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Abstract: Compositional Data analysis (CoDa) is the standard statistical methodology when data contain information about the relative importance of parts of a whole. Many research questions in the field of management are either related to the distribution of a whole (e.g., market share, product or investment portfolios, family budgets, etc.), or to relative importance (e.g., financial ratios, relative prices, etc.). This paper presents the manner in which CoDa solves statistical problems that arise when treating compositional data with classical statistical methods (e.g., spurious correlations, meaningless distances, violation of statistical assumptions). It next presents three applications. The first concerns the evolution of tourist spending in Spain between 2006 and 2012 and constructs market segments on the basis of how tourists distribute their trip budget among transportation, accommodation & food, and activities. The second relates innovated product portfolios of firms to their open innovation and their marketing innovation activities. The third is an analysis of risk sources in an investment along time. In this case, we show that predictive models for compositional data improve those that work with non-compositional values. Some other case studies are briefly descried,

Keywords: Compositional data analysis, log-ratio methodology, market segmentation, tourist spending, cluster analysis, MANOVA, open innovation, risk allocation, time series

Short Bios: Germà Coenders Gallart received his PhD in Management Sciences at the Ramon Llull University in 1996 and is currently a Professor of Quantitative Methods for the Economy and Business in the Economics Department of the University of Girona. At this university, he belongs to the Research Group in Statistics, Econometrics and Health (GRECS), the Consolidated Research Group Compositional and Spatial Data Analysis-COSDA-(2014SGR551; 2017SGR656), and the Food and Gastronomy Campus. Currently his main research interest is the analysis of compositional data in economics and management, and has pioneered some applications in the field. He is a founding member of the Association for Compositional Data CoDa-Association.

Montserrat Guillén Estany is Professor of Quantitative Methods at UB and she is currently Honorary Visiting Professor in the Faculty of Actuarial Science and Insurance at City, University London. She is director of the Institute of Applied Economics and the Riskcenter research group. In 2018 she was an invited speaker at the Consortium for Data Analytics in Risk at the University of California, Berkeley. She is associate editor of the Journal of Risk and Insurance, a senior editor of Astin Bulletin – the official journal of the International Actuarial Association-, co-editor for the North American Actuarial Journal and editor of SORT-Statistics and Operations Research Transactions. She is the ranked the first woman in actuarial science by number of academic citations.