A Hierarchical Rater Model for Longitudinal Data

Research studies in psychology and education often seek to detect changes or growth in an outcome over a duration of time. This research provides a solution to those interested in estimating latent traits from psychological measures that rely on human raters. Rater effects potentially degrade the quality of scores in constructed response and performance assessments. We develop an extension of the hierarchical rater model (HRM), which yields estimates of latent traits that have been corrected for individual rater bias and variability, for ratings that come from longitudinal designs. The parameterization, called the longitudinal HRM (L-HRM), includes an autoregressive time series process to permit serial dependence between latent traits at adjacent timepoints, as well as a parameter for overall growth. We evaluate and demonstrate the feasibility and performance of the L-HRM using simulation studies. Parameter recovery results reveal predictable amounts and patterns of bias and error for most parameters across conditions. An application to ratings from a study of character strength demonstrates the model. We discuss limitations and future research directions to improve the L-HRM.