AT discusses [link broken; see P.P.S. below] a new paper of his that casts doubt on the robustness of the controversial Christakis and Fowler papers. AT writes that he ran some simulations of contagion on social networks and found that (a) in a simple model assuming the contagion of the sort hypothesized by Christakis and Fowler, their procedure would indeed give the sorts of estimates they found in their papers, but (b) in another simple model assuming a different sort of contagion, the C&F estimation would give indistinguishable estimates. Thus, if you believe AT’s simulation model, C&F’s procedure cannot statistically distinguish between two sorts of contagion (directional and simultaneous).
I have not looked at AT’s paper so I can’t fully comment, but I don’t fully understand his method for simulating network connections. AT uses what he calls a “rewiring” model. This makes sense: as time progresses, we make new friends and lose old ones—but I am confused by the details (“First, some number of ties are assigned to have a new receiver, but the same sender; this changes the distribution of in-degree but keeps out-degree the same. Then, some number of ties are assigned to have a new sender, but the same receiver, changing the out-degree but maintaining in-degree.”) This just seems like an oddly elaborate way to do the simulation.
The interesting part is that, according to AT, C&F’s model would actually work if they were analyzing continuous data. It is only with binary data that the nature of the contagion becomes non-identifiable.
I’ll leave it to others to pursue this further. As AT writes, Christakis and Fowler’s work has spurred a lot of controversy, and I think a lot of this derives from the difficult nature of their data, in which only a very small fraction of the total network connections are ever observed. Hard cases make bad law. But you can’t just sit there and leave the case unresolved. Whatever happens with their claims, and whatever one might think about how their research claims have been presented in the press, I admire C&F for taking the big step for trying to learn about network effects from this unusual and sparse datasets. It’s a lot better than one more analysis of the degree distribution of the scientific collaboration network, the fractal dimension of Wikipedia, or power laws anywhere.
P.S. There are only two things about AT’s post I don’t like:
1. In the first sentence, AT writes, “In stuffy academic fashion, I discuss . . .”
I think that sort of apology is usually a bad idea. If you’re really writing too stuffily, try lightening up. If the academic “stuffiness” is appropriate, there’s no need to apologize.
2. AT refers to studies published by several other people but does not refer to them by name, instead merely mentioning “a pair of economists” and “a scathing review.” Why not mention names such as Hans Noel, Brendan Nyhan, Ethan Cohen-Cole, Jason Fletcher, and Russell Lyons? At the very least, they’re more likely to notice their names and read your post.
P.P.S. AT says that for copyright reasons he had to take his post down. So you’ll just have to imagine the content of his paper for now.