I compared the standardizations (yours and Martin's) on a matrix of 11
variables (for a total of 55 non-redundant, 2 variable comparisons).
They are highly correlated (~.99) so it's probably a matter of taste at
one level. Or am I missing something?
Thanks again for your help on this.
Steve
Date: Thu, 30 Mar 2006 18:34:16 +0100
From: "Nick Cox" <n.j.cox@durham.ac.uk>
Subject: RE: st: manipulating matrix elements
Thanks for the references. I found the second reference
once I had worked out that the volume number is 107.
Martin does, as you say, use the quantity
SUM p ln p + ln #cells
In fields I know a bit about, it is more common
to use
- SUM p ln p = H
as a basic quantity. This is what is used in
my program -ineq- on SSC, for example.
Also, if this H is based on K categories, it can vary
between 0 and ln K, so a simple scaling is H / ln K.
(In the limiting case of a single category with p = 1,
you have to trap the 0 / 0 calculation.) There is
no assumption or approximation in this.
I am not clear that this is what you doing, but no
matter.
Looking at my little program, it is easy to generalise
it so that it can take one variable or two. This is me
modifying the program so it does things I sometimes
want to do, no more.
*! 1.0.0 NJC 30 March 2006
program myentropy, rclass
version 9
syntax varlist(min=1 max=2) [if] [in] [fweight aweight]
marksample touse
qui count if `touse'
if r(N) == 0 error 2000
tempname matname
tab `varlist' [`weight' `exp'] if `touse', matcell(`matname')
mat `matname' = `matname' / r(N)
mata: subroutine("`matname'")
di
di as txt "entropy " as res %7.4f r(entropy)
di as txt "scaled [0,1] " as res %7.4f r(scaled)
return scalar entropy = r(entropy)
return scalar scaled = r(scaled)
end
mata:
void subroutine(string scalar matname)
{
real matrix X
real scalar H
X = st_matrix(matname)
H = -sum(X :* ln(X))
scaled = H == 0 ? 0 : H / ln(rows(X) * cols(X))
st_numscalar("r(entropy)", H)
st_numscalar("r(scaled)", scaled)
}
end
Nick
n.j.cox@durham.ac.uk
Steve Vaisey
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