Advancing clustering methods in physics education research: A case for mixture models

TL;DR

This paper advocates for using mixture models, specifically latent class analysis, as a model-based alternative to traditional clustering methods like k-modes in physics education research, enhancing subgroup identification.

Contribution

It compares k-modes clustering with latent class analysis, illustrating their differences and similarities through parallel analyses and providing R code for replication.

Findings

Mixture models account for classification errors better than k-modes.

Parallel analyses demonstrate the advantages of mixture models in subgroup identification.

Provided R code enables researchers to apply these methods in their own studies.

Abstract

Clustering methods are often used in physics education research (PER) to identify subgroups of individuals within a population who share similar response patterns or characteristics. K-means (or k-modes, for categorical data) is one of the most commonly used clustering methods in PER. This algorithm, however, is not model-based: it relies on algorithmic partitioning and assigns individuals to subgroups with definite membership. Researchers must also conduct post-hoc analyses to relate subgroup membership to other variables. Mixture models offer a model-based alternative that accounts for classification errors and allows researchers to directly integrate subgroup membership into a broader latent variable framework. In this paper, we outline the theoretical similarities and differences between k-modes clustering and latent class analysis (one type of mixture model for categorical data). We also present parallel analyses using each method to address the same research questions in order to demonstrate these similarities and differences. We provide the data and R code to replicate the worked example presented in the paper for researchers interested in using mixture models.