Title: Partial-Mastery Cognitive Diagnosis Models Authors: Elena A. Erosheva, Zhuoran Shang, Gongjun Xu Affiliation: University of Washington Abstract: Cognitive Diagnosis Models (CDMs) usually assume that test items require mastery of specific skills -- also known as latent attributes -- and that each attribute is either fully mastered or not mastered by a given subject. As a consequence, the concept of partial mastery -- when subjects are able to apply a skill correctly in some situations, more frequently than with guessing, but not always -- may not be well accounted for by standard CDMs. We propose a new class of models, partial mastery CDMs (PM-CDMs). This class generalizes both CDMs by allowing for partial mastery and mixed membership models by specifying mixed membership for each latent attribute dimension. Here, the latent dimensions are pre-determined by expert knowledge about skills required for each item. We demonstrate that PM-CDMs can be represented as restricted latent class models. Relying on the latent class representation, we propose a Bayesian approach for estimation. We present simulation studies to demonstrate parameter recovery, to investigate the impact of model misspecification with respect to partial mastery, and to develop diagnostic tools that could be used by practitioners to decide between CDMs and PM-CDMs. We use two examples of real test data -- the fraction subtraction and the English tests -- to demonstrate that employing PM-CDMs not only improves model fit, compared to CDMs, but also can make substantial difference in conclusions about attribute mastery. We conclude that PM-CDMs can lead to more effective remediation programs by providing detailed individual-level information about skills learned and skills that need study.