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A Family of Generalized Diagnostic Classification Models for Multiple Choice Option-Based Scoring

机译：基于选择题评分的一类广义诊断分类模型

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This article proposes a new family of diagnostic classification models (DCM) called the Generalized Diagnostic Classification Models for Multiple Choice Option-Based Scoring (GDCM-MC). The GDCM-MC is created for multiple choice assessments with response options designed to attract particular kinds of student thinking and understanding, both desired (correct) thinking and problematic (incorrect or partially correct) thinking. Key features that combine to distinguish GDCM-MC are: (a) an expanded latent space that can include both desirable and problematic facets of thinking, (b) an expanded >Q matrix that includes a row for each response option and that uses a three-valued coding scheme to specify which latent states are strongly attracted to that option, (c) a guessing component that responds to the forced choice aspect of multiple choice questions, and (d) a general modeling framework that can incorporate the diagnostic modeling functionality of almost any dichotomous DCM, such as deterministic input, noisy ``and'' gate (DINA), reparameterized unified model (RUM), loglinear cognitive diagnosis model (LCDM), or general diagnostic model (GDM). The article discusses these four components and presents the GDCM-MC model equation as a mixture of cognitive and guessing components. Two identifiability theorems are presented. A Bayesian Markov Chain Monte Carlo (MCMC) model estimation algorithm is discussed, and real and simulated data studies are reported.
机译：本文提出了一种新的诊断分类模型（DCM）系列，称为基于选择题评分的通用诊断分类模型（GDCM-MC）。 GDCM-MC的创建是为了进行多项选择评估，其回答选项旨在吸引特定类型的学生思维和理解，包括期望的（正确的）思维和有问题的（不正确或部分正确的）思维。结合起来可以区分GDCM-MC的关键特征是：（a）扩展的潜在空间，可以同时包含期望和有问题的思维面；（b）扩展的> Q 矩阵，其中每个响应均包含一行选项，并使用三值编码方案来指定该选项强烈吸引了哪些潜在状态；（c）回答多项选择问题的强制选择方面的猜测组件；以及（d）可以整合了几乎所有二分DCM的诊断建模功能，例如确定性输入，嘈杂的``和''门（DINA），重新参数化统一模型（RUM），对数线性认知诊断模型（LCDM）或常规诊断模型（GDM）。本文讨论了这四个组成部分，并提出了GDCM-MC模型方程式，将认知和猜测组成部分混合在一起。提出了两个可识别性定理。讨论了贝叶斯马尔可夫链蒙特卡洛（MCMC）模型估计算法，并报告了实际数据和模拟数据。

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