INFERENCE AND HIERARCHICAL MODELING IN THE SOCIAL-SCIENCES

Hierarchical models (HMs; Lindley & Smith, 1972) offer considerable promise to increase the level of realism in social science modeling, but the scope of what can be validly concluded with them is limited, and recent technical advances in allied fields may not yet have been put to best use in implementing them. In this article, I (a) examine 3 levels of inferential strength supported by typical social science data-gathering methods, and call for a greater degree of explicitness, when HMs and other models are applied, in identifying which level is appropriate; (b) reconsider the use of HMs in school effectiveness studies and meta-analysis from the perspective of causal inference; and (c) recommend the increased use of Gibbs sampling and other Markov-chain Monte Carlo (MCMC) methods in the application of HMs in the social sciences, so that comparisons between MCMC and better-established fitting methods-including full or restricted maximum likelihood estimation based on the EM algorithm, Fisher scoring, and iterative generalized least squares-may be more fully informed by empirical practice.