ABSTRACT
This chapter revisits some of the methods through a Bayesian framework. The Bayesian approach has several advantages. The most important of these is that latent variables can be treated as variables that are entirely missing. In Bayesian modeling, missing data are treated as parameters to be estimated in the model in exactly the same way that any other parameters are treated. The chapter demonstrates how to perform Bayesian A-M scaling using Martyn Plummer’s rjags package. The least squares unfolding procedures are quite effective, but the Bayesian multidimensional unfolding model offers two distinct advantages. First, the Bayesian multidimensional unfolding model uses the log-normal distribution to model the estimated distances. Second, Bayesian estimation “illuminates” the posterior distributions of the parameters, which produces better estimates of uncertainty for the parameters. The Bayesian framework also effectively deals with multimodal distributions, whereas maximum likelihood or least squares optimization methods will settle on one of the modes and report it as the point estimate.
