主成份分析和共同因素分析相關議題之探究

Issues Related to Principal Component Analysis and Common Factor Analysis

傅粹馨(Tsuey-Shing Fu)

《教育與社會研究》 3期 (2002/02) Pp. 107-131

https://doi.org/10.6429/FES.200202.0107

摘要

主成份分析與共同因素分析廣爲研究者所使用抽取因素的方法。主成份分析與共同因素分析是不同的。共同因素分析之目的在抽取因素來解釋變項間的關係，而主成份分析之目的在作變項的減縮。
本文探討八個主題：(1)緒論：(2)主成份分析之意義；(3)共同因素分析之意義；(4)主成份分析與共同因素分析之異同；(5)主成份分析與共同因素分析結果近似；(6)共同因素分析較主成份分析爲宜；(7)目前普遍使用之因素分析方法；(8)實例分析。
執行因素分析時宜瞭解研究之目的與決定抽取多少個因素是相當重要的，這些會影響因素的抽取與轉軸後的結果，研究者不能太依賴電腦提供之內設選項。

關鍵字

共同因素分析 ； 因素抽取 ； 主成份分析 ； 轉軸 ； 陡坡圖

並列摘要

The principal component analysis (PCA) and common factor analysis (CFA) are the most basic and frequently used factor analytic models. In fact, PCA and CFA are two different procedures. Their goals are also divergent. That is, CFA is used to extract as many factors as necessary to explain the correlations among the variables. On the other hand, PCA is meant to create summaries of variables.
This paper consists of eight main parts: (1) to introduce the purpose of this study; (2) to review the basic concepts of PCA; (3) to review the basic concepts of CFA; (4) to compare the characteristics of PCA and CFA; (5) to describe the similarity between PCA and CFA based on empirical researches; (6) to discuss the reason that CFA is more appropriate than PCA; (7) to present the common methods for using factor analysis; and (8) to display an example by using PCA and CFA.
The critical decisions in the selection of factor analysis are to understand the purpose of the study and to determine the number of factors to extract. The results of extraction and rotation are affected by these decisions. Users should not rely on the default options provided by computer programs.

並列關鍵字

common factor analysis ； factor extraction ； principal component analysis ； rotation ； scree plot

參考文獻

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Borgatta, E. F.,Kercher, K.,Stull, D. E.(1986).A cautionary note on the use of principal component analysis.Sociological Methods and Research.15(1-2),160-168.