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From |
<S.Jenkins@lse.ac.uk> |

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

Subject |
st: Zeros and measures of inequality or concentration |

Date |
Thu, 9 Feb 2012 11:00:15 -0000 |

------------------------------ 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 * * 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/

**Follow-Ups**:**Re: st: Zeros and measures of inequality or concentration***From:*"Roger B. Newson" <r.newson@imperial.ac.uk>

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