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題 名 | On Factor Model of Multivariate Statistical Analysis=談多變量統計分析中的因子模式 |
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作 者 | 陳榮治; | 書刊名 | 嘉義技術學院學報 |
卷 期 | 67 1999.12[民88.12] |
頁 次 | 頁127-164 |
分類號 | 518 |
關鍵詞 | 因子; 載分量; 共通數; 主要分量法; 最大概似法; 因子旋轉與因子分數; Factor; Loading; Community; Principal component method; Maximum likelihood method; Factor rotation; Factor score; |
語 文 | 英文(English) |
中文摘要 | 因子分析在多變量統計分析中,是頗受歡迎的方法,其本質上的目的,是想藉助於少數幾個觀察不到的隨機因子,來描述一些吾人所接觸到的變數之間彼此共變數關係。我們希望能找出幾個潛伏的重要因子,最終目的是使所搜集到的資料能夠簡化,並進一步易於對所含的資料作出解釋。本文重點著眼於因子模式X - u = LF + ε中的參數估計及相關影響。為清楚整個分析過程,我們用一個實例來仔細分析,分別用主要分量法(pca)及最大概似法(mlfa),對於因子數目m = 2 及m = 3,依未經旋轉及經過旋轉,分別進行估計,並得到各參數估計值,及有關的係數等,如各誤差項,各特徵值,以及各殘餘矩陣。這些均是我們最終決定選取重要因子數目m = 3的有用依據。最後,我們也作出各卡方圖形,以便檢視常態性。另外,並分別作出各因子分數的圖形,從而偵測可能奇異點與瞭解一致性。 |
英文摘要 | Factor analysis is one of the most useful statistical methods for disovering or examining the latent measurement structure. It can extract the information from the correlations between the observed indicator variables to identify the latent variables of interest. In this paper, our interest is centered on the parameters of the factor model and the associated effects. For the sake of practice, one numerical example is carefully demonstrated, first, we use both of the most popular methods of parameter estimation--the principal component method and the maximum likelihood method. Moreover, we also try to find some clues to choose appropriate m, the number of common factors. We can compare the results of given example for m=2 and m=3 respectively, hopefully, all variables within a particular group are highly correlated but they have relatively small correlation with variables in a different group. In fact, our ideal objectives include data reduction and easily interpretaton. Basically, we can view factor approach as attempt to approximate the covariance matrix Σ, and we are also concerned whether the data are consistent with a prescribed structure. |
本系統中英文摘要資訊取自各篇刊載內容。