A multilevel item response theory model for time structured data.

摘要

The feasibility of a Markov Chain Monte Carlo (MCMC) method to estimate a multi-level Item Response Theory (IRT) model for the repeated assessments on individuals was examined. The IRT portion of the model was limited to uni-dimensional constructs having polytomous responses. This approach was applied to simulated data to demonstrate its ability to recover known parameter estimates, and on data obtained from the National Center for early Development and Learning Multi-State Study of Pre-kindergarten (NCEDL) study to determine experimental parameters. The MCMC techniques used Gibbs sampling in conjunction with a data augmentation procedure. Results were compared to estimates obtained under Maximum Likelihood methods. For the simulated data, the parameter recovery was successful for the IRT slope and location parameters, showing strong associations for fixed and random effects. Recovery proved less successful for the IRT offset and structural parameters with the expected weaker associations. From results of the real-life NCEDL study, it was recognized that small-sized clusters lack sufficient information for these complex models. The different methods gave similar estimates although the conclusions differed for the NCEDL application. Implications for future research are discussed including the effects of MCMC adjustments, missing data, and model extension.