Fitting Bayesian item response models in Stata and Stan

Stata users have access to two easy-to-use implementations of Bayesian inference: Stata’s native bayesmh command and StataStan, which calls the general Bayesian engine, Stan. We compare these implementations on two important models for education research: the Rasch model and the hierarchical Rasch model. StataStan fits a more general range of models than can be fit by bayesmh and uses a superior sampling algorithm, that is, Hamiltonian Monte Carlo using the no-Uturn sampler. Furthermore, StataStan can run in parallel on multiple CPU cores, regardless of the flavor of Stata. Given these advantages and given that Stan is open source and can be run directly from Stata do-files, we recommend that Stata users interested in Bayesian methods consider using StataStan.