Item Response Models for Partially Ordered Data

该项目将开发先进的分析工具，用于分析多个部分排序的答复。虽然偏序集(偏序集)数据在社会和行为科学的许多分支中普遍存在，但它们的存在一直没有得到充分的报道，其重要性也没有得到充分认识。一个简单的例子是响应类别同意、中立、不同意和不知道，其中前三个类别可以排序，最后一个类别形成自己的类别。该项目将建立在POSET之前的工作基础上，并将这些方法扩展到多个POSET响应。这些方法是基于项目反应理论(IRT)的模型的扩展。具体地说，该项目将调整分级、名义和顺序响应IRT模型--能够处理多个响应和混合响应类型的工具--以适应部分排序的响应。模拟研究将被用来建立该方法的有效性。分析数据的分析方法很少，其中一些信息是有序的，而另一些则是无序的。由于缺乏分析工具，这一大类数据类型经常不必要地被“强迫”为其他数据类型--例如，通过总结或人为地折叠答复类别--以便它们可以通过现有的顺序或名义数据方法进行分析。在这样的数据简化过程中，微妙的和潜在的重要信息往往会丢失。虽然这个问题在二十多年前就被认为对心理和教育测量理论的发展产生了负面影响，但从那时起实际上几乎没有取得什么进展。这项研究将直接解决测量中的这一差距。由于项目反应理论(IRT)在教育、社会和心理科学、健康测量和商业营销研究等各个领域都得到了广泛的应用和采用，因此在IRT中分析这一数据类型的方法的发展有可能为研究人员和从业者在广泛的研究领域提供更精确的测量工具。

The project will develop advanced analytic tools for analyzing multiple partially orderedresponses. While partially ordered set (poset) data are prevalent in many branches of the social and behavioral sciences, their presence has been under-reported and their importance underrecognized. A simple example is response categories Agree, Neutral, Disagree, and Don't Know, of which the first three can be ordered and the last forms a category of its own. The project will build upon previous work in poset and extend the methods to multiple poset responses. The methods will be extensions of models based on the item response theory (IRT). Specifically, the project will adapt the graded, nominal, and sequential response IRT models - tools that are able to handle multiple responses and mixed-response types - for partially ordered responses. Simulation studies will be used to establish the validity of the methodology.Very few analytic methods exist for analyzing data in which some of the information is ordered and some is not. Because of the lack of analytic tools, this broad class of data types is often unnecessarily being "forced" into other data types - e.g., through summarization or artificially collapsing response categories - so they can be analyzed by existing ordinal or nominal data methods. Subtle and potentially important information is often lost through such data reduction. While this problem was recognized more than two decades ago as having a negative impact on the development of theory for psychological and educational measurement, little progress has actually been made since then. This research will directly address this gap in measurement. Because item response theory (IRT) has been widely used and adopted in various fields - education, social and psychological sciences, health measurement, and business marketing research - the development of methods for analyzing this data type in IRT has the potential to provide more precise measurement tools for researchers and practitioners in a broad range of areas of study.