Hand rolling empirical Bayes estimation of a hierarchical model to learn how it works
This is a quick experiment to teach myself if I can just use full likelihood optimization to get well-behaved empirical Bayes estimate of both the trial-level random effects and the metastudy group-level hyperparameters in a mixed model.
Why? Because proper statisticians say you aren’t supposed to use a full likelihood to estimate random effects and hyperparameters because it’s biased for the group-level variance components, but how much does it matter for model fitting metastudy applications?