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
Från: Ilan Talmud [[log in to unmask]]
Skickat: den 17 december 2010 21:42
Till: Carl Nordlund
Kopia: [log in to unmask]
Ämne: Re: Correlation formula as measure for SE
It is either:
But you could try straightforward Euclidean distance measure as :
Carl Nordlund wrote:***** To join INSNA, visit http://www.insna.org *****Hi list,_____________________________________________________________________ SOCNET is a service of INSNA, the professional association for social network researchers (http://www.insna.org). To unsubscribe, send an email message to [log in to unmask] containing the line UNSUBSCRIBE SOCNET in the body of the message.
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
-- Prof. Ilan Talmud, Ph.D. Head, Economic Sociology, Department of Sociology and Anthropology, University of Haifa Phones: 972-4-8240992 (office direct) 972-4-8240995 / 8249505 (secretaries) (cell) 972-522-220914 Fax: 972-4-8240819 http://soc.haifa.ac.il/~talmud/
-- Prof. Ilan Talmud, Ph.D. Head, Economic Sociology, Department of Sociology and Anthropology, University of Haifa Phones: 972-4-8240992 (office direct) 972-4-8240995 / 8249505 (secretaries) (cell) 972-522-220914 Fax: 972-4-8240819 http://soc.haifa.ac.il/~talmud/