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st: Re: manipulating matrix elements


From   "Michael Blasnik" <michael.blasnik@verizon.net>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: manipulating matrix elements
Date   Tue, 28 Mar 2006 16:23:46 -0500

-findit matmap- will lead you to the matmap package which can perform arbitrary elementwise operations on matrices, but since you want the sum of the calculation across all elements, I think you should just do the looping yourself. Here's one approach (untested):

scalar x=0
tab var1 var2, matcell(Cell)
matrix P = Cell/r(N)
local rows=rowsof(P)
local cols=colsof(P)
forvalues i=1(1)`rows' {
forvalues j=1(1)`cols' {
scalar p=P[`i',`j']
scalar x=x+p*ln(p)
}
}
scalar x=x+ln(`rows'*`cols')
di x

I've renamed your Proportions matrix as P for brevity and the result you want should be in scalar x when you are done. The code could be made more compact (by not calculating rows, cols, or p separately), but this approach is a little easier to understand. It would be simple to turn this into a Stata program (ado) file that accepts a variable list, -if- and -in- qualifiers, and perhaps other command options. I'm not familiar with this statistic, but perhaps someone has already done this.

Michael Blasnik
michael.blasnik@verizon.net

----- Original Message ----- From: "Steve Vaisey" <vaisey@unc.edu>
To: <statalist@hsphsun2.harvard.edu>
Sent: Tuesday, March 28, 2006 3:49 PM
Subject: st: manipulating matrix elements



Hello all,

I am trying to implement the following formula for estimating the (standardized) informational entropy of a RxC contingency table: sum(p*ln(p))+ln(M) where p (subscript ij omitted) is the proportion of cases in each cell and M is the total number of cells. So far, I've only managed to accomplish the following:

tab var1 var2, matcell(Cell)
matrix Proportions = Cell/r(N)

Frankly, I'm amazed I've managed even this much, but now I'm stuck. What I need to do (as I understand it) is take the natural log of each element of the Proportions matrix, multiply it times its corresponding proportion, sum up all the elements, and add ln(M).

For some (probably good) reason, while you can easily multiply matrix elements by a scalar, you can't do something like:

matrix LnP = ln(Proportions)

I've tried this, but it gives a type mismatch error. Again, I'm sure this is for a good reason, but I'm not sure what to do.

So any idea what I should do?

Thanks,

Steve
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