Informed priors in regression analysis
Hi,
I am running a replication study and used the (t-test) methods from Alexander Ly and Josine Verhagen to compute meta-analytic bayes factors and replication bayes factors to test my group effects. However, the main interest of the study is to see whether a group x age interaction might exist. Is a comparable replication method also developed for regression analysis (i.e. getting meta-analytic/replication bayes factors)? I am not sure how to come up with straightforward informative priors based on the summary stats of the original study for such an analysis. One way might be to consider the beta from the group x age interaction as a simple t-test and use the same method, but then you simply ignore all information on model fit. Also, it feels rather weird to have a distribution of cohen's d as the posterior for a regression analysis.
Many thanks,
Carolien
Comments
Hi Carolien,
Yes, this is not trivial. In general one could use the sequential procedure outlined in this paper:
Ly, A., Etz, A., Marsman, M., & Wagenmakers, E.-J. (2019). Replication Bayes factors from evidence updating. Behavior Research Methods, 51, 2498-2508. (https://link.springer.com/article/10.3758/s13428-018-1092-x)
but the trick is to simulate/use data that produce the approximately correct posterior distributions from the original experiment. Only if it is a very direct replication would it be warranted to concatenate the original and replication data.
Cheers,
E.J.