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From |
Marc Philipp <marcphilipp@ymail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Wed, 6 May 2009 09:51:08 -0700 (PDT) |

Dear all, 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? Many thanks in advance for your support! Best regards, Marc . 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 ----- Original Message ---- From: Marc Philipp <marcphilipp@ymail.com> To: statalist@hsphsun2.harvard.edu Sent: Wednesday, May 6, 2009 10:00:04 AM Subject: Re: st: Jackknife and standard error in NEGBIN model Dear Jeff, Many thanks for your very clear explanation! Now I understand why the two reported standard errors are different. You are right I should use method (1) since I am interested in the jackknife standard error of delta. Many thanks again, your help is very valuable! Best regards, Marc ----- Original Message ---- From: "Jeff Pitblado, StataCorp LP" <jpitblado@stata.com> To: statalist@hsphsun2.harvard.edu Sent: Tuesday, May 5, 2009 1:46:12 PM Subject: Re: st: Jackknife and standard error in NEGBIN model Marc Philipp <marcphilipp@ymail.com> is using the -jackknife:- prefix command with -nbreg-, and asks why the reported standard errors differ for the 'delta' parameter between two different -jackknife:- specifications: > I have a problem with the jackknife command. Hopefully there are some > experienced users who will be able to help me. I am estimating a negative > binomial model (NEGBIN 1), regressing a count variable y on a continuous > variable x and on some other control variables z1, z2, ... > > Since I am only interested in the parameter of x and in the overdispersion > parameter delta, I specified the command in this way: > > jackknife _b[x] e(delta), cluster(t): nbreg y x z*, dispersion(constant) > nocons > > However, I observed that if I specify the command in this way, without > collecting the two parameters I am interested in: > > jackknife, cluster(tt): nbreg y x z*, dispersion(constant) nocons, > > something strange happens: the estimated parameters are exactly the same, > but the jackknife standard error of delta is completely different, much > higher than in the previous case, whereas the jackknife standard error of > b[x] is exactly the same. > > I read the Stata user guide and scanned the web to find some hints, but > unsuccessfully. I don't understand why the standard error of the > overdispersion parameter is so different, and don't know which command I > should use. > > Have you already encountered such a problem with the jackknife command? > > Many thanks in advance for your help! Marc is using -jackknife:- in the following two ways (1) . jackknife _b[x] e(delta), cluster(tt): nbreg y x z*, disp(c) nocons (2) . jackknife, cluster(tt): nbreg y x z*, disp(c) nocons and wants to know why the standard error for 'delta' is bigger in (2) than in (1). In (1), -jackknife:- works with -e(delta)- directly; where -e(delta)- is generated by ereturn scalar delta = exp(_b[/lndelta]) so the reported standard error comes from the Jackknife replication method. In (2), -jackknife:- works with -_b[/lndelta]- (the natural log of 'delta') directly, then uses a standard transformation result to get the standard error of 'delta' (coincidentally, this transformation is typically known as the delta-method and has nothing special to do with our 'delta'). Thus the standard error for the reported value of 'delta' in (2) is computed as abs(_b[/lndelta])*SE(_b[/lndelta]) where 'SE(_b[/lndelta])' was computed via the Jackknife replication method. If Marc really meant to compute the jackknife standard error of 'e(delta)', then he should use (1). Stata always uses the delta-method for computing standard errors for derived ancillary parameters like 'delta'. --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/ * * 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**:**Re: st: Jackknife and standard error in NEGBIN model***From:*jpitblado@stata.com (Jeff Pitblado, StataCorp LP)

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

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