Priority attribute algorithm for Q-matrix validation: A didactic

The Q-matrix is one of the core components of cognitive diagnostic assessment, which is a matrix describing the relationship between items and the attributes being assessed. Numerous studies have shown that inaccuracies in defining the Q-matrix can degrade parameter estimation and model fitting results. Currently, Q-matrix validation often involves exhaustive search algorithms (ESA), which traverse through all possible q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-vectors and determine the optimal q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q$$\end{document}-vector for items based on indicators or criteria corresponding to different validation methods. However, ESA methods are time-consuming, especially when the number of attributes is large, as the search complexity grows exponentially. This study proposes a more efficient search algorithm, the priority attribute algorithm (PAA), which conducts searches one by one according to the priority of attributes, greatly simplifying the search process. Simulation studies indicate that PAA can significantly enhance search efficiency while maintaining the same or even higher accuracy than ESA, particularly when dealing with a large number of attributes. Moreover, the Q-matrix validation method employing PAA demonstrates better applicability to small samples. A real-data analysis indicates that applying the PAA-based Q-matrix validation method may yield suggested Q-matrices with higher model-data fit and greater practical utility.