Appendix平行分析隨機矩陣特徵值迴歸式估計之比較

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

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。

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.