Using standard financial ratios as variables in statistical analyses has been related to several serious problems, such as extreme outliers, asymmetry, non-normality, and non-linearity. The compositional-data methodology has been successfully applied to solve these problems and has always yielded substantially different results when compared to standard financial ratios. An under-researched area is the use of financial log-ratios computed with the compositional-data methodology to predict bankruptcy or the related terms of business default, insolvency or failure. Another under-researched area is the use of machine learning methods in combination with compositional log-ratios. The present article adapts the classical Altman bankruptcy prediction model and some of its extensions to the compositional methodology with pairwise log-ratios and three common statistical and machine learning tools: logistic regression models, k-nearest neighbours, and random forests, and compares the results with standard financial ratios. Data from the sector in the Spanish economy with the largest number of bankrupt firms according to the first two digits of the NACE code (46XX "wholesale trade, except of motor vehicles and motorcycles") were obtained from the Iberian Balance sheet Analysis System. The sample size (31,131 firms, of which 97 were bankrupt) was divided into a training and a validation dataset. The training data set was downsampled to one healthy firm to each bankrupt firm. No outliers were removed. Focusing on predictive performance, the results show that compositional methods are better than standard ratios in terms of sensitivity, with mixed results regarding specificity, compositional random forests and compositional logistic regression behaving the best.

翻译：在统计分析中使用标准财务比率作为变量已引发若干严重问题，例如极端异常值、不对称性、非正态性和非线性。成分数据方法论已成功应用于解决这些问题，并且与标准财务比率相比，始终得出显著不同的结果。一个研究不足的领域是使用基于成分数据方法论计算的财务对数比率来预测破产或相关的商业违约、资不抵债或失败术语。另一个研究不足的领域是将机器学习方法与成分对数比率结合使用。本文通过成对对数比率以及三种常见的统计和机器学习工具（逻辑回归模型、k近邻和随机森林），将经典的Altman破产预测模型及其部分扩展适应于成分方法论，并将结果与标准财务比率进行比较。根据NACE代码前两位（46XX“批发贸易，除机动车和摩托车外”）对应西班牙经济中破产企业数量最多的行业数据，从伊比利亚资产负债表分析系统中获取样本。样本量（31,131家企业，其中97家破产）被分为训练集和验证集。训练集通过下采样使每家企业对应一家破产企业。未移除任何异常值。聚焦于预测性能，结果表明成分方法在敏感性方面优于标准比率，在特异性方面结果不一，其中成分随机森林和成分逻辑回归表现最佳。