因素數目決定法：特徵值大於一之再探

Abstract

進行因素分析時，因素數目的決定為一關鍵步驟，決定過多或過少因素均會影響後續分析結果。Guttman（1954）與Kaiser（1960）提出以相關係數矩陣特徵值大於一的個數為因素數目後，此法即被廣泛地應用於各領域的研究中。但在比較各種因素數目決定法之優劣的研究中，特徵值大於一的表現並不佳。因此詳細探討此方法的表現可瞭解特徵值大於一能正確決定因素數目的情境，以供研究者參考，避免因誤用此法而得到不適當之因素結構。此外，亦可提供對過去的研究結果重新再思之依據，以評估過去以此法決定因素數目的研究是否適宜。本研究即藉由操弄因素負荷量、變項因素比、因素數目、樣本人數、及因素模式複雜度以瞭解特徵值大於一能正確決定因素數目的情境為何。研究結果顯示，當因素負荷量為.8且變項因素比為4以上時，特徵值大於一多能正確決定因素數目。若因素負荷量為.6，變項因素比為4時，此法在中樣本（n = 200）以上多能正確決定因素數目；變項因素比為6與8時，則需達大樣本（n = 500, 1000）時方能正確決定因素數目。而因素負荷量為.4時，此法僅在少數情境下能正確決定因素數目。

Determining the number of factors is a critical step in factor analysis. Since Guttman (1954) and Kaiser (1960) proposed the eigenvalue-greater-than-one rule to determine the number of factors, this rule has been widely applied in different research fields. Besides this rule, other researchers have proposed different methods to determine the number of factors. Previous researches on the comparison of the performances of different methods have repeatedly shown that the rule of eigenvalue-greater-than-one is the least accurate and the most unstable method. However, due to its popularity, a thorough evaluation on the method is called for. This study was therefore designed to reexamine the performance of this rule in order to offer appropriate guidelines for its application. Factor loading, the ratio of number of variables to factors, the number of factors, sample size, and the complexity of factor model were manipulated in the present study to investigate the performance of the eigenvalue-greater-than-one rule. The results showed that when the factor loading was high (.8), and the ratio of number of variables to factors was equal to or greater than 4, eigenvalue-greater-than-one rule could correctly determine the number of factors in most conditions. When factor loading was equal to .6, and the ratio of number of variables to factors equaled to 4, this rule performed well in identifying the number of factors if the sample size was equal to or greater than 200. When the ratio of number of variables to factors was 6 or 8 with a factor loading of .6, only under large samples (n = 500, 1000) could this rule yield the correct number of factors. When factor loading was equal to .4, eigenvalue-greater-than-one rule performed poorly in most conditions.