MOOCs are characterized as being courses to which a large number of students enroll, but only a small fraction completes them. An understanding of students' engagement construct is essential to minimize dropout rates. This research is of a quantitative design and exploratory in nature and investigates the interaction between contextual factors (demographic characteristics), student engagement types (academic, behavioral, cognitive and affective), and learning outcomes, with the objective of identifying the factors that are associated with completion of massive and open online courses. Two logistic models were adjusted in two samples, general and secondary, with the binary dependent variable defined as completes the course yes/no. The results in the general sample (15% completion rate) showed that the probabilities of a participant completing the course are positively and significantly related to participation in the forum and the participant educational level, and negatively related to gender (female) and age. The results in the secondary sample (87% completion rate) showed that the probabilities of a participant completing the course are positively and significantly related to participation in the forum, gender (female), and the motivation and satisfaction indexes, and negatively related to age, having previous experience in other MOOCs, and self-efficacy and task strategies indexes. The results lead to ideas on how these variables can be used to support students to persist in these learning environments.