臺灣博碩士論文加值系統

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.

第一章 緒論 1
第一節 前言 1
第二節 因素分析的基本模式 3
第三節 特徵值大於一的理論基礎與發展 5
第四節 特徵值大於一方法的理論評論 7
第五節 影響特徵值大於一的因素 18
第二章 研究方法 26
第一節 研究變項 26
第二節 模擬資料產生歷程 30
第三節 資料分析 31
第三章 研究結果 33
第一節 模擬資料之特性 33
第二節 特徵值大於一之正確率 34
第四章 結論與討論 49
第一節 各研究變項對特徵值大於一之影響 49
第二節 建議 56
第三節 研究限制及未來研究方向 58
參考文獻 60
附錄 65
附錄A 斜交因素模式對應正交因素模式之因素負荷量 65
附錄B 模擬資料之分配 70
附錄C 特徵值大於一高估與低估因素數目之百分比 82
附錄D 不同因素負荷量下特徵值大於一決定因素數目之正確率
88
附錄E 母群特徵值與樣本特徵值之平均數與標準誤 91

圖目錄

圖一 變項因素比為4之三因素模型 29
圖二 因素模式複雜度與變項因素比之交互作用 38
圖三 因素負荷量與變項因素比之交互作用 39
圖四 樣本人數與因素負荷量之交互作用 41


表目錄

表一 本研究之研究變項與操弄情境 30
表二 各模式中觀察變項之四基本統計量的平均數與標準誤之範圍
34
表三 各模式中特徵值大於一正確率之五因子變異數分析表 36
表四 特徵值大於一於模式一至三中各研究變項操弄情境之正確率
37
表五 因素負荷量為.4時特徵值大於一正確決定因素數目之百分比
46
表六 因素負荷量為.6時特徵值大於一正確決定因素數目之百分比
47
表七 因素負荷量為.8時特徵值大於一正確決定因素數目之百分比
48

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