Exploratory Data Analysis for Cognitive Diagnosis: Stochastic Co-blockmodel and Spectral Co-clustering

Exploratory data analysis (EDA) is an essential stage in statistical analysis that extracts information from data to assist confirmatory statistical modeling. Diagnostic classification models (DCMs) are a confirmatory approach to cognitive diagnosis, for which EDA tools need to be developed to assist the design of DCM-based tests. In this chapter, we propose a stochastic co-blockmodel that approximates the structure of many DCMs and an efficient spectral co-clustering algorithm for fitting the model. The proposed approach explores the structure of assessment data by clustering students and items into latent classes and analyzing the relationship between the student classes and the item classes. The performance of the proposed algorithms is evaluated through simulation studies. A real data example is provided to illustrate the use of the proposed method.