Bridging Parametric and Nonparametric Methods in Cognitive Diagnosis

TL;DR

This paper introduces a unified framework that connects parametric and nonparametric methods in cognitive diagnosis models, enhancing understanding and providing practical algorithms with proven consistency.

Contribution

It proposes a novel unified estimation framework, develops iterative algorithms, and establishes their theoretical properties to bridge the gap between parametric and nonparametric CDM methods.

Findings

The framework effectively unifies parametric and nonparametric approaches.

Iterative algorithms show consistent estimation properties.

Simulation results demonstrate the framework's practical advantages.

Abstract

A number of parametric and nonparametric methods for estimating cognitive diagnosis models (CDMs) have been developed and applied in a wide range of contexts. However, in the literature, a wide chasm exists between these two families of methods, and their relationship to each other is not well understood. In this paper, we propose a unified estimation framework to bridge the divide between parametric and nonparametric methods in cognitive diagnosis to better understand their relationship. We also develop iterative joint estimation algorithms and establish consistency properties within the proposed framework. Lastly, we present comprehensive simulation results to compare different methods, and provide practical recommendations on the appropriate use of the proposed framework in various CDM contexts.