The current study seeks to validate a second-order, multifaceted model of engagement that contains a behavioral, an emotional, and a cognitive subtype as proposed by Fredericks, Blumenfeld, and Paris' (2004), while also incorporating literature on student interactions. The second-order, 12-factor model proposed and tested for its validity partitioned engagement into the second-order constructs of academic and social engagement and examined each of the three engagement subtypes in relation to the interactions that students experience with their course material, with their classmates, and with their instructors/teaching assistants. Since the proposed model did not meet accepted standards of fit, the dataset was randomly split into two approximately equal halves and a follow-up exploratory factor analysis (EFA) was conducted on the first half of the dataset, which yielded a second-order, five-factor solution. The second-order academic engagement constructs that emerged from the EFA consisted of students' behavioral, emotional, and cognitive engagement with their course material. In addition, two first-order factors emerged from the EFA, consisting of students' emotional and cognitive engagement with their fellow students or classmates.

These constructs and relationships were consistent with the theory that drove the original proposed model, but differed slightly in their composition and relationship with one another. After establishing this empirical model through EFA procedures, the model was cross-validated on the second-half of the randomly split dataset and examined for invariance across students enrolled in online courses and students enrolled in traditional, in-person college courses, as well students from ethnically and economically diverse backgrounds. Latent mean comparisons revealed differences in levels of academic and social engagement between these three groups of students, suggesting that students enrolled in online courses and students from African-American and Latino/a ethnicities were slightly more academically engaged than their counterparts. However, students enrolled in online courses scored much lower than students enrolled in face-to-face courses on the social engagement measures, while students from African-American and Latino/a ethnic groups scored higher on the social engagement measures than did students from Asian and Caucasian ethnicities. Interestingly, no differences emerged between groups of students from lower and higher economic backgrounds.