Cognitive diagnosis models (CDMs) are restricted latent class models widely used to measure attributes of interest in diagnostic assessments across education, psychology, biomedical sciences, and related fields. Partial-mastery CDMs (PM-CDMs) are an important extension of CDMs. They model individuals' status for each attribute as continuous to measure partial mastery levels, thereby relaxing the restrictive discrete-attribute assumption of classical CDMs. As a result, PM-CDMs often yield better fits to real-world data and more refined measurements of the substantive attributes of interest. However, these models inherit strong parametric assumptions from traditional CDMs about item response functions and thus still face a significant risk of model misspecification. This paper proposes a generalized additive PM-CDM (GaPM-CDM) that substantially relaxes the parametric assumptions of PM-CDMs. This proposal leverages model parsimony and interpretability by modeling each item response function as a mixture of nonparametric monotone functions of attributes. A method for estimating GaPM-CDM is developed that combines the marginal maximum likelihood estimator with a sieve approximation of the nonparametric functions. The new model is applicable in both confirmatory and exploratory settings, depending on whether prior knowledge of the relationship between observed variables and attributes is available. The proposed method is evaluated and compared with PM-CDMs through extensive simulation studies and further applied to two measurement problems from educational testing and healthcare research, respectively.

翻译：认知诊断模型（CDMs）是受限潜在类别模型，广泛应用于教育、心理学、生物医学及相关领域的诊断性评估中，以测量感兴趣的属性。部分掌握CDMs（PM-CDMs）是CDMs的重要扩展，它将每个属性的个体状态建模为连续变量，以测量部分掌握程度，从而放松了经典CDMs中严格的离散属性假设。因此，PM-CDMs通常能更好地拟合实际数据，并对实质性兴趣属性提供更精细的测量。然而，这些模型继承了传统CDMs关于项目反应函数的强参数假设，因此仍面临模型误设的重大风险。本文提出了一种广义可加PM-CDM（GaPM-CDM），显著放松了PM-CDMs的参数假设。该模型通过将每个项目反应函数建模为属性非参数单调函数的混合，充分利用了模型的简洁性和可解释性。我们开发了一种结合边际最大似然估计与筛子逼近非参数函数的GaPM-CDM估计方法。新模型既适用于验证性设置，也适用于探索性设置，具体取决于是否存在关于观测变量与属性之间关系的先验知识。通过广泛的模拟研究，对所提方法进行了评估，并与PM-CDMs进行了比较，进一步将其分别应用于教育测试和医疗保健研究中的两个测量问题。