Mathematical Sciences: Modeling & Statistical Analysis of Multivariate, Rank, & Mental Test Data, with Social Science Applications

Stout的统计维数评估程序DIMTEST的各种改进建议。特别是，适应部分信用评分的项目的程序提出。对DIMTEST大样本理论进行了改进。现代非参数回归技术的结合。为了提高DIMTEST确认简单结构的能力，建议使用更复杂的聚类分析。还提出了两个估计量的发展缺乏一维性。对Shealy和Stout的统计检验偏差检测方法SIBTEST进行了各种改进。特别是，适应部分信贷项目评分的程序。将继续进行开发SIBTEST版本以处理交叉偏倚的工作。提出了SIBTEST和交叉SIBTEST的大样本理论的发展。本文建议运用心理学的构想效度理论，使教育工作者能够使用SIBTEST来区分单纯的项目功能差异和实际的测试不公平。建议开发基于计算似然的算法用于Dibello和Stout的统一认知诊断模型中的参数估计。本文提出了一个关于霍兰德的荷元二参数猜想的真实性问题。 工作提出的心理测量建模和心理测试数据的统计分析。本研究对改进标准化测验的编制和评分方法，以及开展认知诊断和教育补救具有重要价值。这也将有助于心理测验模型化理论的发展。特别强调的是潜在能力维度的统计评估（即影响考试成绩的能力的数量），简单结构的统计评估（测试项目的丛，使得每个丛中的项目测量基本潜在能力的类似配置），心理测试偏差的建模和统计评估（即考试不公平），以及考生认知属性知识状态的建模与统计诊断。

Various improvements in Stout's statistical dimensionality assessment procedure DIMTEST are proposed. In particular, adapting the procedure for partial-credit scoring of items is proposed. Improvements in the DIMTEST large sample theory are proposed. The incorporation of modern nonparametric regression techniques is proposed. Use of more sophisticated versions of cluster analysis is proposed in order to improve the capability of DIMTEST to confirm simple structure. The development of two estimators of the amount of lack of unidimensionality is also proposed. Various improvements in Shealy and Stout's statistical test bias detection procedure SIBTEST are proposed. In particular, adapting the procedure for partial-credit item scoring is proposed. Work on the development of a version of SIBTEST to handle crossing bias is to be continued. The development of a large sample theory for SIBTEST and crossing SIBTEST is proposed. It is proposed that psychological construct validity theory be applied to enable educational practioners to use SIBTEST to distinguish between mere differential item functioning and actual test unfairness. It is proposed that computational likelihood-based algorithms be developed for parameter estimation in the unified cognitive diagnostic model of Dibello and Stout. It is proposed that the truth of Holland's Dutch Identity two parameters per item conjecture be investigated. Work is proposed on the psychometric modeling and statistical analysis of mental test data. This research promises to be of great value in improving the manufacture and scoring of standardized tests and in carrying out cognitive diagnoses for educational remediation purposes. It also should contribute to the advancement of the theory of mental test modeling. Special emphasis is placed upon the statistical assessment of latent ability dimensionality (that is, the number of abilities influencing test performance), the statistical assessment of simple structure (clumps of test items such that items within eac h clump measure a similar configuration of basic latent abilities), the modeling and statistical assessment of mental test bias (i.e. test unfairness), and the modeling and statistical diagnosis of examinee cognitive attribute knowledge states.