  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.
