Diagnostic classification models (DCMs) offer statistical tools to inspect the fined-grained attribute of respondents' strengths and weaknesses. However, the diagnosis accuracy deteriorates when misspecification occurs in the predefined item-attribute relationship, which is encoded into a Q-matrix. To prevent such misspecification, methodologists have recently developed several Bayesian Q-matrix estimation methods for greater estimation flexibility. However, these methods become infeasible in the case of large-scale assessments with a large number of attributes and items. In this study, we focused on the deterministic inputs, noisy "and" gate (DINA) model and proposed a new framework for the Q-matrix estimation to find the Q-matrix with the maximum marginal likelihood. Based on this framework, we developed a scalable estimation algorithm for the DINA Q-matrix by constructing an iteration algorithm that utilizes stochastic optimization and variational inference. The simulation and empirical studies reveal that the proposed method achieves high-speed computation, good accuracy, and robustness to potential misspecifications, such as initial value's choices and hyperparameter settings. Thus, the proposed method can be a useful tool for estimating a Q-matrix in large-scale settings.
翻译:诊断性分类模型(DDCMs)提供了统计工具,以检查被调查者优缺点的细微属性;然而,在预先定义的物品归属关系中出现误分时,诊断性准确性会恶化,这种误分已编码成Q矩阵;为了防止这种误分,方法学家最近开发了几种贝叶西亚Q矩阵估计方法,以便提高估计灵活性;然而,这些方法在使用大量属性和项目进行大规模评估的情况下变得不可行;在本研究中,我们侧重于确定性投入、噪音“和”门(DINA)模型,并提议了一个“Q矩阵”评估新框架,以找到最边际可能性的Q矩阵。基于这个框架,我们为DINAQ矩阵制定了一个可缩放的估算算法,以构建一种使用随机优化和变性推断的迭代算法。模拟和实证研究显示,拟议的方法能够实现高速计算、良好准确性和稳健度的门(DINA)模型估算,从而找到可能的误差分、大比例的模型。