With all due respect, and very grateful for your help, I do still think that there is some problems with the indices in the formula you supplied in your email. In the nominator,
first term, it seems strange that each column value for actor i is to be compared with the mean column value for actor j, especially since the next bracket compares column values for actor j with the same mean column value for actor j. In addition, the sum
statements seems wrong: it says "i,j=1" in the nominator and "i,j,k=1" in the denominator, when, I believe, the iterative variable in these sum statements should be over k (where i!=k and j!=k).

I also had a look in your paper "Structural equivalence and international conflict" (J of Confl Resol, 2006), where the Pearson correlation formula (p. 11) doesn't have a plus sign in the denominator - instead, similar to Wasserman/Faust (which you refer to as a source for this formula), there is an implicit multiplication between the two square root terms in the denominator. In addition, judging by the index order of the various terms in that formula, column values are compared with the row mean for each actor and vice versa.

So I'm still all confused!

Yours,

Carl

**Från:** Ilan Talmud [[log in to unmask]]

**Skickat:** den 17 december 2010 22:37

**Till:** Carl Nordlund

**Kopia:** [log in to unmask]

**Ämne:** Re: SV: Correlation formula as measure for SE

`It is the correct one. I used it many times. `

Carl Nordlund wrote:

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I also had a look in your paper "Structural equivalence and international conflict" (J of Confl Resol, 2006), where the Pearson correlation formula (p. 11) doesn't have a plus sign in the denominator - instead, similar to Wasserman/Faust (which you refer to as a source for this formula), there is an implicit multiplication between the two square root terms in the denominator. In addition, judging by the index order of the various terms in that formula, column values are compared with the row mean for each actor and vice versa.

So I'm still all confused!

Yours,

Carl

Dr Carl Nordlund

carl.nordlund(at)hek.lu.se

Human Ecology Division, Lund university

www.hek.lu.se

carl.nordlund(at)hek.lu.se

Human Ecology Division, Lund university

www.hek.lu.se

Carl Nordlund wrote:

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 :

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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/