複選式類別資料的對應分析之探討

An Application of Correspondence Analysis for Multiple Response Categorical Data

會薰瑤(Shun-Yao Tseng)

《調查研究-方法與應用》 17期 (2005/04) Pp. 175-201

https://doi.org/10.7014/TCYCFFYYY.200504.0175

摘要

本論文嘗試應用類別資料的專屬分析手法：「對應分析（Correspondence Analysis; 簡稱CA）」，以及搭配資料縮減技巧的集群分析來處理複選式類別資料，並且以縮減空間的圖形表達方式解析多變數種選類別資料之間的關係。研究中將以實證說明資料處理的過程，研究設計包含兩部份，其一爲：當複選類別項自衆多、資料矩陣龐大且雜亂無章時，搭配應用對應分析和K-means集群分析的量化與分類之特色，在不漏失資料的情況下進行複選變項縮減的工作；其二爲：應用”CA of concatenated tables”方法的「壓縮(condense)」概念，將多變數複選類別項之間的關聯性壓縮成一張聯合CA圖來解說之，此外並且在聯合CA圖中藉由適當輔助線的加入來描述不同變數的影響力強度。實證分析部份，是以學生性格特質、主修科系與職業期待的關聯性研究爲例，資料分析結果顯示：首先將受訪學生依31項複選性格特質在解釋力爲100%的30維CA空間中，不漏失資訊地縮減區隔分類爲六群組，之後再藉由加入補助線說明的CA二維平面圖表達三變數間的關係結構，則同時清晰地顯示出受訪學生在選擇未來職業類別方面，除了與學生本身的性格特質相呼應之外，同時明顯地受到外在主修藝科系的影響。

關鍵字

複選式類別資料 ； 集群分析 ； 對應分析

並列摘要

A real-world example is used to illustrate how reduced-space approach is used to analyze multiple-response-categorical-data. When the data matrix is large and amorphous, we provide a two-part statistical analysis approach. First, a c1assification is performed by complementary use of CA and K-means c1uster analysis in the full-dimensional space without losing information. Then, a reduced space that condenses the results of CA maps by the ”CA of concatenated tables” is used to show the relationships between all multi-variable categories.
Using data from a study on the relationship between students' characters, their majors and their future careers. Multiple selections were permitted from 31 categories of a student character survey (313 students). Respondents were c1ustered into 6 distinct character segments by K-means c1uster analysis based on their coordinates in the full-information-used space (i.e., 30-dimension CA space) which accounts for 100% of the total variance. Then a reduced-space was used to reveal simultaneously the relationship between 'character', 'major' and 'future career'. The result shows that the students' careers are influenced by their character and major, especially the latter.

並列關鍵字

Multiple-Response-Categorical-Data ； Correspondence Analysis ； Cluster Analysis

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