雙因素模型下測驗分數信度係數之比較

A Comparison of Reliability Coefficients for Test Scores Under Bi-factor Models

鄧祈允(Chi-Yun Deng) ； 黃柏僩(Po-Hsien Huang)

《測驗學刊》 68卷3期 (2021/09) Pp. 209-231

摘要

在估計測驗分數的信度時，應先考慮測驗的向度（dimensionality），若測驗結構為多向度時，則應使用多向度信度估計法，常見的方法包括分層α、Revelle的β、多向度ω，以及階層ω。然而，過往研究並未仔細檢驗前述多向度估計法的差異，故本研究在真實模型為雙因素模型（bi-factor model）的假設下，系統性地操弄一般因素負荷量、子因素負荷量、子因素數目，以及樣本數，以探討前述四種信度估計法之表現。當以各信度係數之母體參數作為真實數值時，模擬研究結果顯示僅在子因素負荷量較高時，階層ω才會與另外三個信度係數有明顯不一致之真實數值，此意味著在子因素負荷量的真實數值較小時，分層α、β、多向度ω所得到的測驗分數信度估計值仍具有相當高之參考性，其中的β與階層ω展現最為一致之真實數值。當比較各方法的估計表現時，結果顯示相較於多向度ω、分層α，以及β，階層ω橫跨所有情境都展現較大的相對偏誤（relative bias）與變異性（variability），此顯示階層ω雖在估計概念較為合理，但於有限樣本之實徵表現不佳。本研究結果建議，在估計多向度測驗分數的信度時，不應僅參考階層ω，仍需使用其他多向度信度估計指標做為輔助，以對測驗分數的信度有較佳的估計與詮釋。

關鍵字

Revelle的β ； 分層α ； 多向度ω ； 信度 ； 階層ω ； 雙因素模型

並列摘要

When estimating a test score's reliability, the dimensionality of the test needs to be considered. If the test is not unidimensional, multidimensional reliability coefficients, such as stratified alpha, Revelle's beta, multidimensional omega, and hierarchical omega, should be used. However, these multidimensional coefficients might not be carefully distinguished in practical works. This study aimed to investigate these coefficients' meanings and properties. We used bi-factor models as true models for data generation and manipulated loadings of general and group factors, numbers of group factors, and sample sizes. The results showed that: (1) the true value of hierarchical omega was significantly different from other coefficients only when group factor loadings were high; (2) the true value of Revelle's beta was most similar to the hierarchical omega; (3) hierarchical omega yielded larger relative bias and variability than other coefficients under all conditions. These results implied other multidimensional reliability coefficients were still valuable when group factor loadings were low and hierarchical omega didn't perform well under finite sample settings, although hierarchical omega's meaning was most interpretable. These results suggested hierarchical omega should not be considered as ＂golden standard＂, other coefficients were still useful to interpret measurement results.

並列關鍵字

bi-factor model ； hieratical omega ； multidimensional omega ； reliability ； Revelle's beta ； stratified alpha

參考文獻

Reise, S. P., Morizot, J., & Hays, R. D. (2007). The role of the bifactor model in resolving dimensionality issues in health outcomes measures. Quality of Life Research, 16(1), 19-31. doi:10.1007/s11136-007-9183-7

Revelle, W. (1979). Hierarchical cluster analysis and the internal structure of tests. Multivariate Behavioral Research, 14(1), 57-74. doi:10.1207/s15327906mbr1401_4

Revelle, W., & Condon, D. M. (2019). Reliability from to : A tutorial. Psychological Assessment, 31(12), 1395-1411. doi:10.1037/pas0000754

Rosseel, Y. (2012). Lavaan: An r package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. doi:10.18637/jss.v048.i02

Schmid, J., & Leiman, J. M. (1957). The development of hierarchical factor solutions. Psychometrika, 22(1), 53-61. doi:10.1007/BF02289209