Bayesian multilevel modeling

Groups may represent different levels of hierarchy, such as hospitals, doctors nested within hospitals, and patients nested within doctors nested within hospitals. Multilevel models incorporate group-specific effects in the regression model and assume that they vary randomly across groups according to some a priori distribution, commonly a normal distribution. This assumption makes multilevel models natural candidates for Bayesian analysis. Bayesian multilevel models additionally assume that other model parameters such as regression coefficients and variance components—variances of group-specific effects—are also random.

In this presentation, I will discuss some of the advantages of Bayesian multilevel modeling over the classical frequentist estimation. I will cover some basic random-intercept and random-coefficients modeling using the bayes: mixed command. I will then demonstrate more advanced model fitting by using the new-in-Stata-17 multilevel syntax of the bayesmh command, including multivariate and nonlinear multilevel models.