Detecting outlying variables in multigroup data: A comparison of different loading similarity coefficients. (20th March 2020)

• Record Type: Journal Article
• Authors: Gvaladze, Sopiko; De Roover, Kim; Tuerlinckx, Francis; Ceulemans, Eva
• Other Names: Tauler Roma guestEditor.; Ruckebusch Cyril guestEditor.; Smilde Age guestEditor.
• Is Part Of: Journal of chemometrics. Volume 35:Number 2(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-03-20
• Subjects: component similarity -- multivariate multigroup data -- PCA -- SCA -- Tucker's congruence; Chemistry -- Mathematics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; 542.85
• DOI: 10.1002/cem.3233
• Languages: English
• ISSNs: 0886-9383

Abstract

Abstract: Multivariate multigroup data are collected in many fields of science, where the so‐called groups pertain to, for instance, experimental groups or countries the participants are nested in. To summarize the main information in such data, principal component analysis (PCA) is highly popular. PCA reduces the variables to a few components that are linear combinations of the original variables. Researchers usually assume those components to be the same across the groups and aim to apply a simultaneous component analysis. To investigate whether this assumption is reasonable, one often analyzes the groups separately and computes a similarity index between the group‐specific component loadings of the variables. In many cases, however, most variables have highly similar loadings across the groups, but a few variables, which we will call "outlying variables, " behave differently, indicating that a simultaneous analysis is not warranted. In such cases, the outlying variables should be removed before proceeding with the simultaneous analysis. To do so, the variables are ranked according to their relative outlyingness. Although some procedures have been proposed that yield such an outlyingness ranking, they might not be optimal, because they all rely on the same choice of similarity coefficient without evaluating other alternatives. In this paper, we give an overview of other options and report extensive simulations in which we investigate how this choice affects the correctness of the outlyingness ranking. We also illustrate the added value of the outlying variable approach by means of sensometric data on different bread samples. Abstract : We start by elucidating that the assumption underlying simultaneous component analysis—component loadings are the same across the groups—is often too strict. We introduce a recent psychometric method for outlying variable detection that aims to detect the source of the discrepancy, by pinpointing outlying variables. We investigate different similarity measures and how they perform in regard to outlying variable detection.