Sequential Multiple Hypothesis Testing in Multiple-Class Classification Problems Under Graded Response Model

Hung-Yi Lu

《International Journal of Intelligent Technologies and Applied Statistics》 14卷1期 (2021/03) Pp. 47-60

https://doi.org/10.6148/IJITAS.202103_14(1).0004

摘要

Purpose: The polytomous scoring model has been widely applied in studies on educational testing and psychological measurement, which typically require conducting multiple-class classifications of examinees to achieve results. Based on the premise of modeling, multiple-class classification problems can be converted into multiple hypothesis testing problems. Methodology: In this study, under the assumptions of a graded response model, the generalized sequential probability ratio test (GSPRT) was employed to solve multiple-class classification problems. Findings: The results indicated that in a situation involving an unlimited maximum number of test questions, the accuracy rate of GSPRT classification was approximately 80%. However, when the maximum number of test questions was limited, the accuracy rate declined because numerous examinees could not be classified despite completing the maximum number of test questions. Furthermore, maximum likelihood function values were adopted to categorize the examinees. This effectively addressed the problem of failing to determine examinee's abilities at the termination of testing. Originality/value: This study explores the problems associated with sequential multiple hypothesis testing based on the polytomous scoring model. The GSPRT was adopted to solve multi-category classification problems and examine the accuracy and efficiency of the resulting classifications.

關鍵字

Generalized sequential probability ratio test ； Graded response model ； Multiple-class classification ； Multiple hypothesis testing