The Scaling Individuals and Classifying Misconceptions (SICM) model is an advanced psychometric model that can provide feedback to examinees’ misconceptions and a general ability simultaneously. These two types of feedback are represented by a discrete and a continuous latent variable, respectively, in the SICM model. The complex structure of the SICM model brings difficulties in estimating both misconception profile and ability efficiently in a linear test. To overcome this challenge, this study proposes a flexible computerized adaptive test (FCAT) design as a new test delivery method to increase test efficiency by administering an individualized test to examinees. We propose three item selection methods and two transition criteria to determine adaptive steps based on the needs of estimating one or two latent variables. Through two simulation studies, we demonstrate how to select an appropriate item selection method for an adaptive step and what transition criterion should be used between two adaptive steps. Results reveal the combination of the item selection method and the transition criterion could improve the estimation accuracy of a specific latent variable to a different extent and thus provide further guidance in designing an FCAT.

SICM（Scaling individual and Classifying Misconceptions）模型是一种先进的心理测量模型，可以同时为考生的误解和一般能力提供反馈。在 SICM 模型中，这两种类型的反馈分别由离散潜变量和连续潜变量表示。 SICM 模型的复杂结构给线性测试中有效估计误解概况和能力带来了困难。为了克服这一挑战，本研究提出了一种灵活的计算机自适应测试（FCAT）设计作为一种新的测试交付方法，通过对考生进行个性化测试来提高测试效率。我们提出了三种项目选择方法和两种转换标准，以根据估计一或两个潜在变量的需要来确定自适应步骤。通过两个模拟研究，我们演示了如何为自适应步骤选择合适的项目选择方法以及两个自适应步骤之间应使用什么转换标准。结果表明，项目选择方法和转移准则的结合可以不同程度地提高特定潜变量的估计精度，从而为 FCAT 的设计提供进一步的指导。