Item Response Models for Partially Ordered Data

该项目将开发用于分析多个部分有序响应的先进分析工具。虽然部分有序集（偏序集）数据在社会和行为科学的许多分支中都很普遍，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的认识。一个简单的例子是回答类别同意，中立，不同意和不知道，其中前三个可以排序，最后一个形成自己的类别。该项目将建立在先前在偏序集方面的工作基础上，并将方法扩展到多个偏序集响应。这些方法将是基于项目反应理论（IRT）的模型的扩展。具体而言，该项目将采用分级响应、标称响应和顺序响应IRT模型——能够处理多种响应和混合响应类型的工具——用于部分有序响应。模拟研究将用于确定方法的有效性。很少有分析数据的方法，其中一些信息是有序的，而另一些则不是有序的。由于缺乏分析工具，这类广泛的数据类型经常被不必要地“强制”到其他数据类型中——例如，通过汇总或人为地压缩响应类别——因此它们可以通过现有的有序或名义数据方法进行分析。在这种数据缩减过程中，往往会丢失微妙和潜在重要的信息。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任何进展。本研究将直接解决这一测量差距。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得到了广泛的应用和采用，开发用于分析IRT中这种数据类型的方法有可能为广泛研究领域的研究人员和实践者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.