A Generalized Additive Partial-Mastery Cognitive Diagnosis Model

2025-11-25

AI Summary

Traditional partially mastered cognitive diagnostic models (PM-CDMs) suffer from model misspecification due to restrictive parametric item response functions and the assumption of discrete attribute mastery. To address this, we propose the Generalized Additive Partial Mastery model (GAPM), which replaces classical parametric forms with nonparametric monotonic functions, enabling continuous and fine-grained modeling of attribute mastery levels. GAPM employs sieve approximation coupled with marginal maximum likelihood estimation, ensuring interpretability while substantially reducing misspecification risk; it supports both confirmatory and exploratory diagnostic applications. Simulation and empirical studies demonstrate that GAPM achieves superior model fit and more accurate parameter recovery compared to existing PM-CDMs. Its flexibility and robustness make it broadly applicable across domains requiring fine-grained diagnostic inference, including educational assessment and healthcare diagnostics.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Cognitive diagnosis models (CDMs) are restricted latent class models widely used for measuring attributes of interest in diagnostic assessments in education, psychology, biomedical sciences, and related fields. Partial-mastery CDMs (PM-CDMs) are an important extension of CDMs. They model individuals' status for each attribute to be continuous for measuring the partial mastery level, which relaxes the restrictive discrete-attribute assumption of classical CDMs. As a result, PM-CDMs often yield better fits for real-world data and refined measurement of the substantive attributes of interest. However, these models inherit some strong parametric assumptions from the traditional CDMs about the item response functions and, thus, still suffer from a significant risk of model misspecification. This paper proposes a generalized additive PM-CDM (GaPM-CDM) that substantially relaxes the parametric assumptions of PM-CDMs. This proposal leverages model parsimony and interpretability by modeling each item response function as a mixture of nonparametric monotone functions of attributes. A method for the estimation of GaPM-CDM is developed, which combines the marginal maximum likelihood estimator with a sieve approximation of the nonparametric functions. The new model is applicable under both confirmatory and exploratory settings, depending on whether prior knowledge is available about the relationship between observed variables and attributes. The proposed method is applied to two measurement problems from educational testing and healthcare research, respectively, and further evaluated and compared with PM-CDMs through extensive simulation studies.

Problem

• Relaxing parametric assumptions in partial-mastery cognitive diagnosis models
• Addressing model misspecification risks in attribute measurement
• Enabling flexible item response functions via nonparametric monotone modeling

Innovation

• Nonparametric monotone functions model item response
• Combines marginal maximum likelihood with sieve approximation
• Applicable in both confirmatory and exploratory settings