Massive open online courses (MOOCs) continue to see increasing enrollment and adoption by universities, although they are still not fully understood and could perhaps be significantly improved. For example, little is known about the relationships between the ways in which students choose to use MOOCs (e.g., sampling lecture videos, discussing topics with fellow students) and their overall level of engagement with the course, although these relationships are likely key to effective course implementation. In this paper we propose a multilevel definition of student engagement with MOOCs and explore the connections between engagement and students' behaviors across five unique courses. We modeled engagement using ordinal penalized logistic regression with the least absolute shrinkage and selection operator (LASSO), and found several predictors of engagement that were consistent across courses. In particular, we found that discussion activities (e.g., viewing forum posts) were positively related to engagement, whereas other types of student behaviors (e.g., attempting quizzes) were consistently related to less engagement with the course. Finally, we discuss implications of unexpected findings that replicated across courses, future work to explore these implications, and relevance of our findings for MOOC course design.