Abstract: A variety of cognitive diagnosis models has been proposed in the literature to achieve diagnostic functions in a wide range of practical settings, but most of them assume that all students use the same strategy to solve problems. However, it is universal that an item has multiple strategies in psychological and educational cognitive diagnostic tests. Ignoring multiple strategies and fitting data using single-strategy CDMs could result in model misspecifications and inadequate model-data fit, which, in turn, causes concerns as to the validity of inferences. Although a few multi-strategy cognitive diagnosis models have been proposed in recent years, they are all parameterized models requiring a sufficient sample size to ensure the accuracy of model estimation, which is difficult to satisfy in class-level cognitive diagnostic tests.
To further enrich and improve the research of multi-strategy cognitive diagnosis models and provide methodological support for small sample size conditions, methods from a non-parametric perspective may be feasible and promising. A nonparametric and efficient diagnostic classification method, called NCNPMSC method (Non-compensatory Nonparametric Multiple-strategy Classification), was proposed in this study based on a single-strategy nonparametric diagnostic classification method. The principal steps of this method are as follows: first, the ideal response pattern of each strategy was constructed for each potential attribute pattern( α ) depending on the Q-matrix and unobservable α; then, the ideal response pattern of α_i on item j is defined as the maximum ideal response pattern among all strategies of item j; finally, the Hamming distances between the ideal response patterns and the observed item response vector are calculated, and the attribute pattern α corresponding to the minimum Hamming distance is selected as the attribute pattern of the subject i. This method can be performed with any sample size, and only requires a matrix that associates items with attributes.
Simulation research and empirical data analysis were conducted to verify the effectiveness of the NCNPMSC method and to compare it with the MS-DINA model and GMS-DINA model. The results showed that the proposed NCNPMSC method had a higher diagnostic accuracy rate, which was higher than that of the MS-DINA model and the GMS-DINA model. The NCNPMSC method was efficient and not affected by the sample size, which has potential advantages over other parameterized models. When the number of attributes increased to 7 and the number of strategies increased to 4, the NCNPMSC model still had a robust classification accuracy. The results from real data analysis showed that the NCNPMSC model had the same classification accuracy under different sample conditions, while the classification accuracy of the MS-DINA model and GMS-DINA model decreased significantly as the sample size decreased.
This study innovatively developed a simple and high-precision multi-strategy cognitive diagnosis method from a non-parametric perspective, which provides a solution for multi-strategy cognitive diagnosis under small sample conditions. The rationality and feasibility of the NCNPMSC method were proved by simulation research and theoretical derivation, which not only enriched and deepened the research of multi-strategy cognitive diagnosis but also provided methodological support for multi-strategy cognitive diagnosis in practice.

Key words: cognitive diagnosis, multi-strategy, nonparametric method, hamming distance

摘要： 心理与教育认知诊断测验中常常存在一个题目包含多种解题策略的情况,参数化的多策略认知诊断模型需要足够的样本量以保证模型参数估计的准确性,而学校和班级规模的诊断测验难以满足参数化模型的样本量要求。本研究开发了一种新的简洁高效的非参数化多策略认知诊断分类（NCNPMSC）方法,该方法不需要进行参数估计,即使样本量为1人也能实现诊断分类。本文通过两个模拟研究和实证数据分析证明了NCNPMSC方法进行多策略诊断分类的合理性和可行性,为多策略认知诊断提供了新的方法支持。

关键词: 认知诊断, 多策略, 非参数化, 海明距离