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

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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.