Moreover, when the measurement model and the variance decomposition model are estimated simultaneously, the variance decomposition deals appropriately with the dependency in the data when estimating IRT model parameters and testing the model’s assumptions, and the IRT measurement model deals appropriately with the estimation of the heritability coefficient (correcting for attenuation to obtain an unbiased point estimate) and the reporting of the confidence intervals (correcting for location-dependent uncertainty of person scores on the latent trait).
