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Re: st: zero truncated negative binomial (ztnb) with sampling weight


From   Steve Samuels <sjsamuels@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: zero truncated negative binomial (ztnb) with sampling weight
Date   Fri, 14 May 2010 15:17:45 -0400

The form of the weighted likelihood (independent data) is given in the
Stata Manual reference for -ztnb-.  As you have probability weights,
you probably have a complex survey design (clusters, strata). If so,
you should -svyset-your data and use -svy: ztnb-. For survey data, the
general survey form of likelihood estimating equations is shown in the
"Variance Estimation" chapter of Stata's Survey Data Manual.

-predict- following -svy: ztnb- will give two kinds of predictions
("n" and "cm") from which you can form residuals. Use the first if
zero was a possible value that could not be observed for some reason;
otherwise- if the data are inherently positive- use the second.

You appear to want to standardize the residual in some way. I don't
recognize the denominator in your residual so I cannot comment on it.
I would guess, however, that the denominator appropriate for the
non-truncated negative binomial will suffice for all practical
purposes.

Steve

On Tue, May 11, 2010 at 2:45 PM, Kim, Seung Gyu <sgkim@utk.edu> wrote:
> Dear all:
>
> I am struggling with ZTNB with sampling weight. The residuals of
> "negative binomial regression" are calculated as
> (y-yhat)/(1+yhat*alpha), but I could not find the residuals if it is
> "truncated" and "weighted by sampling weight" at the same time. I would
> appreciate if someone gives me the functional form of residuals or
> loglikelihood function for ZTNB with sampling weight.
>
> FYI, log likelihood function of zero truncated negative binomial is
> Y*ln(alpha*exp(xb)/(1+alpha*exp(xb))-ln(1+alpha*exp(xb))/alpha+ln
> Gamma(y+1/alpha)-ln Gamma(y+1)-ln
> Gamma(1/alpha)-ln(1-(1+alpha*exp(xb))^(-1/alpha).
> Thanks.
>
> SG Kim
> sgkim@utk.edu
>
>
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-- 
Steven Samuels
sjsamuels@gmail.com
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Saugerties NY 12477
USA
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