探討含有缺失資料的Mokken scale之量表係數

A Study on The Coefficients of Scalability of Mokken Scale with Missing Data

楊茵筑(Yin-Chu Yang)

指導教授 ： 林定香

國立臺北大學/商學院/統計學系/碩士(2010年)

摘要

問卷調查與量表設計對某些研究是占很重要的地位，也是對個人行為與態度的一種測量技術。以試題反應理論為核心的當代測驗理論被廣泛應用於測驗的編制、計分、分析與解釋，但測量工具常會發生受試者遺漏作答，卻沒有考慮到缺失資料的問題。本研究主要探討含有缺失值的資料，量表能力的係數之分配，由係數的變異數來判斷量表的穩定 ，並且尋找對量表能力係數有影響的因子。本研究發展3種計算含有缺失值之係數的方法：(1)所有組合法、(2)期望值估計法、(3)隨機抽取法，並比較其結果。在模擬研究中，設定4個缺失比例與樣本數為可能影響係數分配的因子。最後以缺失比例、樣本數與處理缺失值的方法當作迴歸模型的自變項，量表能力的係數之變異數為依變項，來評斷各因子對量表能力的係數之變異數的影響為何。
研究結果顯示，當雙向正答比例、觀察/缺失比例、雙向缺失比例愈高時，其H值的變異則愈低。其中這三種方法導致廣泛的分佈，以隨機抽取法形成H之分配的變異最小，期望值估計法形成H之分配的變異最大。

關鍵字

無母數試題反應理論 ； 缺失資料 ； Mokken量表 ； 量表能力的係數 ； 葛特曼錯誤

並列摘要

The survey and psychological scale are important in research of many fields since it is a technique to measure human behavior and attitude. In modern test theory, item response theory has been widely used in testing in test writing, scoring, analysis and interpretation. The subjects often fail to complete the instrument and the missing data are often not taken account. This research is to study the distribution of H- coefficient when missing data exists, evaluate the stability of the variance of the coefficient, and explore the possible influential factors. This research proposed three methods to calculate H- coefficient: (1) all combinations (2) expectation (3) random sample, and compared the results.In the simulation study, four missing rates and sample sizes are designed as influential factors for distributions of H- coefficient. Finally, these factors and methods were used as independent variable and variance of H- coefficient was used as depend variable, a regression analysis was conducted to decide the impact and relationship.
The results showed, when two-way positive response rate increased, there is more variation;when observe to missing rate increased, there is more variation; when two-way missing rate increased, there is less variation. Among the three methods, random sample has least variation while random sample resulted in widest distribution, expectation has most variation while expectation resulted in widest distribution .

並列關鍵字

nonparametric item response theory ； missing data ； Mokken scale ； coefficients of scalability ； Guttman error

參考文獻

Clogg, C.C., & Sawyer, D.O. (1981). A comparison of alternative models for analyzing the scalability of response patterns. In S. Leinhardt (ed.) Sociological Methodology 1981. San Francisco:Jossey-Bass.

Cohen, R. J., Montague, P., Nathanson, L., & Swerdlik, M. E. (1988). Psychological testing today: An introduction to tests and measurement. Mountain View, CA: Mayfield Publishing Company.

Hambleton, R. K., & Swaminathan, H, & Rogers, H. J. (1991).Fundamentals of Item Response Theory.Newburry Park,CA:SAGE.

Van Der Ark , L. A., Croon, M.A., & Sijtsma, K. (2007).Mokken Scale Analysis for Dichotomous Items Using Marginal Models.Psychometrika,73(2),183-208.

Van Schuur,W. H. (2003).Mokken Scale Analysis:Between the Guttman Scale and Parametric Item Response Theory.Political Analysis,11,139-163.