Toward a unified perspective on assessment models, a perspective on KST, CDA, and IRT

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.