The Impact of Latent Density Misspecification on Item Response Theory Equating Methods

Item response theory (IRT) observed and true score equating are often conducted assuming that the latent variable is normally distributed. Although this might be a reasonable assumption for many educational and psychological assessments, not all variables can be approximated by a normal distribution. Under the common-item nonequivalent groups design, the current study examined the impact of latent density misspecification on IRT observed and true score equating. Specifically, equating results provided by two separate calibration estimates based on the Stocking–Lord linking method with normal and uniform weights and three concurrent calibration estimates obtained with different characterizations of the latent densities for the old and new groups were compared using both simulated and real data sets. In general, the concurrent calibration method with the latent densities for the two groups estimated using the empirical histogram method provided equating results with the least amount of error for most of the study conditions. Using normal weights with the Stocking–Lord method generally performed much better than using uniform weights; however, the overall performance of the Stocking–Lord method with normal weights was acceptable only if the latent densities for the two groups were normal distributions or close to normal distributions.