Cognitive Diagnosis with Multinomial Response Distributions

本研究的目的是扩展认知诊断自适应测试的能力，以纳入多个响应结果。 感兴趣的认知诊断自适应测试方法采用的基本认知模型是有限偏序集（偏序集）。 主要的研究目标包括了解如何将误解和错误的反应信息到认知偏序集模型，建立技术，识别错误的反应，都是认知和统计上有趣的，并扩展数据分析框架的项目模型拟合和分析的情况下，项目有两个以上的不同类条件反应分布。 拥有通过数据分析验证方法实施的手段至关重要，因为潜在的认知过程是复杂和潜在的。 将采用马尔可夫链蒙特卡罗估计技术。 认知诊断自适应测试可以形成“智能”辅导系统的基础。 简化多项响应应该允许这样的系统更充分地利用响应信息，提供关于学生的增强的认知信息，甚至可能用更少的项目对学生进行分类。 认知诊断自适应测验是认知测量的重要统计工具。 实施涉及建立集中的认知模型，这使洞察解决问题的过程。 本研究的方法将应用于语言学领域的实际数据。

The purpose of this study is to extend the capabilities of cognitively diagnostic adaptive testing to incorporate multiple response outcomes. The cognitively diagnostic adaptive testing methodology of interest employs underlying cognitive models that are finite partially ordered sets (posets). Main research objectives include understanding how to incorporate misconception and erroneous response information into cognitive poset models, establishing techniques for identifying erroneous responses that are both cognitively and statistically interesting, and extending a data-analytic framework for model fitting and analysis of items to the case when items have more than two different class conditional response distributions. Having the means to validate implementation of the methodology through data analysis is critically important, as the underlying cognitive processes are complex and latent. Markov Chain Monte Carlo estimation techniques will be employed. Cognitively diagnostic adaptive testing can form the basis of `intelligent` tutoring systems. Incorporating multinomial responses should allow such systems to utilize response information more fully, provide enhanced cognitive information about students, and perhaps even classify students with fewer number of items. Cognitively diagnostic adaptive testing can be viewed as an important statistical tool for cognitive measurement. Implementation involves building focused cognitive models, which gives insight into the processes of problem-solving. The resulting methods of this research will be applied to actual data from a linguistics domain.