A Higher-Order Cognitive Diagnosis Model with Ordinal Attributes for Dichotomous Response Data

Most existing cognitive diagnosis models (CDMs) assume attributes are binary latent variables, which may be oversimplified in practice. This article introduces a higher-order CDM with ordinal attributes for dichotomous response data. The proposed model can either incorporate domain experts' knowledge or learn from the data empirically by regularizing model parameters. A sequential item response model was employed for joint attribute distribution to accommodate the sequential mastery mechanism. The expectation-maximization algorithm was employed for model estimation, and a simulation study was conducted to assess the recovery of model parameters. A set of real data was also analyzed to assess the viability of the proposed model in practice.