Analyzing Transitions in Sequential Data with Marginal Models

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Published Jun 27, 2024
Jeffrey Matayoshi Shamya Karumbaiah

Abstract

Various areas of educational research are interested in the transitions between different states—or events—
in sequential data, with the goal of understanding the significance of these transitions; one notable example
is affect dynamics, which aims to identify important transitions between affective states. Unfortunately,
several works have uncovered issues with the metrics and procedures commonly used to analyze
these transitions. As such, our goal in this work is to address these issues by outlining an alternative
procedure that is based on the use of marginal models. We begin by looking at the specific mechanisms
responsible for a recently discovered statistical bias with several metrics used in sequential data analysis.
After giving a theoretical explanation for the issue, we show that the marginal model procedure appears
to adjust for this bias. Next, a related problem is that the common practice of removing transitions to
repeated states has been shown to have unintended side-effects—to account for this issue, we develop
a method for extending the marginal model procedure to this specific type of analysis. Finally, in a
recent study evaluating the problem of multiple comparisons and sequential data analysis, the Benjamini-
Hochberg (BH) procedure, a commonly used approach to control for false discoveries, did not perform
as expected. By applying a technique from the biostatistics and epidemiology literature, we show that the
performance of the BH procedure, when used with the marginal model method, can be brought back to its
expected level. In all of our analyses, we evaluate the proposed method by both running simulations and
using actual student data. The results indicate that the marginal model procedure seemingly compensates
for the problems observed with other transition metrics, thus resulting in more accurate estimates of the
importance of transitions between states.

How to Cite

Matayoshi, J., & Karumbaiah, S. (2024). Analyzing Transitions in Sequential Data with Marginal Models. Journal of Educational Data Mining, 16(1), 197–232. https://doi.org/10.5281/zenodo.12179681
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Keywords

sequential data, transition metrics, marginal models, affect dynamics

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