Analysis of composition on the original scale of measurement

TL;DR

This paper proposes a direct statistical modeling approach for compositional data on the original measurement scale, offering advantages over traditional log-ratio methods, especially in handling zeros and interpretability.

Contribution

It introduces a variance-covariance function based on multiplicative errors and advocates for quasi-likelihood analysis as a robust alternative to log-ratio transformations.

Findings

Robustness to zero or near-zero measurements

More direct interpretation of compositional data

Applicability of quasi-likelihood methods to composition analysis

Abstract

In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for the arithmetic mean on the original scale of measurement. Central to the approach is a general variance-covariance function, derived by assuming multiplicative measurement error. Quasi-likelihood analysis of logit models for composition is then a general alternative to the use of multivariate linear models for log-ratio transformed measurements, and it has important advantages. These include robustness to secondary aspects of model specification, stability when there are zero-valued or near-zero measurements in the data, and more direct interpretation. The usual efficiency property of quasi-likelihood estimation applies even when the error covariance matrix is unspecified. We also indicate how the derived variance-covariance function can be used, instead of the variance-covariance matrix of log-ratios, with more general multivariate methods for the analysis of composition. A specific feature is that the notion of `null correlation' -- for compositional measurements on their original scale -- emerges naturally.