Compositional Data Analysis

The use of financial and sustainability ratios to map a sector. An approach using compositional data ArXiv ID: 2509.06468 “View on arXiv” Authors: Elena Rondós-Casas, Germà Coenders, Miquel Carreras-Simó, Núria Arimany-Serrat Abstract Purpose: The article aims to visualise in a single graph fish and meat processing company groups in Spain with respect to long-term solvency, energy, waste and water intensity and gender employment gap. Design/methodology/approach: The selected financial, environmental and social indicators are ratios, which require specific statistical analysis methods to prevent severe skewness and outliers. We use the compositional data methodology and the principal-component analysis biplot. Findings: Fish-processing companies have more homogeneous financial, environmental and social performance than their meat-processing counterparts. Specific company groups in both sectors can be identified as poor performers in some of the indicators. Firms with higher solvency tend to be less efficient in energy and water use. Two clusters of company groups with similar performances are identified. Research limitations/implications: As of now, few firms publish reports according to the EU Corporate Sustainability Reporting Directive. In future research larger samples will be available. Social Implications: Firm groups can visually see their areas of improvement in their financial, environmental and social performance compared to their competitors in the sector. Originality/value: This is the first time in which visualization tools have combined financial, environmental and social indicators. All individual firms can be visually ordered along all indicators simultaneously. ...

Accounting statement analysis at industry level. A gentle introduction to the compositional approach ArXiv ID: 2305.16842 “View on arXiv” Authors: Unknown Abstract Compositional data are contemporarily defined as positive vectors, the ratios among whose elements are of interest to the researcher. Financial statement analysis by means of accounting ratios a.k.a. financial ratios fulfils this definition to the letter. Compositional data analysis solves the major problems in statistical analysis of standard financial ratios at industry level, such as skewness, non-normality, non-linearity, outliers, and dependence of the results on the choice of which accounting figure goes to the numerator and to the denominator of the ratio. Despite this, compositional applications to financial statement analysis are still rare. In this article, we present some transformations within compositional data analysis that are particularly useful for financial statement analysis. We show how to compute industry or sub-industry means of standard financial ratios from a compositional perspective by means of geometric means. We show how to visualise firms in an industry with a compositional principal-component-analysis biplot; how to classify them into homogeneous financial performance profiles with compositional cluster analysis; and how to introduce financial ratios as variables in a statistical model, for instance to relate financial performance and firm characteristics with compositional regression models. We show an application to the accounting statements of Spanish wineries using the decomposition of return on equity by means of DuPont analysis, and a step-by-step tutorial to the compositional freeware CoDaPack. ...