Re: st: Zeros and measures of inequality or concentration

["Roger B. Newson" <r.newson@imperial.ac.uk>]

The -scsomersd- package (downloadable from SSC) was also updated 
recently to allow estimation (with asymmetric confidence limits using 
the hyperbolic arctangent or Fisher's z transformation) of Gini 
inequality coefficients for populations where some of the subjects have 
zero wealth. An example of estimating a Gini inequality coefficient 
appears in the on-line help for this package. If you install it, then 
you must also install -somersd- and -expgen-, also downloadable from SSC.

Best wishes

Roger


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: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 09/02/2012 11:00, S.Jenkins@lse.ac.uk wrote:
> ------------------------------
>
> Date: Wed, 8 Feb 2012 20:17:24 -0900
> From: Troy Payne<paynetc@gmail.com>
> Subject: st: Zeros and measures of inequality or concentration
>
> I have a more statistical question than a Stata-related question:  Which
> measure of inequality or concentration is best for data with a large
> number of observations with a value of zero?
>
> While I haven't used them before, it seems that Lorenz curves, Gini
> coefficients, and other related measures of inequality would be a good
> way to examine concentrations of crime at addresses.  Like income, crime
> tends to be highly concentrated, with a relative handful of places
> contributing large proportions to the total crime count.  In fact, at
> the place-level (address or street segment) the most common crime count
> is often zero.
>
> I have crime data at apartment buildings in a midwestern city.  In my
> data, 45% of apartments had zero crimes in any given year.  If I include
> only violent crimes, then 74% of apartments have zero crimes in any
> given year.
>
> Posts here on Statalist lead me to -inequal-, -sgini-, -lorenz-, and
> -glcurve- (all installed in Stata 12.1, all available via SSC).  Judging
> from the r(N) returned, -inequal- seems to explicitly exclude
> observations with values of zero, while -sgini- does not.  It's
> difficult for me to tell if -lorenz- and -glcurve- include observations
> with values of zero, even after reading the help files and other
> documentation provided.
>
> Nearly all of what I've read about these various inequality measures so
> far seems to assume non-zero values, or at least that zero values are
> rare.  I'm unsure what the practical impact of a large proportion of
> zeros would have, even for user-written commands that appear to allow
> them.
>
> Until two days ago, I had never dug into the details of Gini
> coefficients.  It's possible that the documentation has the answer and
> I've just missed it.  I'd very much appreciate any guidance list members
> could give.
>
> -
> Troy Payne
> paynetc@gmail.com
>
> +++++++++++++++++++++++++++
>
> The Lorenz curve is defined for zero values, and indeed negative ones.
> -glcurve- will draw a curve if the data include such values. (It reports
> the number of negative ones.)
>
> Many "standard" indices of inequality are defined only for positive
> values. As Troy says, the Gini is well-defined in the case in which
> there are zeros; so too is the coefficient of variation (CV) and
> transformations of it, such as .5*CV^2 (generalised entropy index with
> coeff = 2).
>
> -ineqdec0- on SSC will calculate these 2 indices, allowing zero values.
> (Its sibling, -ineqdeco-, does calculations using positive values only,
> and for a wider range of indices.)
>
>
> Stephen
> ------------------
> Professor Stephen P. Jenkins<s.jenkins@lse.ac.uk>
> Department of Social Policy and STICERD
> London School of Economics and Political Science
> Houghton Street, London WC2A 2AE, UK
> Tel: +44(0)20 7955 6527
> Changing Fortunes: Income Mobility and Poverty Dynamics in Britain, OUP
> 2011, http://ukcatalogue.oup.com/product/9780199226436.do
> Survival Analysis Using Stata:
> http://www.iser.essex.ac.uk/survival-analysis
> Downloadable papers and software: http://ideas.repec.org/e/pje7.html
>
>
>
> Please access the attached hyperlink for an important electronic communications disclaimer: http://lse.ac.uk/emailDisclaimer
>
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