Bayesian Estimation of Multilevel Models
This chapter is meant as a first introduction into Bayesian estimation for readers already familiar with multilevel modeling. We begin with discussing a number of general arguments for considering Bayesian estimation. This is followed by a section on the basics of Bayesian estimation, and a section on Bayesian estimation of multilevel models. To illustrate some of the features and details of Bayesian estimation, we make use of an empirical illustration, which is included as a running example throughout these two sections. All the analyses in this chapter are performed using WinBUGS (Spiegelhalter, Thomas, Best, & Lunn, 2003), which was called from R using the function bugs() from the package R2WinBUGS (Sturtz, Ligges, & Gelman, 2007; for a thorough description of how to use bugs(), see Gelman & Hill, 2007). Both WinBUGS and R can be downloaded freely. We end this chapter with a discussion of the specific merits of Bayesian estimation for multilevel modeling.