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Re: st: Jackknife and standard error in NEGBIN model


From   jpitblado@stata.com (Jeff Pitblado, StataCorp LP)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Jackknife and standard error in NEGBIN model
Date   Tue, 05 May 2009 13:46:12 -0500

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
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