From my limited understanding, the difference is mainly that hierarchical Bayes (HB) incorporates parameter distribution priors that will "constrain" the individual parameters to one side of the distribution. Conversely, random parameter/effects models (RPM) simply pick the individual parameter randomly from the distribution, but one can constrain the parameter to a location of the distribution by incorporating other covariates such as socio-demographic variables.
Is this the main difference? If so, I see that in theory HB would predict better in small samples. What I am not sure about is how controlling for individual covariates (to constrain the parameter to a location of the distribution) in a RPM would produce worse (or better) predictions than a HB model.
Does anyone know of any good tutorials in R (or any other software) that show how to incorporate parameter distribution priors in HB? Unfortunately, I've read too many "Hierarchical Bayes" tutorials that leave this out.
Any other suggested material to read is greatly appreciated.