This paper synthesizes ideas from the fields of graphical modeling and education testing, particularly item response theory (IRT) applied to computerized adaptive testing (CAT). Graphical modeling can offer IRT a language for describing multifaceted skills and knowledge, and disentangling evidence from complex performances. IRT-CAT can offer graphical modelers several ways of treating sources of variability other than including more variables in the model. In particular, variables can enter into the modeling process at several levels: (1) in validity studies (but not in the ordinarily used model); (2) in task construction (in particular, in defining link parameters); (3) in test or model assembly (blocking and randomization constraints in selecting tasks or other model pieces); (4) in response characterization (i.e., as part of task models that characterize a response); or (5) in the main (student) model. The Graduate Record Examination is used to illustrate ideas in the context of IRT-CAT, and extensions are discussed in the context of language proficiency testing. (Contains 1 table, 9 figures, and 49 references.) (Author/SLD)