Title: Toward a Unified Perspective on Assessment Models, a Perspective on
KST, CDA, and IRT

Authors: Stefano Noventa, Jürgen Heller, Augustin Kelava

Abstract:
In the past years, several theories for assessment have been developed within
the overlapping fields of Psychometrics and Mathematical Psychology. The most
notable are Item Response Theory (IRT), Cognitive Diagnostic Assessment (CDA),
and Knowledge Structure Theory (KST). In spite of their common goals, these
frameworks have been developed largely independently, focusing on slightly
different aspects. Yet various connections between them can be found in
literature (see, e.g., Junker & Sijtsma, 2001; von Davier, 2005; Stefanutti,
2006; Di Bello, Roussos, & Stout, 2007; Ünlü, 2007; Hong et al., 2015; Heller
et al., 2015; Noventa et al., 2019, to name only a few). A unified perspective
is suggested that uses two primitives (structure and process) and two
operations (factorization and reparametrization) to derive IRT, CDA, and KST
models. A Taxonomy of models is built using a two-processes sequential
approach that captures the similarities between the conditional error
parameters featured in these models and separates them into a first process
modeling the effects of individual ability on item mastering, and a second
process representing the effects of pure chance on item solving.