Brewer, M.J., Filipe, J.A.N., Elston, D.A., Dawson, L.A., Mayes, R.W., Soulsby, C. and Dunn, S.M.
Journal of Agricultural, Biological, and Environmental Statistics 10, 19-34.
compositional analysis, MCMC, chemical marker data
||This paper introduces a hierarchical model for the analysis of
compositional data. Our approach models both the source and
mixture data simultaneously, and accounts for several different
types of variation: these include measurement error on both the
mixture and source data; variability in the sample from the source
distributions; and variability in the mixing proportions
themselves, generally of main interest. The method is an
improvement on some existing methods in that estimates of mixing
proportions (including their interval estimates) are sure to lie
in the range [0,1]; in addition, it is shown that our model can
help in situations where identification of appropriate source data
is difficult, especially when we extend our model to include a
covariate. We first study the likelihood surface of a base model
for a simple example, and then include prior distributions to
create a Bayesian model which allows analysis of more complex
situations via Markov chain Monte Carlo sampling from the
likelihood. Application of the model is illustrated with two
examples using real data: one concerning chemical markers in
plants, and another on water quality.