同時轉軸的探索性二階因素分析

One-stage Rotation Method For Second-order Factor Analysis

謝幸娟(Hsieh, Hsingchuan)

指導教授 ： 鄭中平 ； 蘇雅蕙

國立中正大學/社會科學院/心理學系/碩士(2012年)

摘要

傳統處理探索性二階因素分析時，先藉由斜交轉軸來得到一階的因子，估計一階樣式矩陣，再將這些因子視為新觀察變項抽出二階因子，估計二階樣式矩陣。上述的二階段方法有可能會造成問題，因為二階因子是被一階因子與其樣式矩陣所決定的，當一階因子抽取有誤，二階因子抽取也就可能不合適。
　　一個較好的方法是，在估計一階因子的同時，即能考慮到其對二階因子的影響。因此研究目的就是發展一次抽取出兩階因子的技術(即同時轉軸)；技術上來說，我們開發了一個可以同時評估一階與二階樣式矩陣的轉軸法，而此方法也把估計過程縮減為一階段方法。最後再以模擬與真實資料來呈現其效果。
　　為了測試本研究開發的一階段方法之效能，我們進行不同情境的模擬實驗 (分別為情境CS、SC及SS)並分析一筆真實資料，最後比較一階段與二階段方法的結果差異。模擬結果顯示，我們的一階段方法在一階樣式矩陣的型態為複雜時，結果表現最好；然而當二階樣式矩陣的型態為複雜時，表現最差。
　　在未來研究上，尚有其他的不同定義的轉軸法(本研究只藉用一種轉軸法)能夠應用於我們的一階段方法。此外，本研究皆假設一階與二階因子的數目為已知，但在很多情境下此假設並不為真，因此，在未來研究上，開發一個能夠正確決定兩階因子數目的技術仍是必要的。

關鍵字

因素分析 ； 斜交轉軸 ； 梯度投影算則

並列摘要

Traditionally, in second-order factor analysis, the first-order factors are extracted and such factors are subsequently regarded as new observed variables so second- order factors are extracted. Since the second-order factors are determined by the first-order ones, the conventional two-staged method will cause problems if the preselection for the first-order factors is inappropriate.
An intuitive way to solve the problem is, when extracting the first-order factors, to evaluate its effect upon the second -order ones. Specifically, we’d like to define a new rotation criterion to assess the performance for both pattern matrices simultaneously. Such estimation process is hence reduced to a one-staged method.
To testify the efficiency of such criterion, we analyzed three simulated and one real datasets, then compared the results between the two-staged and one-staged methods. The results showed that the proposed method performed better when the first-order pattern matrix is complex but worse when so is the second-order pattern matrix. The proposed method can also apply to other rotation criteria. Besides, assumption about the correct numbers of first- and second-order factors is not always the case. A future research for determining the numbers of these factors is needed.

並列關鍵字

factor analysis ； oblique rotation ； gradient-projection algorithm

參考文獻

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