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Abstract

In Ramsay-curve item response theory (RC-IRT), the latent variable distribution is estimated simultaneously with the item parameters. In extant Monte Carlo evaluations of RC-IRT, the item response function (IRF) used to fit the data is the same one used to generate the data. The present simulation study examines RC-IRT when the IRF is imperfectly matched to the data. In particular, guessing is ignored: The two-parameter logistic IRF is fitted to data generated from the three-parameter logistic IRF. The empirical histogram method (EHM) implemented in the BILOG-MG program is also applied for comparison. Results indicate that apparent nonnormality in a density estimate from either RC-IRT or the EHM can be entirely due to misspecification of the IRF, and it may be difficult to tell which IRF is best when the latent density is estimated. It is recommended that practitioners first identify the best IRF with the latent density fixed at normal and then subsequently examine the normality assumption about the latent density.

Keywords

Ramsay curve RC-IRT normality assumption model misspecification empirical histogram

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