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From |
jpitblado@stata.com (Jeff Pitblado, StataCorp LP) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Jackknife and standard error in NEGBIN model |

Date |
Wed, 06 May 2009 16:42:57 -0500 |

Marc Philipp <marcphilipp@ymail.com> is trying to reproduce the standard error calculations produced by the -jackknife:- prefix command: > I am still trying to understand how the -jackknife:- command computes the > standard errors of the parameters. I made some progress, but I still have a > problem that is puzzling me. Actually, I tried to replicate these standard > errors using the method outlined in Miller (1974), which is based on Tukey > (1958). According to Stata user guide, this is the method implemented in > Stata. > > However, I don't manage to get the same standard errors. I send you my > output below, where you can see how I tried to replicate the results. You > can see that the Jackknifed parameters are exactly the same, but the > standard errors produced by the -jackknife:- command are smaller than those > I computed. They should be the same. Am I making a mistake or is Stata > using another method to compute these standard errors? > . jackknife _b[x] e(delta), cluster(tt) saving(jack, replace): nbreg y x d*, disp(c) nocons > (running nbreg on estimation sample) > > Jackknife replications (3) > ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 > ... > > Jackknife results Number of obs = 300 > Number of clusters = 3 > Replications = 3 > > command: nbreg y x d*, disp(c) nocons > _jk_1: _b[x] > _jk_2: e(delta) > n(): e(N) > > ------------------------------------------------------------------------------ > | Jackknife > | Coef. Std. Err. t P>|t| [95% Conf. Interval] > -------------+---------------------------------------------------------------- > _jk_1 | 1.013864 .1062226 9.54 0.011 .5568252 1.470903 > _jk_2 | 1.362775 .0625554 21.79 0.002 1.093621 1.631929 > ------------------------------------------------------------------------------ > > . matrix bet = e(b) > . matrix list e(b_jk) > > e(b_jk)[1,2] > _jk_1 _jk_2 > y1 1.0350594 2.6554469 > > . use jack.dta, clear > (jackknife: nbreg) > > . gen beta_i = 3*bet[1,1]-2*_jk_1 > . gen delta_i = 3*bet[1,2]-2*_jk_2 > . su beta_i delta_i > > Variable | Obs Mean Std. Dev. Min Max > -------------+-------------------------------------------------------- > beta_i | 3 1.035059 .1839829 .8623033 1.228518 > delta_i | 3 2.655447 .108349 2.582983 2.780004 In the above code, Marc is using -jackknife- to save a dataset with the jackknife replicates of his statistics of interest, there are only 3 replicates because of clustering. He then uses these replicates to generate his own 'pseudo' values. Finally he uses -summarize- on the newly generated variables. While -summarize- computed the standard deviation of Marc's new variables, the standard error produced by -jackknife- comes from the standard error of the mean of the pseudo values. In Marc's example above, the difference is due to a factor of 'sqrt(1/n)' where 'n' is the number of replicates, n=3 in Marc's example. .1062226 = .1839829 * sqrt(1/3) .0625554 = .108349 * sqrt(1/3) Marc could use the -ci- command instead of -summarize- to reproduce the standard error calculations of -jackknife-. --Jeff jpitblado@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/

**Follow-Ups**:**Re: st: Jackknife and standard error in NEGBIN model***From:*Marc Philipp <marcphilipp@ymail.com>

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