Shaky Student Growth? A Comparison of Robust Bayesian Learning Progress Estimation Methods

Monitoring the progress of student learning is an important part of teachers' data-based decision making. One such tool that can equip teachers with information about students' learning progress throughout the school year and thus facilitate monitoring and instructional decision making is learning progress assessments. In practical contexts and research, estimating learning progress has relied on approaches that seek to estimate progress either for each student separately or within overarching model frameworks, such as latent growth modeling. Two recently emerging lines of research for separately estimating student growth have examined robust estimation (to account for outliers) and Bayesian approaches (as opposed to commonly used frequentist methods). The aim of this work was to combine these approaches (i.e., robust Bayesian estimation) and extend these lines of research to the framework of linear latent growth models. In a sample of N = 4970 second-grade students who worked on the quop-L2 test battery (to assess reading comprehension) at eight measurement points, we compared three Bayesian linear latent growth models: (a) a Gaussian model, (b) a model based on Student's t-distribution (i.e., a robust model), and (c) an asymmetric Laplace model (i.e., Bayesian quantile regression and an alternative robust model). Based on leave-one-out cross-validation and posterior predictive model checking, we found that both robust models outperformed the Gaussian model, and both robust models performed comparably well. While the Student's t model performed statistically slightly better (yet not substantially so), the asymmetric Laplace model yielded somewhat more realistic posterior predictive samples and a higher degree of measurement precision (i.e., for those estimates that were either associated with the lowest or highest degree of measurement precision). The findings are discussed for the context of learning progress assessment.