KST and CDA models can be systematized within a single theory and taxonomy

KST and early CDA approaches are based on the factorization operation

Modern CDA approaches are based on the reparametrization operation

A general CDA model is discussed that encompasses most models and frameworks

A general kernel of the link functions is used to classify CDA models and frameworks

In the past years, several theories for assessment have been developed within the 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 theories have been developed largely independently, focusing on slightly different aspects. In Part I of this three-part work, a general framework was introduced with the aim of achieving a unified perspective. The framework consists of two primitives (structure and process) and two operations (factorization and reparametrization) that allow to derive the models of these theories and systematize them within a general taxonomy. In this second contribution, the framework introduced in Part I is used to derive both KST and CDA models based on dichotomous latent variables, thus achieving a two-fold result: On the one hand, it settles the relation between the frameworks; On the other hand, it provides a simultaneous generalization of both frameworks, thus providing the foundations for the analysis of more general models and situations.

Item response theory

Knowledge space/structure theory

Cognitive diagnostic models

Conditional probabilities

Assessment models

© 2025 The Authors. Published by Elsevier Inc.