Very productive meeting = I have a busy week of work!
Literature Review
1 – Look into power analysis work for cross-classified models. Since these are similar to p1 models, maybe there’s something there about adapting them.
2 – Look into papers on consistency of MLEs (in particular when the data are not identically distributed).
Regarding the Single Network stuff: We can look at the OLS estimate as a function of beta + a linear combination of gammas (see notes). We’re essentially estimating a lower bound on the treatmenteffect. Can we push it further?
Multiple Networks: Brian also had the idea to focus on the multiple networks. We have independent networks (that are not distributed identically). Perhaps there are some assumptions (either ones that can be relaxed or not) that will allow us to say the mle (i.e. treatment effect estimator) is in fact consistent. I need to look at some papers.
1- I need to look at the Lehmann book examples (6.4 and 6.8).
2 – I need to read the paper Brian sent (thm 4.1 which is an example of this method of proving consistency from Serfling’s book).
3 – Read the pdf on this too.