| Summary: | Based on nonlinear models between the measured latent variable and the item response, item response theory (IRT) enables independent estimation of item and person parameters and local estimation of measurement error. These properties of IRT are also the main theoretical advantages of IRT over classical test theory (CTT). Empirical evidence, however, often failed to discover consistent differences between IRT and CTT parameters and between invariance measures of CTT and IRT parameter estimates. In this empirical study a real data set from the Third International Mathematics and Science Study (TIMSS 1995) was used to address the following questions: (1) How comparable are CTT and IRT based item and person parameters? (2) How invariant are CTT and IRT based item parameters across different participant groups? (3) How invariant are CTT and IRT based item and person parameters across different item sets? The findings indicate that the CTT and the IRT item/person parameters are very comparable, that the CTT and the IRT item parameters show similar invariance property when estimated across different groups of participants, that the IRT person parameters are more invariant across different item sets, and that the CTT item parameters are at least as much invariant in different item sets as the IRT item parameters. The results furthermore demonstrate that, with regards to the invariance property, IRT item/person parameters are in general empirically superior to CTT parameters, but only if the appropriate IRT model is used for modelling the data.
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