Revisiting the Regularity of Student Learning Rate: Sensitivity to Which Observations Are Included

TL;DR

This study investigates how the estimates of student learning rates from mixed-effects models vary depending on data inclusion choices, challenging the assumption of their stability and interpretability.

Contribution

It demonstrates that estimates of student learning rate are highly sensitive to data inclusion criteria, highlighting the need for careful reporting and interpretation.

Findings

Student variation in initial knowledge remains stable across specifications.

Learning rate variation estimates inflate significantly with different data inclusion.

Model estimates of learning rate are highly sensitive to which observations are used.

Abstract

Mixed-effects models fit to observational practice data are widely used in learning analytics to estimate student-level variation in initial knowledge and learning rate, and the resulting estimates increasingly inform substantive claims about learners. We examine whether such estimates can be read as properties of learners or whether they depend on choices about which observations the model is fit to. As a case study, we revisit the ``astonishing regularity'' reported by Koedinger et al. (2023): that students vary substantially in initial knowledge but much less in learning rate. The finding is based on fits of the individual Additive Factors Model (iAFM) to 27 educational datasets, and rests on a model-derived estimate of student-level learning-rate variation being small in absolute terms. We refit the same model on the same datasets under two specifications, each varying how much of each student's practice on a given skill is used in fitting. The estimate of student-level variation in initial knowledge stays approximately stable across both specifications. The estimate of student-level variation in learning rate does not: it inflates by a median of 118\% under one specification and is several times larger under the other. The same model, fit to the same data, returns substantially different estimates of how much students vary in learning rate depending on which observations are included. When estimates from mixed-effects models on observational practice data are used to support substantive claims about learners, sensitivity to such choices deserves a central place in how those estimates are reported and read.