Exploratory data structure comparisons: three new visual tools based on principal component analysis

J Appl Stat. 2020 May 27;48(9):1675-1695. doi: 10.1080/02664763.2020.1773772. eCollection 2021.

Abstract

Datasets are sometimes divided into distinct subsets, e.g. due to multi-center sampling, or to variations in instruments, questionnaire item ordering or mode of administration, and the data analyst then needs to assess whether a joint analysis is meaningful. The Principal Component Analysis-based Data Structure Comparisons (PCADSC) tools are three new non-parametric, visual diagnostic tools for investigating differences in structure for two subsets of a dataset through covariance matrix comparisons by use of principal component analysis. The PCADCS tools are demonstrated in a data example using European Social Survey data on psychological well-being in three countries, Denmark, Sweden, and Bulgaria. The data structures are found to be different in Denmark and Bulgaria, and thus a comparison of for example mean psychological well-being scores is not meaningful. However, when comparing Denmark and Sweden, very similar data structures, and thus comparable concepts of well-being, are found. Therefore, inter-country comparisons are warranted for these countries.

Keywords: 62H25; 62P15; Principal component analysis; covariance matrix; data structure; exploratory data analysis.