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PEP 0004 Geographically Nested Inequality based on the Geary Statistic
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Author    Boris Dev <boris.dev@gmail.com>
          Charles Schmidt <schmidtc@gmail.com>
Status    Draft
Created   9-Aug-2010
Updated   
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Abstract
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I propose to extend the Geary statistic to describe inequality
patterns between people in the same geographic zones. Geographically nested
associations can be represented with a spatial weights matrix defined jointly
using both geographic and social positions. The key class in the proposed
geographically nested inequality module would sub-class from class
``pysal.esda.geary`` with 2 extensions: 1) as an additional argument, an array
of regimes to represent social space; and 2) for the output, spatially nested
randomizations will be performed for pseudo-significance tests.  

Motivation
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Geographically nested measures may reveal inequality patterns that are masked
by conventional aggregate approaches. Aggregate human inequality statistics
summarize the size of the gaps in variables such as mortality rate or income
level between different different groups of people. A geographically nested
measure is computed using only a pairwise subset of the values defined by
common location in the same geographic zone.  For example, this type of
measure was proposed in my dissertation to assess changes in income inequality
between nearby blocks of different school attendance zones or different racial
neighborhoods within the same cities. Since there are no standard statistical
packages to do this sort of analysis, currently such a pairwise approach to
inequality analysis across many geographic zones is tedious for researchers
who are non-hackers. Since it will take advantage of the currently existing
``pysal.esda.geary`` and ``pysal.weights.regime_weights()``, the proposed
module should be readable for hackers. 
  
Reference Implementation
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I suggest adding the module ``pysal.inequality.nested``.


References
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[Dev2010] Dev, B. (2010) "Assessing Inequality using Geographic Income Distributions: Spatial Data Analysis of States,
Neighborhoods, and School Attendance Zones" http://dl.dropbox.com/u/408103/dissertation.pdf.

