Accuracy of the Q-matrix-validation algorithm and sensitivity of model fit indices toward different types of Q-matrix misspecification for diagnostic classification models (DiaFit)

诊断分类模型（DCM）代表了国际上广泛讨论但在德国鲜为人知的一类验证性概率多维潜变量模型，其中分类潜变量提供了基于诊断驱动的多变量分类的有意义的熟练程度概况。这些概况可以使学生和教师了解某一学术领域的具体优势和弱点，并有助于采取适当的支助性干预措施。对于DCM的估计，需要Q矩阵中的项目的解决方案过程中涉及的属性的规范。Q矩阵的确定是非常重要的，因为它代表了DCM的理论基础。然而，在实际应用中，真正的Q矩阵是未知的，并且可能包含不正确的条目。这种现象被称为Q矩阵误指定。通常可以区分三种不同类型的Q矩阵误指定：欠指定、过指定和平衡。在文献中已经提出了几种算法的Q-矩阵的经验验证。然而，他们的准确性进行了调查，只有选定类型的Q-矩阵误指定。此外，尽管过去已经提出了DCM的各种绝对和相对模型拟合指数，但评估DCM的模型拟合仍然是一个挑战。DiaFit项目在一项复杂的模拟研究和一项应用研究中调查了与模型拟合评估相关的重要方法学问题，以及对数线性DCM不同类型Q矩阵错误指定的Q矩阵验证算法的准确性。在模拟研究中，将研究不同绝对和相对模型拟合测量（例如AIC、BIC、MAD、RMSEA）对三种不同类型的错误指定Q矩阵（欠指定、超指定、平衡）的灵敏度。此外，这三种类型的Q-矩阵误指定的Q-矩阵验证算法的准确性将得到解决。在模拟中，回答者的数量，属性和项目以及Q矩阵中的项目结构复杂性将是不同的。这些结果将基本上扩展对数线性DCM的模型拟合评估和Q矩阵验证算法稳健性的最新技术水平，并为在应用环境中评估DCM的模型拟合提供建议。模拟的结果将应用于已经收集的关于小学基本算术技能的两个不同数据集的二次分析。Q矩阵也可用于这些数据集。本应用研究将说明如何不同的模型拟合指数和Q矩阵验证方法可以在实际应用中使用时，真正的数据生成Q矩阵是未知的。

Diagnostic classification models (DCM) represent an internationally widely discussed but in Germany little known class of confirmatory probabilistic multidimensional latent-variable models with categorical latent variables providing meaningful proficiency profiles based on statistically-driven multivariate classifications. These profiles can inform students and teachers about the particular strengths and weaknesses in a given academic area and allow for the derivation of appropriate supportive interventions. For the estimation of DCM the specification of attributes involved in the solution process of items in a Q-matrix is required. The determination of the Q-matrix is of key importance, as it represents the theoretical basis of DCM. In practical applications, however, the true Q-matrix is unknown and may contain incorrect entries. This phenomenon is called Q-matrix misspecification. It is common to distinguish between three different types of Q-matrix misspecification: underspecified, overspecified, and balanced. Several algorithms have been proposed in the literature for the empirical validation of the Q-matrix. However, their accuracy has been investigated only for selected types of Q-matrix misspecification. Moreover, assessing model fit for DCM continues to be a challenge, although various absolute and relative model fit indices for DCM have been proposed in the past. The project DiaFit investigates in a complex simulation study and an application study important methodological issues related to the assessment of the model fit and the accuracy of the Q-matrix validation algorithm for different types of Q-matrix misspecification for log-linear DCM. In the simulation study the sensitivity of different absolute and relative model fit measures (e.g. AIC, BIC, MAD, RMSEA) to three different types of misspecified Q-matrices (underspecified, overspecified, balanced) will be investigated. Moreover, the accuracy of the Q-matrix validation algorithm for these three types of Q-matrix misspecification will be addressed. In the simulation the number of respondents, attributes, and items as well as the item-structure complexity in the Q-matrix will be varied. The results will essentially extend the state of the art in model fit assessment and robustness of the Q-matrix validation algorithm for log-linear DCM and enable recommendations for the assessment of the model fit of DCM in applied settings. The results of the simulation will be applied in a secondary analysis to two different datasets on basic arithmetic skills in elementary school that have already been collected. The Q-matrices are also available for these datasets. This application study will illustrate how different model fit indices and the Q-matrix validation method can be used in practical applications when the true data-generating Q-matrix is unknown.