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I want to quantify the effect of a node attribute on the tie formation.
I've already done some analysis but not sure what is the best/right/proper
way to do, so looking for some advice. Thanks !

This is a bipartite (two-mode) network :

Actors (MCs): 66 , Events (news): 7376, edges (non-weighted): 4938

There is an edge between an actor (Member of Congress) and an event (news)
if MC tweets about (commentates on) that event.

This can be reduced to one-mode network:

A co-commentation network of congress members (MCs) (N=66, # of edges:

Each weighted edge represents the number of events incident MCs have
commentated on Twitter.

Nodes have a single attribute: the political party they belong to.

What I've done so far:

1. Clustering (modularity based community detection) on the one-mode
network. 95% of the MCs are found to be in the same group as their actual
co-party members. So, this clearly indicates an effect of node attribute
(party-match) on tie formation. But this does not look like the right way
to quantify its effect from a statistical perspective?

2. Attempted ERGM on the bipartite network (using statnet) to see the
effect of node match (when parties are not differentiated). Not sure what
other parameters can be added. And how should I interpret ~0.32 here?




Summary of model fit


Formula:   two_mode ~ edges + b1nodematch("party")

Iterations:  20 out of 20

Monte Carlo MLE Results:

                  Estimate     Std. Error MCMC % p-value

edges             -4.82148    0.02591      1  <1e-04 ***  0.31572    0.02996      1  <1e-04 ***


Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

     Null Deviance: 674870  on 486816  degrees of freedom

 Residual Deviance:  52736  on 486814  degrees of freedom

AIC: 52740    BIC: 52762    (Smaller *is* better.)

3. Now considering calculating the likelihood of tie formation with
co-party members. For each MC *mi* I’ll get (sum of edge weights with
co-party members) / (weighted node degree*) and then average them.

* : i.e., sum of all the edge weights *mi* incident to

Any pointers and feedbacks are more than welcome.


PS. Here is the IPYNB

-Talha OZ

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