Item Response Modeling of Forced-Choice Questionnaires
by Anna Brown & Alberto Maydeu Olivares (20 11 ) .
This paper is extended the Thurstonian IRT model from single latent trait to multiple latent traits. It is a Thurstonian factor model reparameterized as a first order model. Three reasons for reparameterizing the Thurstonian factor model are that, first, in psychometric testing applications, the first-order factors (the latent utilities) are not of interest; rather, interest lies in estimating the second-order factors (the latent traits). Second, the use of the Thurstonian IRT model instead of the Thurstonian factor model speeds up computations considerably in the case of large models. Third, because the residual error variances of the latent responses variables are zero in the Thurstonian factor model, the residual error variances of the latent response variables are no longer zero, enabling latent trait estimation.
Two simulation studies were conducted to evaluate the performance of this new model. In simulation 1, the purpose is to show the empirical behavior of the multidimensional Thurstonian IRT model with the smallest number of traits, two. The purpose of simulation 2 is to investigate the effect of using different block sizes. This new model can be used with any forced-choice instrument composed of items fitting the dominance response model, with any number of meausured traits and any block sizes.
Question:
1. What is the difference between equation (7) and (8)?