Modernizing use of regression models in physics education research: a review of hierarchical linear modeling

TL;DR

This paper emphasizes the importance of using hierarchical linear models instead of single-level regression models in physics education research to accurately analyze nested data structures and avoid biased conclusions.

Contribution

It provides a theoretical comparison and practical demonstration of hierarchical linear modeling's advantages over traditional regression in physics education data analysis.

Findings

Hierarchical models better account for nested data structures.

Using inappropriate models can bias research findings.

Hierarchical modeling improves the reliability of physics education research.

Abstract

Physics education researchers (PER) often analyze student data with single-level regression models (e.g., linear and logistic regression). However, education datasets can have hierarchical structures, such as students nested within courses, that single-level models fail to account for. The improper use of single-level models to analyze hierarchical datasets can lead to biased findings. Hierarchical models (a.k.a., multi-level models) account for this hierarchical nested structure in the data. In this publication, we outline the theoretical differences between how single-level and multi-level models handle hierarchical datasets. We then present analysis of a dataset from 112 introductory physics courses using both multiple linear regression and hierarchical linear modeling to illustrate the potential impact of using an inappropriate analytical method on PER findings and implications. Research can leverage multi-institutional datasets to improve the field's understanding of how to support student success in physics. There is no post hoc fix, however, if researchers use inappropriate single-level models to analyze multi-level datasets. To continue developing reliable and generalizable knowledge, PER should use hierarchical models when analyzing hierarchical datasets. The supplemental materials include a sample dataset, R code to model the building and analysis presented in the paper, and an HTML output from the R code.