The challenges of modeling students' performance in computer-based interactive assessments include accounting for multiple aspects of knowledge and skill that arise in different situations and the conditional dependencies among multiple aspects of performance. This article describes a Bayesian approach to modeling and estimating cognitive models in such situations, both in terms of statistical machinery and actual instrument development. The method taps the knowledge of experts to provide initial estimates for the probabilistic relations among the variables in a multivariate latent variable model and refines these estimates using Markov chain Monte Carlo procedures. This process is illustrated in the context of Networking Performance Skill System (NetPASS), a computer-based interactive assessment in the domain of computer networking. We describe a parameterization of the relations in NetPASS via an ordered polytomous item-response model and detail the updating of the model with observed data via Bayesian statistical procedures ultimately being provided by Markov chain Monte Carlo estimation.