Estimation and goodness-of-fit in latent trait models: A comparison among theoretical approaches

Two theoretical approaches are usually employed for the fitting of ordinal data: the underlying variables approach (UV) and the item response theory (IRT). In the UV approach, limited information methods [generalized least squares (GLS) and weighted least squares (WLS)] are employed. In the IRT approach, fitting is carried out with full information methods [Proportional Odds Model (POM), and the Normal Ogive (NOR)]. The four estimation methods (GLS, WLS, POM and NOR) are compared in this article at the same time, using a simulation study and analyzing the goodness-of-fit indices obtained. The parameters used in the Monte Carlo simulation arise from the application of a political action scale whose two-factor structure is well known. The results show that the estimation method employed affects the goodness-of-fit to the model. In our case, the IRT approach shows a better fitting than UV, especially with the POM method.