The Generalized Multilevel Facets Model for Longitudinal Data

In the human sciences, ability tests or psychological inventories are often repeatedly conducted to measure growth. Standard item response models do not take into account possible autocorrelation in longitudinal data. In this study, the authors propose an item response model to account for autocorrelation. The proposed three-level model consists of multiple facets (e.g., person, item, and rater facets) and slope parameters. Level 1 is an item response (within-occasion) model; Level 2 is a between-occasion and within-person model; and Level 3 is a between-person model. Parameters can be estimated using the computer software WinBUGS, which uses Markov Chain Monte Carlo (MCMC) algorithms. Through a series of simulations, it was found that the parameters in the proposed model can be recovered fairly well. Real data of job performance judged by raters at various time points were analyzed to illustrate the implications and application of the proposed model.