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# Re: st: Zeros and measures of inequality or concentration

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: Zeros and measures of inequality or concentration Date Mon, 13 Feb 2012 09:08:45 +0000

```I don't see that this necessarily means measures of inequality. The
usual summary measures, say mean and standard deviation, perhaps
supplemented by the fraction of zeros, should be helpful.

Nick

On Thu, Feb 9, 2012 at 5:00 PM, Troy Payne <paynetc@gmail.com> wrote:
> Thanks to Nick Cox and David Hoaglin for the suggestion to use Poisson
> or zero-inflated models.  I've used those in the past when modeling
> the effect of independent variables on crime.  Here, my purpose is
> more descriptive; I have no predictors to model.
>
> Thanks also to Stephen Jenkins and Roger Newson for suggestions to use
> -ineqdec0- and -scsomersd- packages.  I'll do that and read their
> documentation.
>
>
> On Wed, Feb 8, 2012 at 8:17 PM, 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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