The Gibbs sampling algorithms presented by M. H. Seltzer (1993) are fully generalized to a broad range of settings in which vectors of random regression parameters in the hierarchical model are assumed multivariate normally or multivariate "t" distributed across groups. The use of a fully Bayesian approach is discussed. (SLD)

Practical problems with multilevel techniques are discussed. These problems relate to terminology, computer programs employing different algorithms, and interpretations of the coefficients in either one or two steps. The usefulness of hierarchical linear models (HLMs) in common situations in educational research is explored. While elegant, HLMs…