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Re: st: Zeros and measures of inequality or concentration


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Zeros and measures of inequality or concentration
Date   Thu, 9 Feb 2012 08:07:29 -0500

It may be helpful to take a broader view of the analysis and consider
whether a hurdle model or a zero-inflated model would be appropriate.
One reference is the book by Cameron and Trivedi:
Cameron, A.C. and Trivedi, P.K. Regression Analysis of Count Data.
Cambridge University Press, 1998.

David Hoaglin

On Thu, Feb 9, 2012 at 12:17 AM, Troy Payne <paynetc@gmail.com> wrote:
> 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.

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