Visualizing Class Specific Heterogeneous Tendencies in Categorical Data

In multiple correspondence analysis, both individuals (observations) and categories can be represented in a biplot that jointly depicts the relationships across categories and individuals, as well as the associations between them. Additional information about the individuals can enhance interpretation capacities, such as by including class information for which the interdependencies are not of immediate concern, but that facilitate the interpretation of the plot with respect to relationships between individuals and categories. This article proposes a new method which we call multiple-class cluster correspondence analysis that identifies clusters specific to classes. The proposed method can construct a biplot that depicts heterogeneous tendencies of individual members, as well as their relationships with the original categorical variables. A simulation study to investigate the performance of the proposed method and an application to data regarding road accidents in the United Kingdom confirms the viability of this approach. Supplementary materials for this article are available online.

在多重对应分析（multiple correspondence analysis）中，个体（观测样本）与类别均可被绘制于双标图（biplot）之中，该图可联合呈现类别间、个体间的关联，以及二者之间的联系。关于个体的额外信息可提升该分析的解读能力——例如纳入类别归属信息，尽管此类信息的相互依存关系并非当前关注的核心，却有助于基于个体与类别间的关联对双标图进行解读。本文提出一种新方法，我们将其命名为多类聚类对应分析（multiple-class cluster correspondence analysis），该方法可识别针对类别的聚类。所提方法能够构建双标图，用以呈现个体成员的异质性趋势，以及它们与原始分类变量之间的关联。通过模拟研究验证所提方法的性能，并将其应用于英国道路交通事故数据集，结果证实了该方法的可行性。本文的补充材料可在线获取。