Identifying collaboration between learners in a course is an important challenge in education for two reasons: First, depending on the courses rules, collaboration can be considered a form of cheating. Second, it helps one to more accurately evaluate each learners competence. While such collaboration identification is already challenging in traditional classroom settings consisting of a small number of learners, the problem is greatly exacerbated in the context of both online courses or massively open online courses (MOOCs) where potentially thousands of learners have little or no contact with the course instructor. In this work, we propose a novel methodology for "collaboration-type identification," which both "identifies" learners who are likely collaborating and also "classifies" the type of collaboration employed. Under a fully Bayesian setting, we infer the probability of learners succeeding on a series of test items solely based on graded response data. We then use this information to jointly compute the likelihood that two learners were collaborating and what collaboration model (or type) was used. We demonstrate the efficacy of the proposed methods on both synthetic and real-world educational data; for the latter, the proposed methods find strong evidence of collaboration among learners in two non-collaborative take-home exams.