Investigating the Impact of Residualized Likelihoods in Bayesian Multilevel Models

• In Event: Statistical Inference and Bayesian Estimation

Abstract

Multilevel models are used to predict outcomes with one or more sources of dependency. In frequentist settings, the dominant estimation method for multilevel models with Gaussian residuals at each level is residual maximum likelihood (REML), which provides unbiased estimates of variance components. Use of non-residualized Gaussian distributions (i.e., maximum likelihood) results in negatively biased estimates of the variance components. In Bayesian multilevel models, the data likelihood most commonly used is the non-residualized Gaussian distribution. In this talk, we show preliminary results for our attempt to bring an analog to the residualized likelihood of REML into Bayesian estimation methods—the development of a residualized likelihood function in a Markov chain Monte Carlo algorithm for Bayesian multilevel models.

Authors

• Jonathan Templin, The University of Iowa

• Lesa Hoffman, The University of Kansas

• Tyler Hicks, The University of Kansas

• Ryan W Walters, University of Nebraska - Lincoln