A Multilevel Higher Order Item Response Theory Model for Measuring Latent Growth in Longitudinal Data

In educational and psychological testing, individuals are often repeatedly measured to assess the changes in their abilities over time or their latent trait growth. If a test consists of several subtests, the latent traits may have a higher order structure, and traditional item response theory (IRT) models for longitudinal data are no longer applicable. In this study, various multilevel higher order item response theory (ML-HIRT) models for simultaneously measuring growth in the second- and first-order latent traits of dichotomous and polytomous items are proposed. A series of simulations conducted using the WinBUGS software with Markov chain Monte Carlo (MCMC) methods reveal that the parameters could be recovered satisfactorily and that latent trait estimation was reliable across measurement times. The application of the ML-HIRT model to longitudinal data sets is illustrated with two empirical examples.