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st: Ancestry nominal dispersion measures like the Herfindahl, was Re: st: loops for regions


From   "Lacy,Michael" <Michael.Lacy@colostate.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: Ancestry nominal dispersion measures like the Herfindahl, was Re: st: loops for regions
Date   Fri, 7 Sep 2012 16:41:37 +0000

(Given the tangential relevance of the original thread subject to this followup, I thought it better to start a new one.)


On 09/05/2012, Nick Cox <njcoxstata@gmail.com> wrote:

>>> This index, although often attributed to Herfindahl by economists who
>>> know only their only literature, was in essence invented decades
>>> before by Gini. I don't have the reference in my head, but I think it
>>> is in Bishop, Y., Fienberg, S.E. and Holland, P.W. 1975. Discrete
>>> multivariate analysis. Cambridge, MA: MIT Press. Please trump me by
>>> providing a yet earlier reference.
>>>

I can't resist the rare opportunity to trump Nick Cox, or at least be invited to try. <grin?


One canonical source on this kind of index  is:

Simpson, E.H.  1949 "Measurement of diversity." Nature 163:688.
who cites the following (his citation style, not mine):

Yule, "Statistical Study of Literary Vocabulary" (Cambridge,1944).
Fisher, Corbet and Willbarns, J. Animal Ecol., 12, 42 (194s).
WilIIams, Nature, 157. 482 (1946).

A very thorough source with standing among sociologists is:

Agresti, A. and Finlay, B. 1978.  " Statistical Analysis of Qualitative Variation.  Sociological Methodology, Vol. 9.  Wiley-Blackwell.
who mentions Gini in passing and more specifically cites (inter alia):

Mueller, J.H. and Schuessler, K. F. 1961.  Statistical Reasoning in Sociology. Boston: Houghton Mifflin.
(See their "Index of Qualitative Variation")


Regards,

Mike Lacy
Dept. of Sociology
Colorado State University
Fort Collins CO 80523-1784







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