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First: plenty of thanks for your reply. Much appreciated as you know! I 
will motivate it as I had planned to then: simply arguing that I remove 
these 6 countries from the dataset as the REGE algorithm deemed these as 
having unique roles. They are insignificant, both with respect to their 
engagement with other actors in the data set, but more significantly: 
they are insignificant in the world economy from an attributional 
perspective as well.

Yes, I am familiar with the inherent problems of the REGE algorithm: its 
point-scoring behaviour is not very well suited for, especially, valued 
networks. As such, it feels a bit like a modern, regular counterpart to 
the Concor algorithm: widely used, yielding results which do seem 
intuitively conceivable (mostly), but still an algorithm/heuristic where 
its Fortran source code seems to be mildly separated from the 
theoretical definitions and foundations (at least with respect to the 
point-scoring part when it comes to valued networks and REGE). However, 
also similar to how Concor used to be state-of-the-art, REGE is widely 
used and - as far as I know - there is no other implemented alternative. 
The type of coloring-scheme for identifying regular-role-equivalent 
positions that you (right?) presented in an article looks very nice - 
and I also recall seeing another article by you et al where two 
alternative algorithms for regular equivalence are presented - plus all 
the great work done by Batagelj, Doreian, Ziberna etc on generalized 
blockmodels - but still, REGE is what is accessible in implemented format.

For my dataset, I have tried with 3, 4,5 and 6 iterations. Although 
there are slight variations between the partitioning done (and slight 
differences in the number of partitions as recommended by the Anova 
Density check), these variations are indeed slight (the range of 
number-of-actors-in-each position varies as follows when doing 3-6 
iterations of the REGE algorithm and choosing an 8-positional partition: 
4-8, 3, 24-28,7-9,15-19,18-22,7-9,6-7. The bulk of actors remain 
together in the same positions for each of these tests with 3-6 
iterations). I have also tried pre-processing, square-rooting all the 
values in the original dataset, and interestingly, the resulting 
partition was very much alike the one I got when using the raw data. 
(This type of pre-processing of continuous trade flow data has 
occasionally been done before: from Breiger 1981 to Mahutga 2006. I will 
though use the raw trade data as this type of peak-smoothing hasn't been 
studied enough).

But it would indeed be nice if more formal tools for establishing 
regular equivalence could be developed. Or at least if the REGE 
algorithm could be studied more thoroughly - not only theoretically (as 
you have done in a number of papers) but also practically, on 
trivial/typological networks. World-system analysis would benefit 
greatly if an algorithm for measuring regular-equivalence in valued 
datasets could be developed...

Still: using the REGE algorithm, and using 3 iterations, seems to be 
some sort of standard for establishing regular-equivalence in 
world-system studies (used by Smith/White 1992, Mahutga 2006, Srholec 
2006 etc). Thus, I guess the choice of 3 iterations is advicable from a 
comparative point of view, even though 4, 5, 6 or more iterations indeed 
yields different partitions.


Martin Everett wrote:

>First of all the workings of REGE are not all together clear and you may be
>attributing an accuracy to the results beyond what is there. In particular
>the three iterations is left over from the days when computing these values
>was very slow. You may get rather different results if you increase from the
>three iterations. However, let us assume that what you have done is correct
>and the partitions do indeed reflect regular equivalence classes.
>At the first stage you do not give any information about the relationships
>between the groups you find and the rest of the network. From a structural
>point of view these positions must be significant but at the same time you
>indicate they are marginal.
>Suppose this was a friendship network and the values of the links represented
>strength of friendship. If one group have  weak links to an individual and
>another group have say no links to the same individual and further suppose
>the groups have stronger internal ties and stronger ties to each other
>(across the groups) than to the outsider. Then REGE will focus on the
>structural properties of the outsider and place the outsider in a single
>group before looking at the differences in the two groups. It will then find
>the two groups because of their different relationship with the outsider. But
>these two groups may not be two groups since they only have weak links to the
>outsider. Since REGE does not rank strength but looks for similarity of ties
>then it has formed the groups on very weak evidence. In this case it is quite
>legitimate to remove the outsider and look for the structure which represents
>the patterning without the excluded individual.
>In other words what you do is completely justifiable provided the groups you
>remove are really marginal and not just inconvenient. 
>In essence you need to determine if these nodes are really peripheral and if
>they are then you are OK. If they are not then you really should not do this.
>Martin Everett
>-----Original Message-----
>From: Social Networks Discussion Forum [mailto:[log in to unmask]] On
>Behalf Of Carl Nordlund
>Sent: 22 May 2007 15:29
>To: [log in to unmask]
>Subject: Arbitrary removal of nodes in reg eq-analysis?
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>Hi all,
>Having a little dilemma here which I guess others before me have 
>confronted. Being self-taught in everything SNA, I pose my question to 
>this email list, hoping for some tutoring on the subject!
>I'm currently doing a reg. equivalence analysis on energy flows (energy 
>content in four fuel commodities) between the countries of the world - 
>data is valued, directional with quite a large value span among the flow 
>values. Using the REGE-algorithm in the Ucinet package, 3 iterations, 
>selecting the number of partitions based on an Anova Density check for 
>different number of partitions (as used in Luczkovich et al).
>When using 99 countries in my dataset, I get an optimal split at 11 
>partitions (i.e. positions containing role-equivalent actors). Two of 
>these are singleton positions, i.e. containing only singular countries, 
>and two positions contain only two countries each. All these 6 countries 
>are fairly small and uninteresting, covering only 0.27% of total world 
>population, 0.04% of total world GDP, and 0.03% of total flow values in 
>the dataset.
>Thus, what I would like to do is to remove these 6 countries from my 
>dataset and repeat the analysis with only 93 countries. When doing so, I 
>get an optimal number of positions at 8, the two smallest of these 
>positions containing 3 and 4 countries respectively. I find this 1) much 
>easier to analyze, 2) much easier to visualize (as a reduced/image 
>graph), 3) giving a higher resolution (more partitions) regarding the 
>positions containing the bulk of countries, and 4) removing countries 
>that I feel could "disturb" the REGE algorithm in finding the major 
>positions, removing countries that though might be unique but not very 
>significant with respect to their coverage (as given by share of total 
>flow values and attributional measures such as population and GDP).
>However: how on earth can I motivate this? Can I just simply argue that 
>"well, first I included these 6 countries, but as these countries 
>resultet in 4 unique positions containing only these countries, I chose 
>to remove these countries from the dataset and try without them - they 
>are so small and insignificant anyhow..."? I could probably find some 
>criteria for removing these based on their attributes, net degrees or 
>similar, but that would not be very scientifically honest now, would it?
>How have other people done in analyses that yields a bunch of trivial 
>and singleton positions, i.e. positions that only contain 1-2 actors 
>that are of fairly minor importance anyway? Suggestions?
>(And sorry for using this email list as a classroom here - I have 
>nowhere else to turn to...)

Carl Nordlund, BA, PhD student
Human Ecology Division, Lund university

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