Flow With an Intelligent Tutor: A Latent Variable Modeling Approach to Tracking Flow During Artificial Tutoring

Increasing use of intelligent tutoring system (ITS) in education calls for analytic methods that can unravel students' learning behaviors. In this study we suggest a latent variable modeling approach to tracking flow during artificial tutoring. Flow is a mental state a student achieves when immersed in deep learning. Modeling latent flow helps identify when and how students flow during tutoring. The result of the model can also inform the functioning of ITS and provide instrumental information for designing interventions. Three latent variable models are considered to draw discrete inference on the flow state: the (i) latent class model, (ii) latent transition model, and (iii) hidden Markov model. For each of the models, we suggest practical model-fitting strategies, addressing the assumptions and estimation constraints. Using example data from Cognitive Tutor Algebra I, we show that each model provides unique and meaningful information about student's learning process. Through comprehensive survey of the models, we evaluate merits and drawbacks of each modeling framework and illuminate areas that need future development.

Design Effect in Multilevel Settings: A Commentary on a Latent Variable Modeling Procedure for Its Evaluation

A latent variable modeling-based procedure is discussed that permits to readily point and interval estimate the design effect index in multilevel settings using widely circulated software. The method provides useful information about the relationship of important parameter standard errors when accounting for clustering effects relative to conducting single-level analyses. The approach can also be employed as an addendum to point and interval estimation of the intraclass correlation coefficient in empirical research. The discussed procedure makes it easily possible to evaluate the design effect in two-level studies by utilizing the popular latent variable modeling methodology and is illustrated with an example.

Evaluation of Second- and Third-Level Variance Proportions in Multilevel Designs With Completely Observed Populations: A Note on a Latent Variable Modeling Procedure

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity of large-scale studies in these and cognate disciplines. The present note discusses a readily applicable procedure for point-and-interval estimation of the proportions of second- and third-level variances in such multilevel settings, which may also be employed in model choice considerations regarding ensuing analyses for response variables of interest. The method is developed within the framework of the latent variable modeling methodology, is readily utilized with widely used software, and is illustrated with an example.

Seeing the Impossible: Visualizing Latent Variable Models with flexplavaan

Latent variable models (LVMs) are incredibly flexible tools that allow users to address research questions they might otherwise never be able to answer (McDonald, 2013). However, one major limitation of LVMs is evaluating model fit. There is no universal consensus about how to evaluate model fit, either globally or locally. Part of the reason evaluating these models is difficult is because fit is typically reduced to a handful of statistics that may or may not reflect the model’s adequacy and/or assumptions. In this paper we argue that proper evaluation of model fit must include visualizing both the raw data and the model-implied fit. Visuals reveal, at a glance, the fit of the model and whether the model’s assumptions have been met. Unfortunately, tools for visualizing LVMs have historically been limited. In this paper, we introduce new plots and reframe existing plots that provide necessary resources for evaluating LVMs. These plots are available in a new open- source R package called flexplavaan, which combines the model plotting capabilities of flexplot with the latent variable modeling capabilities oflavaan.

Correction to: Beyond SEM: General Latent Variable Modeling

The article Beyond SEM: General Latent Variable Modeling, written by Bengt. O. Muthen.