Compositional data analysis in the study of carcass composition of beef cattle

Allometric regression (AR) has been widely used to model changes in the body composition of animals. However, predicted body component proportions based on AR equations do not necessarily sum to 1 and this discrepancy is confounded with treatment effects on components of the composition. Predicted component proportions are not bounded to lie between 0 and 1. An alternative method, compositional data analysis (CDA), which avoids these difficulties is proposed for beef carcass dissection data. For a composition consisting of D components (e.g. muscle, fat and bone) a new set of D 2 1 variables is created based on the logarithm of the ratios of components to one of the components (e.g. log(muscle / bone) and log(fat /bone)). Any statistical analysis can be applied on this scale, subject to the assumptions for that method of analysis being true. Regression models with simple interpretations in terms of animal development can be fitted to these logratio variables. Some inferences and interpretations are best made on the scale of component proportions. Predictions made from the models on the logratio scale may be back-transformed to give compositions on the proportional scale which obey the constraints that the component proportions sum to 1 and individually cannot exceed 1. The method generalises readily to multiple regression models involving factors and variables. CDA provides a fully multivariate framework for dealing with carcass dissection data within which questions on the effects of treatments and covariates on component composition and the differences between components can be addressed. It is a more natural vehicle than AR for analysing part–part relationships as it respects the symmetry between the components being compared. A simple relationship between CDA and AR models is developed.  2001 Elsevier Science B.V. All rights reserved.