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Analysis of a European Union election using principal component analysis. (Analysis of an European Union election using principal component analysis.) (English) Zbl 1247.91053
Summary: While studying the results from one European Parliament election, the question of principal component analysis (PCA) suitability for this kind of data was raised. Since multiparty data should be seen as compositional data (CD), the application of PCA is inadvisable and may conduct to ineligible results. This work points out the limitations of PCA to CD and presents a practical application to the results from the European Parliament election in 2004. We present a comparative study between the results of PCA, Crude PCA and Logcontrast PCA (cf., e.g., [J. Aitchison, Biometrika 70, 57–65 (1983; Zbl 0515.62057)]). As a conclusion of this study, and concerning the mentioned data set, the approach which produced clearer results was the Logcontrast PCA. Moreover, Crude PCA conducted to misleading results since nonlinear relations were presented between variables and the linear PCA proved, once again, to be inappropriate to analyse data which can be seen as CD.

MSC:
91B12 Voting theory
62H25 Factor analysis and principal components; correspondence analysis
62P25 Applications of statistics to social sciences
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