What is an Ordinal Latent Trait Model?

TL;DR

This paper develops a theoretical framework for ordinal latent trait models, clarifying their definitions in unidimensional and multidimensional contexts and discussing practical implications for linking traits to response categories.

Contribution

It provides the first comprehensive theoretical framework for ordinal models, unifying various concepts and extending definitions to multidimensional trait spaces.

Findings

Unidimensional models have coinciding definitions of ordinalness.

Multidimensional models require trait-specific definitions of ordinality.

Practical considerations on the strength of the trait-category link are discussed.

Abstract

Although various polytomous item response models are considered to be ordinal models there seems no general definition of an ordinal model available. Alternative concepts of ordinal models are discussed and it is shown that they coincide for classical unidimensional models. For multidimensional models the definition of an ordinal model refers to specific traits in the multidimensional space of traits. The objective is to provide a theoretical framework for ordinal models. Practical considerations concerning the strength of the link between the latent trait and the order of categories are considered briefly.