多维题组效应认知诊断模型

当前认知诊断领域还缺少对包含题组的测验进行诊断分析的研究, 即已开发的认知诊断模型无法合理有效地处理含有题组效应的测验数据, 且已开发的题组反应模型也不具有对被试知识结构或认知过程进行诊断的功能。针对该问题, 本文尝试性地将多维题组效应向量参数引入线性Logistic模型中, 同时开发了属性间具有补偿作用的和属性间具有非补偿作用的多维题组效应认知诊断模型。模拟研究结果显示新模型合理有效, 与线性Logistic模型和DINA模型对比研究后表明：(1)作答数据含有题组效应时, 忽略题组效应会导致项目参数的偏差估计并降低对目标属性的判准率; (2)新模型更具普适性, 即便当作答数据不存在题组效应时, 采用新模型进行测验分析亦能得到很好的项目参数估计结果且不影响对目标属性的判准率。整体来看, 新模型既具有认知诊断功能又可有效处理题组效应。

The Multidimensional Testlet-Effect Cognitive Diagnostic Models

Cognitive diagnosis, which is also referred as skill assessment or skill profiling, utilizes latent class models to provide fine-grained information about students’ strength and weakness in the learning process. The outcome of cognitive diagnostic models (CDMs) is a profile with binary element for each examinee to indicate the mastery/nonmastery status of every attribute/skill. Therefore, one major advantage of CDMs is the capacity to provide additional information about the instructional needs of students. In the past decades, extensive research has been conducted in the area of cognitive diagnosis and many statistical models based on a probabilistic approach have been proposed. Examples of CDMs include the deterministic inputs, noisy and gate (DINA) model (Junker & Sijtsma, 2001), the deterministic input, noisy or gate (DINO) model (Templin & Henson, 2006), and the linear Logistic model (LLM) (Maris, 1999). In educational measurement, one of the most commonly used formats is the testlet design, which is a cluster of items that share a common stimulus (e.g., a reading comprehension passage or a figure). Under the framework of item response theory (IRT), various testlet response models (TRM) have been proposed, such as the Rasch testlet model (Wang & Wilson, 2005) and the multidimensional testlet-effect Rasch model (MTERM) (Zhan, Wang, Wang, & Li, 2014). However, limited efforts have been contributed to the development of testlet models for CDMs. A question then naturally arises is the searching for a way to account for testlet effect under CDMs. To address this issue, this study proposed two testlet-CDMs. One followed the compensatory approach and the other followed the noncompensatory approach: (1) the compensatory multidimensional testlet-effect CDM (C-MTECDM) was based on the combination of LLM and MTERM, while (2) the noncompensatory multidimensional testlet-effect CDM (N-MTECDM) was based on the combination of (logit)DINA model and MTERM, respectively. Model parameters can be estimated by the Bayesian methods with Markov chain Monte Carlo (MCMC) algorithms, which have been implemented with the freeware WinBUGS. In study 1, a series of simulations were conducted to evaluate parameter recovery of two new models, and results showed that the model parameters could be recovered fairly well under all simulated conditions. In study 2, the two new models were compared with the LLM and the (logit)DINA model, respectively. Results showed that ignoring testlet effect would result in biased item parameter estimations and worse person classification rates. Additionally, fitting a more complicated model (i.e., MTECDM) to data with a simpler structure did litter harm on parameter recovery. In conclusion, the new models is feasible and flexible.