Item Response Theory With Estimation of the Latent Density Using Davidian Curves

Davidian-curve item response theory (DC-IRT) is introduced, evaluated with simulations, and illustrated using data from the Schedule for Nonadaptive and Adaptive Personality Entitlement scale. DC-IRT is a method for fitting unidimensional IRT models with maximum marginal likelihood estimation, in which the latent density is estimated, simultaneously with the item parameters of logistic item response functions, as a Davidian curve. Simulations compare DC-IRT with Ramsay-curve IRT (RC-IRT) and the empirical histogram method (EHM) for a normal, bimodal, or skewed latent distribution. When the latent density was nonnormal, any of the three density estimation methods improved on the normal model. Both DC-IRT and RC-IRT produced more-accurate results than did the EHM.