I'm using the analytical strategy of Christakis and Fowler to study the spread of behaviors in social networks. Page 566 of this article reviews their method in more details: http://humannaturelab.net/wp-content/themes/human-nature-lab/media/pdf/publications/articles/SIM_special.pdf
Basically, they use GEE approach and the model looks like this:
Y(ego, t2) = Y(alter, t2) + Y(alter, t1) + Y(ego, t1) + X
Y's are the outcomes of interest (smoking, drinking, etc). t2 and t1 are times of data collection. 'Egos' refer to subjects in the networks and 'alter' are those who have connections with egos. That also means in a network an ego can also be an alter and vice versa, depending on the connection we look at.
The authors argue that the method above reasonably address inherent problems with network analysis and I'm close to understand (or have to believe) it. However, there are some caveats that I have not figured it out yet:
For each ego, there are typically multiple alters, i.e., friends who might influence ego. That also means we have multiple independent observations for each dependent observation. In this case, should I take the mean (or combine some other way) of alters? Or is there any way to use individual independent observations? You may as well suggest some further readings of this topic.
The main covariate of interest is Y(alter, t2), i.e., outcome of alter at time 2 to explain outcome of ego at time 2. Because everybody can appear as both ego and alter, this can count the covariance between reciprocal friends as both the influence of person 1 on person 2 and the influence of person 2 on person 1. Thus, this model may estimate the influence to be perhaps twice as strong as it really is.
I think my questions are: Am I right thinking this way? And does GEE appropriately address this? If it does, how will I put it in software statements. I'm not sure how to construct and distinguish Y's for ego and alter of a same time, and how to put in, for instance, the MODEL statement in SAS:
PROC GENMOD; CLASS school; MODEL y = ?
I think it's useful to illustrate with a hypothetical data set, which may look like this: