Abstract
Latent trait models (LTMs) are one type of individual differences scaling models. Most commonly, these models use parametric functions to model the option response functions (ORFs) and latent trait distributions, although recently several nonparametric LTMs have also been proposed. In this paper, the strengths of each of these two approaches are discussed by comparing two models: Muthén's parametric LISCOMP model, and Levine's nonparametric MFS model. It was found that the MFS model is particularly suited for unidimensional scaling since it allows density estimation, it is more flexible at modeling the shape of the ORFs, and therefore may be more robust to mispecifications of the dimensionality of the data. The LISCOMP model, on the other hand, is particularly suited for multidimensional scaling, and for modeling the relationships between the scaling dimensions and external variables. Nonparametric models such as MFS are not easily generalized to multidimensional situations since they usually rely on smoothing constraints to reduce the estimation parameter space. These constraints are based on assumptions about the functional form of the ORFs and the latent trait densities, and it may be difficult to arrive at a set of constraints that will prove appropriate for different sampling schemes and dimensionality hypotheses. Key words: IRT; item response theory.
