Research on academic performance typically revolves around average achievement scores of students or schools. Focusing solely on averages can miss important aspects of the learning experience. The recent development of mixed-effects location scale models (MELSM) has provided a modeling technique that incorporates a scale model that captures and explains the consistency of academic achievement within the cluster of interest. Here, we formally introduce an extension to the MELSM, a Spike-and-Slab Mixed-Effects Location Scale Model (SS-MELSM), for simultaneously modeling location and scale parameters while incorporating a spike-and-slab prior to select or shrink random effects. Our approach identifies clusters with unusually large or small within-cluster variance in academic achievement, which can indicate overly inconsistent or consistent outcomes. To assess the performance of the proposed method, we conducted a simulation study, followed by an application to a dataset of 160 schools from the Brazilian Evaluation System of Elementary Education (Saeb) to illustrate its use in educational data analysis. Moreover, we show how to compare models with varying parameters regarding expected predictive accuracy. The results demonstrate that the SS-MELSM successfully identifies schools with unusually high and low consistency in mathematics achievement and that school- and student-level SES were relevant covariates when modeling the location and scale components. The methods presented in this paper are implemented in the R package ivd.
Carmo et al. (Fri,) studied this question.