圖示量化屬性資料之對應－－集群分析的應用：以學生性格特質、主修科系與職業期待的關聯性研究為例

Graphing and Quantifying Qualitative Data by Correspondence--Cluster Analysis：A study on the relationship among a student’s characters, major and future career

本研究嘗試應用一專門處理多變量類別資料的探索資料分析技巧：「對應分析（Correspondence Analysis, 簡稱CA）」，以有效的縮減空間之圖形表達方式深入地分析、描述多變數多類別之間的相互關聯性，並藉由兩實例說明之。論文中的特色有三；（1）在資料蒐集方面：提出以較普遍、簡易且使受訪者回答意願較強的複選式類別資料勾選的調查方式蒐集到不失詳細且較真確的資料；（2）在資料分析方面：藉著交互應用對應分析與集群分析的優點及特色，克服了以往只能簡單分析多變量類別資料等的限制，而充分、完整地量化類別資料的特質及其關係結構；（3）在結果解說方面：以簡單、清晰、最為大眾接受的適切圖形解說結果。實証分析結果，實例1.搭配應用CA 與K-means 集群分析的特色，提出一種與以往不同的學生性格特質區隔分群過程，不但能將受訪學生依據其所選擇性格類別項目上的異同在不漏失資料的情況下區隔分群，並將所得群組與被選擇的類別項目等之間、之內的關係以CA 圖形方式描述之，同時使用階層集群技巧中的連結關係增加了CA 二維平面圖的解析力。實例 2.提出以一張高解釋力的圖形： ”correspondence-cluster dendrogram” 來同時、完整地描述包括學生性格特質、專業教育與職業期待等多變數眾多類別彼此之間的關聯性，此結果能為未來各科系的經營與教育方向提供更科學、明確及清晰的參考資訊。

In social science research, it is important to collect categorical survey data and interpret relationships among the qualitative variables. For example, the image studies revealing the relationships between and within bands and attributes, or a study on the relationship between students’ characters, their majors and their future careers. Correspondence analysis (CA) is an exploratory data analysis technique for the graphical display of multivariate categorical data (Hoffman & Franke, 1986). When complex multivariate relationships are examined, it often occurs that the results of CA are too complex to be easily read. This situation can be improved with the help of clustering techniques. The purpose of this study is that from the point of data collection, we provide a way of using a multiple-response-categorical-data survey instrument. It is more popular, simpler, and the interviewees find it easier to answer. From the point of data analysis, we provide a method that analyzes qualitative data completely by complementary use of CA and cluster analysis and so, the optimal graphical representation can then be used to reveal the structure in the data clearly. Two examples illustrate how complementary use of correspondence analysis and cluster analysis can provide the graphical display of multivariable categorical survey data. The first example shows how to use the pick-any method to data collection, that is: multiple selections were permitted from 31 categories of a student character survey (313 students). Respondents were clustered into 6 distinct character segments by K-means cluster 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. The result shows that the cluster dendrogram is successfully used in CA map to remedy the distortion of distances due to the planar approximation of this map, which was also found in Lebart (1994). The second example shows to combine the advantages of correspondence analysis and cluster analysis to reduce the two CA maps to just one, named correspondence-cluster dendrogram (Hi, Zhu & Wu, 1995). One of the CA maps is the joint display of ‘major’ and ‘future career’. The other one is the joint display of ‘character’ and ‘future career’. The correspondence-cluster dendrogram which accounts for a high degree of the total variance shows all the relationships that exist within and between the three variables (character, major, and future career). The result shows that the students’ future careers are influenced by their character and major, especially the latter. For example, the group, with its significant characteristics, includes students with ‘optimism’ and ‘self-esteem‘ on the student’s character profile. They are divided into two subgroups: the students who major in hospitality and tourism management are in favor of a hospitality-related career, and the students who major in business administration are in favor of a marketing-related career. Both subgroups are also in favor of the travel industry. Overall, qualitative data are common products of social science research. As the study presents it, the multiple-response categorical scale is easier and less demanding for the respondent. Sometimes, the interviewees are more willing to answer when there are large numbers of attribute categories being measured, which coincides with the findings of Arimond & Elfessi (2001). Complementary use of correspondence analysis and cluster analysis is highly recommended for useful and reduced special representation of multivariate categorical data. For the first example, correspondence analysis and K-means cluster analysis can be used in tandem to provide a category map and a student-character-segmentation process without losing information. The combined use of hierarchical grouping techniques and correspondence analysis can improve the understanding of the data. The second example provides an output of the method: named correspondence-cluster dendrogram, which shows simultaneously and clearly the relationships between all multi-variable categories. Furthermore, the examples provide a clearer and more reliable reference for education improvement.