A general saltus LLTM-R for cognitive assessments

Abstract

The purpose of this paper is to propose a general saltus LLTM-R for cognitive assessments. The proposed model is an extension of the Rasch model that combines a linear logistic latent trait with an error term (LLTM-R), a multidimensional Rasch model, and the saltus model, a parsimonious, structured mixture Rasch model. The general saltus LLTM-R can be used to (1) estimate parameters that describe test items by substantive theories, (2) evaluate the latent constructs that are associated with the knowledge structures of the test items, and (3) test hypotheses on qualitative differences between the sub-populations of subjects with different problem solving strategies, cognitive processes, or developmental stages. Bayesian estimation of the proposed model is described with an application to a test of deductive reasoning in children.