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

对Stout的统计维度评估程序DIMTEST进行了各种改进。特别提出了对项目进行部分信用评分的方法。提出了对DIMTEST大样本理论的改进。提出了现代非参数回归技术的结合。为了提高DIMTEST识别简单结构的能力，建议使用更复杂的聚类分析方法。本文还提出了缺乏单维量的两个估计量的发展。对Shealy和Stout的统计检验偏倚检测程序SIBTEST进行了各种改进。特别提出了对部分信用项目进行评分的方法。处理交叉偏差的SIBTEST版本的开发工作将继续进行。提出了SIBTEST和交叉SIBTEST的大样本理论。建议运用心理构念效度理论，使教育从业者能够在SIBTEST中区分单纯的差异项目功能和实际的测试不公平。在Dibello和Stout的统一认知诊断模型中，提出了基于计算似然的参数估计算法。本文提出对荷兰恒等式每项两个参数猜想的真实性进行研究。提出了心理测量建模和心理测试数据统计分析方面的工作。本研究对改进标准化测试的制作和评分，以及开展认知诊断以进行教育补救具有重要价值。这也有助于心理测试建模理论的发展。特别强调潜在能力维度的统计评估（即影响测试成绩的能力数量），简单结构的统计评估（测试项目的簇，每个簇内的项目测量基本潜在能力的相似配置），心理测试偏差（即测试不公平）的建模和统计评估，以及考生认知属性知识状态的建模和统计诊断。

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.