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Ramsay-Curve Item Response Theory for the Three-Parameter Logistic Item Response Model

In Ramsay-curve item response theory (RC-IRT), the latent variable distribution is estimated simultaneously with the item parameters of a unidimensional item response model using marginal maximum likelihood estimation. This study evaluates RC-IRT for the three-parameter logistic (3PL) model with comparisons to the normal model and to the empirical histogram method (EHM) implemented in BILOG-MG. Results support the validity and utility of RC-IRT for the 3PL model. RC-IRT and the EHM both performed better than the normal model for nonnormal latent distributions and appeared to have complementary strengths. Item parameter estimates tended to be more accurate with the EHM, especially for shorter tests; however, recovery of the latent distribution was better, and scores were less biased, with RC-IRT. Differences between RC-IRT and the EHM diminished as the sample size and especially the test length increased. Practical recommendations for estimating the latent distribution with the 3PL model are provided.