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

Allometric regression (AR) has been widely used to model changes in the bod y composition of animals. However, predicted body component proportions bas ed on AR equations do not necessarily sum to 1 and this discrepancy is conf ounded with treatment effects on components of the composition. Predicted c omponent 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 - 1 variables i s 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 analy sis can be applied on this scale, subject to the assumptions for that metho d 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 pro portions. Predictions made from the models on the logratio scale may be bac k-transformed to give compositions on the proportional scale which obey the constraints that the component proportions sum to I and individually canno t exceed 1. The method generalises readily to multiple regression models in volving factors and variables. CDA provides a fully multivariate framework for dealing with carcass dissection data within which questions on the effe cts of treatments and covariates on component composition and the differenc es between components can be addressed. It is a more natural vehicle than A R for analysing part-part relationships as it respects the symmetry between the components being compared. A simple relationship between CDA and AR mo dels is developed. (C) 2001 Elsevier Science B.V. All rights reserved.