A structural multilevel model is presented in which some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal politicos response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel model. A Bayesian procedure, the Markov Chain Monte Carlo (MCMC) procedure, to estimate all parameters simultaneously is presented. It is shown that certain model checks and model comparisons can be done using the MCMC output. The techniques are illustrated using a simulation study, and applications involving a students achievements on a mathematics test and test results regarding management characteristics of teachers and principals. (Contains 2 figures, 4 tables, and 45 references.) (Author/SLD)