Multi-level IRT with Measurement Error in the Predictor Variables

In this paper a two-level regression model is imposed on the ability parameters in an IRT model. The advantage of using latent rather than observed scores as dependent variables of a multi-level model is that this offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error. Another advantage is that, contrary to observed scores, latent scores are test-independent, which offers the possibility of entering results from different tests in one analysis. Further, it will be shown that also problems of measurement error in covariates in multilevel models can be solved in the framework of IRT-multilevel modeling. In this paper, the two-parameter normal ogive model will be used for the IRT measurement model. It will be shown that the parameters of the twoparameter normal ogive model and the multilevel model can be simultaneously estimated in a Bayesian fraMework using Gibbs sampling. Various examples using simulated data will be given.