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.

在多重对应分析中，个体（观测值）与类别均可通过双图表示，该图共同描绘了类别与个体之间的相互关系，以及它们之间的关联。关于个体的额外信息可以增强解释能力，例如，通过包括那些虽然不直接关注其相互依赖性，但有助于对个体与类别之间关系进行解读的类别信息。本文提出了一种新的方法，我们称之为多重类别聚类对应分析，该方法能够识别特定于类别的聚类。所提出的方法可以构建一个双图，该图描绘了个体成员的异质趋势，以及它们与原始类别变量之间的关系。一项针对该方法性能的模拟研究以及对英国道路交通事故数据的实际应用证实了该方法的可行性。本文的补充材料可在网上获取。