In this paper the authors compare different models to investigate the multidimensional nature of student engagement in online learning. The authors conclude that the B-ESEM model is the best one to understand student engagement in online learning. The topic of this paper is interesting for the research community in the field of educational technology. The paper is well-written with a good academic style, organization, formatting and language. I want to highlight two strong aspects in the paper: the statistical analysis using the B-ESEM approach and the literature review. References are up-to-date and are appropriate. However, I have some concerns that need to be addressed before the paper can be published. Please find my concerns as follows:

The first implication in the highlights “Simultaneously assessing the global factor as well as specific components of student engagement enhances our understanding of the multifaceted nature of the construct…” is not an appropriate implication because it is well known that student engagement is a multidimensional construct as you also pointed out in section 2.1. I suggest revising the implications and better align them to the results obtained in this research.

Please define acronyms EFA and CFA in section 2.2.

At the end of section 2.3 you assert that “Therefore, it is important to further extend the application of this approach in online learning given that student engagement is a malleable concept which is responsive to contextual changes”. However, the lack of application of the B-ESEM approach to investigating student engagement is not a strong justification/motivation on why to conduct this study. In other words, the fact that a technique has not been widely applied to investigate a phenomenon is not a clear justification to conduct a research study with that technique. I suggest removing this justification and justify the use of B-ESEM from the advantages of this technique to study a multidimensional construct.

In section 3.2. please indicate the academic programmes in which the participants were enrolled. This is useful for readers to have an idea of the type of students.

I suggest including a table with the questionnaire items and indicating which item was adapted from which previously validated questionnaire. This will give more information to the readers on how the questionnaire was adapted from other questionnaires instead of indicating that the questionnaire was adapted from others.

The authors conclude that the bi-factor ESEM is an appropriate representation to understand the multidimensional nature of student engagement in online learning. This is interesting, however, the main concern that I have is the following: Is it possible that the data collected fits in this model (B-ESEM) but the model do not fully represent the specificity of student engagement in online learning? Is it possible that in another data collection process with a different research sample the data fits in another model such as the B-CFA? Please clarify these concerns. Moreover, what I see in the model are four constructs (behavioral, affective, cognitive and social) that seem to predict student engagement. However, this is not novel because previous studies have demonstrated these relationships. What I would expect is to see how each construct influences student engagement and to what extent. Consequently, I suggest providing more details on the contribution of the article based on these clarifications. In other words, please make more explicit the main contribution of finding that B-ESEM is an appropriate model to represent student engagement and how this differ from other models that are used to represent student engagement.

Another concern that I have is that the title of the article and the way in which the article is written suggest that readers are going to find a model based on hypotheses that is validated to understand how student engagement works in online learning. However, what readers actually find is more like an instrument validation using B-ESEM. In this case the contribution of the article is different: anew instrument to measure student engagement in online. To avoid this misunderstanding I suggest that the authors provide more details on the real purpose of the article. When you write: “configuration of student engagement” I would expect to see how the different constructs of student engagement are related or how these constructs are affected by other constructs. So, please clarify these aspects in the article.

Dear Authors,

I have gone through the paper again and it improved a lot from the previous version. I see that you successfully addressed all my comments and suggestions. There are only a couple of changes that need to be made in the article:

In section 1 you added the following claim: “Identifying students at risk of disengagement and dropout is a critical task that requires a clear conceptual understanding of the student engagement construct and its underlying structure.”. This might be true but please provide a reference to the literature that supports this claim.

When you reference figure 1, please indicate to which part of the figure you refer to when you describe each one of the models: 1A, 1B, etc.