Schork-Lab/mediator-was

Two sample two stage linear regression

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Implement two sample two stage linear regression based on the works of:

http://www.nber.org/papers/t0311.pdf
https://aje.oxfordjournals.org/content/178/7/1177.full
http://www.mitpressjournals.org/doi/pdf/10.1162/REST_a_00011
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3600630/pdf/dyt023.pdf
https://ije.oxfordjournals.org/content/44/2/512.full

@aksarkar , the case we are working on is this two sample two stage linear regression. However, it requires one to have the genotypes from both stages to calculate correct standard errors on the expression->phenotype relationship. I think we should still explore the measurement error case and the two stage linear regression case..and see if they are just overall less baised than the simple OLS case. Maybe not analytically, but through simulations at least.

Note that this might not be applicable, because of G -> P relationship that's not mediated by G -> E -> P