Multilevel and empirical reliability estimates of learning growth: A simulation study and empirical illustration

Reliable learning progress information is crucial for teachers' interpretation and data-based decision making in everyday classrooms. Slope estimates obtained from simple regression modeling or more complex latent growth models are typically used in this context as indicators of learning progress. Research on progress monitoring has used mainly two ways to estimate reliability of learning progress, namely (a) split-half reliability and (b) multilevel reliability. In this work we introduce empirical reliability as another attractive alternative to quantify measurement precision of slope estimates (and intercepts) in learning progress monitoring research. Specifically, we extended previous work on slope reliability in two ways: (a) We evaluated in a simulation study how well multilevel reliability and empirical reliability work as estimates of slope reliability, and (b) we wanted to better understand reliability of slopes as a latent variable (by means of empirical reliability) vs. slopes as an observed variable (by means of multilevel reliability). Our simulation study demonstrates that reliability estimation works well over a variety of different simulation conditions, while at the same time conditions were identified in which reliability estimation was biased (i.e., with very poor data quality, eight measurement points, and when empirical reliability was estimated). Furthermore, we employ multilevel reliability and empirical reliability to estimate reliability of intercepts (i.e., initial level) and slopes for the quop-L2 test. Multilevel and empirical reliability estimates were comparable in size with only slight advantages for latent variable scores. Future avenues for research and practice are discussed.