特徵值大於一方法正確決定因素數目之再探

Reexaming the Rule of Eigenvalue-Greater-Than-One to Correctly Identify the Number of Factors

特徵值大於一是決定因素數目最常用的方法，但錯估因素數目的情形亦較其他方法嚴重。為因應實徵研究多以李克特式量尺資料題目進行分析之現狀，本模擬研究探討特徵值大於一於李克特式量尺資料的表現，提出該方法能建議合宜因素數目的情境，作為因素分析應用研究之參考。模擬資料為正交多因素模式，操弄因素負荷量、樣本人數、變項因素比、因素數目、量尺點數及分配型態。結果顯示，特徵值大於一於李克特式量尺資料之表現，主要受因素負荷量與樣本人數的影響，惜僅當因素負荷量高且樣本人數大時，方能建議合宜的因素數目。此結果除表示研究者應謹慎使用特徵值大於一決定因素數目外，更重要的，基於此方法之常用率，本研究之發現亦提醒研究者或許需要重新檢視以往因素分析研究結果之合宜性；尤其是對過去單以特徵值大於一決定因素數目所得到的因素結構，研究者或宜再次確認之前的結論是否合宜，以提升研究結論的適當性。

The eigenvalue-greater-than-one rule， also known as the Kaiser-Guttman rule， is widely used in factor analysis to determine the number of factors. Because the most frequently seen factor analysis involves item level data measured by Likert-type scales， a thorough evaluation of the performance of this rule with Likert-type data is called for. The presentsimulation therefore manipulated factor loading， sample size， number of factors， variableto-factor ratio， number of response categories on the Likert-type scales， and distribution of the Likert-type variables to examine the behavior of this popular method when using Likert-type data. The results indicated that the size of major factor loading and sample size played the most significant roles in affecting the behavior of the method. Unless high factor loadings and large sample sizes were utilized， the method failed to detect the correct number of factors. The findings of this study suggest that the eigenvalue-greater-than-one ruleshould be used with care. Moreover， considering its widespread use， there is a need for researchers to reexamine past factor analysis research results， especially those that solely employed the eigenvalue-greater-than-one rule to determine the number of factors.