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From |
"Newson, Roger B" <r.newson@imperial.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Gini index with pweights |

Date |
Thu, 23 Oct 2008 17:09:02 +0100 |

A possible solution might involve the -somersd- package, downloadable from SSC. This can calculate confidence limits for an unweighted Gini index, as demonstrated in Newson (2006) and in Newson (2008). The Gini index is a special case of a between-scenario Somers' D of wealth with respect to "scenario". It is defined by assuming that there are 2 lotteries, in which the sample (or poulation) all participate. In the first lottery, each individual buys one ticket. In the second lottery, each individual buys a number of tickets proportional to his or her wealth. The Gini index is the difference between 2 probabilities, namely the probability that the winner of the second lottery is richer than the winner of the first lottery and the probability that the winner of the first lottery in richer than the winner of the second lottery. This difference will always be non-negative, but will be higher if the distribution of wealth is more unequal. To calculate the unweighted Gini index, we can expand each observation (corresponding to a person) to 2 observations (corresponding to the same person in the 2 lotteries), to produce a dataset with 1 observation per person per lottery. The Gini coefficient is then the Von Mises Somers' D of wealth with respect to lottery sequence (1 or 2), with sampling probability weights equal to 1 for each person in the first lottery and to the amount of wealth owned by each person for that person in the second lottery. To calculate a sampling-probability-weighted Gini coefficient, we must start with the original dataset, with 1 observation per person, and define a second set of sampling probability weights. We then expand the dataset as before, to have one observation per person per lottery, and multiply the second sampling probability weight by the sampling probability weight used to calculate the unweighted Gini index, to produce a third sampling probability weight variable. This third sampling probability weight variable is then used with the -somersd- command to calculate a confidence interval for the weighted Gini index. I hope this helps. Let me know if you have any queries. Best wishes Roger References Newson R. Confidence intervals for rank statistics: Somers' D and extensions. The Stata Journal 2006; 6(3): 309-334. Download pre-publication draft from http://www.imperial.ac.uk/nhli/r.newson/papers.htm Newson R. Confidence intervals for rank order statistics and their differences. Latest version dated 23 September 2008. (This is a manual for the program somersd in the somersd package, downloadable from the SSC archive site, and is a post-publication update of a Stata Technical Bulletin article.) Download from http://www.imperial.ac.uk/nhli/r.newson/papers.htm Roger B Newson BSc MSc DPhil Lecturer in Medical Statistics Respiratory Epidemiology and Public Health Group National Heart and Lung Institute Imperial College London Royal Brompton Campus Room 33, Emmanuel Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM Tel: +44 (0)20 7352 8121 ext 3381 Fax: +44 (0)20 7351 8322 Email: r.newson@imperial.ac.uk Web page: www.imperial.ac.uk/nhli/r.newson/ Departmental Web page: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/pop genetics/reph/ Opinions expressed are those of the author, not of the institution. -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of francesca.modena Sent: 23 October 2008 16:08 To: statalist@hsphsun2.harvard.edu Subject: st: Gini index with pweights Deal all, I would like to estimate the Gini index with sampling weights pweight. Inequal.ado allows only fweights to be used; ineqdeco.ado allows fweights and aweights. How can I do it? Thanks Francesca Modena * * 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**:**st: Gini index with pweights***From:*"francesca.modena" <francesca.modena@email.unitn.it>

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