因素分析的故事：源起與國內應用現況

Stories of Factor Analysis: Origins and Current Practices in Taiwan

因素分析源起於120年前Spearman（1904）對智力之研究，期能以數學模型描繪智力的理論。隨著心理學家對智力本質展開長年的探討，因素分析的發展亦深受智力理論之演變所影響。本文首先回顧因素分析與相關智力理論的早期歷史，講述二者間的關係。經過百餘年的發展，學者對如何進行因素分析漸次形成共識，本文接續討論目前因素分析的主要步驟以及建議作法，並回顧國內因素分析之使用現況。回顧結果發現研究者常以學者未推薦之特徵值大於一的個數與主成分法決定因素數目及估計初始因素負荷量，轉軸則多以斜交為主，且有超過五分之一的分析未清楚說明各步驟之作法。本文最後綜整研究者在呈現因素分析結果與規劃因素分析研究設計時宜注意之處，希望能協助未來研究者適當運用此方法。回溯因素分析的初衷，乃為探究智力理論並以數學模式回應之，此與Thurstone（1937）在心理計量學會創立之初倡議以數學模型表徵心理學現象不謀而合，Spearman於其前30年即展現了一個極佳的典範。誠如Thurstone所言，扎實的心理學理論絕非僅依靠巧妙的實驗儀器或數學即可建立，而是要能夠經得起時間的洗鍊與檢驗。最終，我們宜回頭審視運用因素分析所呈現的潛在因素是否經得起時間的考驗，並得以增進對人類心智與行為的了解。

Spearman (1904) presented factor analysis more than 120 years ago to formulate the theory of intelligence with a mathematical model. With psychologists’interest and exploration of the nature of intelligence over time, the evolution of theories of intelligence has greatly impacted the development of factor analysis. We first review the interplay between early advancement of factor analysis and related theories of intelligence. After the progression of factor analysis for more than a century, methodologists have gradually reached a consensus on the implementation of this popular method. The recommended practices of factor analysis are then presented followed by a review of its current applications in Taiwan. Our review indicated that researchers frequently used the unrecommended eigenvalue-greater-than-one rule to determine the number of factors, the unrecommended principal component method to estimate initial factor loadings, and oblique rotation. In addition, more than one fifth of the analyses failed to report the methods adopted during the analysis. We therefore further summarize the reporting practices suggested for factor analysis along with considerations in designing factor analysis research to assist future researchers in properly applying this method. Factor analysis was originally proposed as a mathematical model to depict theories of intelligence. Spearman’s use of mathematical models to represent psychological phenomena is exactly the focus of Thurstone’s (1937) advocacy at the founding of the Psychometric Society thirty years later. As noted by Thurstone, a solid psychological theory may not be established simply because ingenious experimental apparatus or clever mathematics is employed; it must stand the test of time. Ultimately, we should reflect on whether the latent factors identified through factor analysis have withstood the test of time and have enhanced our understanding of human mind and behavior.