Dear Talha,

If you are interested in testing the effect of a characteristic of a Member of Congress on the probability that s/he sends a tweet on a news issue, why conceptualize the tweet as a tie instead of an action by the MC? Conceptualized as an action, that is, as a variable concerning the MC, you can use ‘ordinary’ statistical methods with the MC as the unit of analysis. If you are interested in also predicting when the MC tweets, you could use event history models.

If you want to use predictors calculated from the network of who tweeted before on what topic, you could use the approach proposed in: Kleinnijenhuis, J., & De Nooy, W. (2013). Adjustment of issue positions based on network strategies in an election campaign: A two-mode network autoregression model with cross-nested random effects. Social Networks, 35(2), 168-177. doi:http://dx.doi.org/10.1016/j.socnet.2011.03.002

Kind regards,

Wouter de Nooy.

Sent: 29 May 2015 23:26
Subject: Proper way of quantifying the effect of a node attribute on tie formation

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Hello,

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: 1863).

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?

two_mode_b<-ergm(two_mode~edges+b1nodematch("party"))

summary(two_mode_b)

==========================

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 ***

b1nodematch.party  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.

Thanks.

PS. Here is the IPYNB.

-Talha OZ
mason.gmu.edu/~toz

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