > From the ado code I can't understand how alpha itself is actually evaluated > as I can't follow this line of code? > _GEEUC `ei' `ww', a(`alpha') ty(`corr') n(`maxni') > where alpha actually appears to be evaluated. David's assertion that alpha is not calculated as listed on page 140 of the [XT] manual is correct. There is a typo in the formula for alpha listed there. The outer sums from i = 1 to M in the two main terms being divided need to be brought into their respective numerators and denominators in order to correspond to the calculation made by -xtgee-. We'll make this correction to the documentation. That stated, the calculation performed currently by -xtgee- does correspond to that of Liang of Zeger (1986), with one exception. Their paper uses a divisor of N - p, where p is the number of regressors, and by default -xtgee- uses a divisor of N. To have -xtgee- use a divisor of N - p instead, you can use option -nmp-, in which case you fully recover the Liang and Zeger estimator. That -xtgee- reproduces Liang and Zeger (1986) can be difficult to see from the ado code, because a key component is calculated by the internal routine -_GEEUC-. However, if David wishes he can email one of us privately and we can supply a .do file that we have developed while researching this question. That do-file reproduces -xtgee-'s alpha calculation on a particular dataset, and does so following Liang and Zeger. Reference: Liang, K.-Y. and S. L. Zeger. 1986. Longitudinal data analysis using generalized linear models. Biometrika 73: 13-22. --Bobby --Theresa rgutierrez@stata.com tboswell@stata.com * * 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/

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