Consequences of Ignoring Guessing When Estimating the Latent Density in Item Response Theory
Carol M. Woods
Washington University in St. Louis
In Ramsay-curve itemresponse theory (RCIRT), the latent variable distribution is estimated simultaneouslywith the item parameters. In extant Monte Carlo evaluations of RC-IRT, the itemresponse function (IRF) used to fit the data is the same one used to generatethe data. The present simulation study examines RC-IRT when the IRF isimperfectly matched to the data. In particular, guessing is ignored: Thetwo-parameter logistic IRF is fitted to data generated from the three parameterlogistic IRF. The empirical histogram method (EHM) implemented in the BILOG-MG programis also applied for comparison. Results indicate that apparent nonnormality ina density estimate from either RC-IRT or the EHM can be entirely due tomisspecification of the IRF, and it may be difficult to tell which IRF is bestwhen the latent density is estimated. It is recommended that practitionersfirst identify the best IRF with the latent density fixed at normal and then subsequentlyexamine the normality assumption about the latent density.
Index terms: Ramsay curve, RC-IRT, normalityassumption, model misspecification, empirical histogram
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