Heterogeneity has been a hot topic in recent educational literature. Several calls have been voiced to adopt methods that capture different patterns or subgroups within students behavior or functioning. Assuming that there is an average pattern that represents the entirety of student populations requires the measured construct to have the same causal mechanism, same development pattern, and affect students in exactly the same way. Using a person-centered method (Finite Gaussian mixture model or latent profile analysis), the present tutorial shows how to uncover the heterogeneity within engagement data by identifying three latent or unobserved clusters. This chapter offers an introduction to the model-based clustering that includes the principles of the methods, a guide to choice of number of clusters, evaluation of clustering results and a detailed guide with code and a real-life dataset. The discussion elaborates on the interpretation of the results, the advantages of model-based clustering as well as how it compares with other methods.

翻译：异质性已成为近期教育文献中的热点议题。多项研究呼吁采用能够捕捉学生行为或功能中不同模式或子群体的方法。假定存在一个代表全体学生群体的平均模式，则要求所测量构念具有相同的因果机制、相同的发展模式，并对学生产生完全一致的影响。本教程采用以人为中心的方法（有限高斯混合模型或潜剖面分析），通过识别三个潜变量或未观测到的聚类，展示了如何揭示参与度数据中的异质性。本章介绍了基于模型的聚类方法，包括方法原理、聚类数量选择指南、聚类结果评估，以及包含代码和真实数据集的详细操作指南。讨论部分深入阐述了结果解读、基于模型的聚类优势及其与其他方法的比较。