A Comparison of Regression Equations for Estimation of Eigenvalues of Random Data Correlation Matrices in Parallel Analysis

平行分析隨機矩陣特徵值迴歸式估計之比較

翁儷禎(Li-Jen Weng) ； 李俊霆(Chun-Ting Lee) ； 吳柏儒(Po-Ju Wu)

《中華心理學刊》 45卷4期 (2003/12) Pp. 323-335

https://doi.org/10.6129/CJP.2003.4504.02

摘要

決定因素數目是因素分析中重要步驟。Horn(1965)提出平行分析方法，利用常態隨機資料矩陣的特徵值決定因素數目，多位學者遂分別發展不同迴歸式，以簡化隨機資料矩陣特徵值之估計。以往評估各方法之優劣表現均重在複相關平方的大小，較少注意估計之特徵值與隨機資料矩陣特徵值間的絕對差異，亦乏系統性比較各迴歸式優劣之研究。故本研究即在不同樣本人數與變項數目組合下，利用平均絕對差值與相關，系統性比較四條迴歸式之表現，評估迴歸式估計之特徵值與常態隨機資料矩陣特徵值間的差異。研究結果顯示Longman等人(1989)所提出之迴歸式的表現最好，Keeling(2000)次之，Lautenschlager等人(1989)再次之，Allen與Hubbard(1986)的表現最差。

關鍵字

平行分析 ； 迴歸式 ； 特徵值 ； 因素分析 ； 因素數目

並列摘要

Determining the number of factors is a critical step in factor analysis. Horn (1965) proposed the method of parallel analysis to use mean eigenvalues of random data correlation matrices for estimation of number of factors. Various regression equations were developed to simplify the estimation of mean eigenvalues of random data correlation matrices. The present research systematically evaluated the performance of four regression equations in estimating the eigenvalues of random data correlation matrices. The results indicated that the regression equation developed by Longman et al. (1989) performed the best, followed closely by Keeling (2000). Lautenschlager et al. (1989) came next, and Allen and Hubbard (1986) had the worst performance.

並列關鍵字

parallel analysis ； regression equations ； eigenvalues ； factor analysis ； number of factors

參考文獻

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Gorsuch, R. L.(1997).Exploratory Factor Analysis: Its Role in Item Analysis.Journal of Personality Assessment.68

Horn, J. L.(1965).A Rationale and Test for the Number of Factors in Factor Analysis.Psychometrika.30

Kaufman, J. D., Dunlap, W. P.(2000).Determining the Number of Factors to Retain: A Windows-based FORTRAN-IMSL Program for Parallel Analysis.Behavior Research Methods, Instruments, ＆ Computers.32