Multilevel models and the index-variable approach

PhD candidate Huaiyu Liu recently reached out with a question about how to analyze clustered data. Liu’s basic setup was an experiment with four conditions. The dependent variable was binary, where success = 1, fail = 0. Each participant completed multiple trials under each of the four conditions. The catch was Liu wanted to model those four conditions with a multilevel model using the index-variable approach McElreath advocated for in the second edition of his text. Like any good question, this one got my gears turning. Thanks, Liu! The purpose of this post will be to show how to model data like this two different ways.