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Compositional data analysis tutorial.
Psychological Methods  (IF10.929),  Pub Date : 2022-01-31, DOI: 10.1037/met0000464
Michael Smithson, Stephen B. Broomell

This article presents techniques for dealing with a form of dependency in data arising when numerical data sum to a constant for individual cases, that is, “compositional” or “ipsative” data. Examples are percentages that sum to 100, and hours in a day that sum to 24. Ipsative scales fell out of fashion in psychology during the 1960s and 1970s due to a lack of methods for analyzing them. However, ipsative scales have merits, and compositional data commonly occur in psychological research. Moreover, as we demonstrate, sometimes converting data to a compositional form yields insights not otherwise accessible. Fortunately, there are sound methods for analyzing compositional data. We seek to enable researchers to analyze compositional data by presenting appropriate techniques and illustrating their application to real data. First, we elaborate the technical details of compositional data and discuss both established and new approaches to their analysis. We then present applications of these methods to real social science data-sets (data and code using R are available in a supplementary document). We conclude with a discussion of the state of the art in compositional data analysis and remaining unsolved problems. A brief guide to available software resources is provided in the first section of the supplementary document.