Assessing parameter invariance in item response theory s logistic two item parameter model: A monte carlo investigation

Statistical properties of the ability level estimate (theta) in item response theory (IRT) were investigated through a Monte Carlo investigation, based on data generated with a four cases multifactor design. Dichotomous items and the logistic two-parameter IRT model in a one-dimensional setting have been chosen. The estimation procedure was the marginalized Bayesian item parameters estimation and EAP estimation for theta. The property of invariance is discussed. Results show that estimation of theta is intrinsically biased, is constrained by the number of items and that it performs better when the number of items and the number of examinees increase. Furthermore, IRT parameters do not seem to perform better nor give more information than those used in classical test theory.