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Ilan,
Thank you for that formula! The first thing I notice is the plus-sign between the two square-root-statements in the denominator - that's something that is missing in the formula given in Wasserman/Faust 1994:368 - instead, in the latter formula, a multiplication between the two square-root factors is implied.

However, looking at the formula you supplied, I suspect it nevertheless contains some errors. In the first part of the nominator, I think it should be x(*,i) rather than x(*,j) (where it first occurs). I also suspect that the first occurrence of x(*,i) in the nominator should be x(i,*). Also, in the denominator, in the 2nd sum-statement, I think it should be x(j,*) rather than x(i,*). For symmetrical matrices, some of these things shouldn't matter though as x(*,i)=x(i,*) for such matrices.

Nevertheless, adjusting for the plus-sign and double-checking my code, I still cannot replicate the results from Ucinet! I think I need to do a broader error-checking here...

Yours,
Carl

Dr Carl Nordlund
carl.nordlund(at)hek.lu.se
Human Ecology Division, Lund university
www.hek.lu.se
________________________________
Skickat: den 17 december 2010 21:42
Till: Carl Nordlund
Ämne: Re: Correlation formula as measure for SE

It is either:

But you could try straightforward Euclidean distance measure as :

Carl Nordlund wrote:
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Hi list,

I am trying to replicate the calculation procedure to obtain Pearson product-moment correlation coefficients as a measure of structural equivalence, but I can't get it to work! I am using the formula given in Wasserman/Faust (1994) on page 368 - pseudocode-translated it looks like this (but I think the formula on W/F94:368 is easier to read...):

r(i,j)=sum( (x(k,i)-xm(*,i))*(x(k,j)-xm(*,j)) ) + sum( (x(i,k)-xm(i,*))*(x(j,k)-xm(j,*)) )
/ ( sqrt( sum( (x(k,i)-xm(*,i))^2) + sum( (x(i,k)-xm(i,*))^2) ) * sqrt( sum( (x(k,j)-xm(*,j))^2) + sum( (x(j,k)-xm(j,*))^2) ) )

(...where xm(*,i) is the mean value of column i, xm(i,*) is the mean value of row i, excluding diagonals.)

I have tested this with the Krackhardt advice relation data, even trying with manual calculation (pen, paper and calculator!), but I simply cannot replicate the results shown in W/F94:373, and the results that Ucinet yields.

Is there any open-source code (in any language) available for calculating Pearson product-moment correlation coefficients for sociomatrices? Or can anyone see directly what I've done wrong in the expression above? (I doubt that there is something wrong with formula (9.3) in Wasserman/Faust 1994:368, but perhaps there are some implicit brackets that I've missed?)

Yours,
Carl

Dr Carl Nordlund
carl.nordlund(at)hek.lu.se
Human Ecology Division, Lund university
www.hek.lu.se<http://www.hek.lu.se>
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