Statistical Modelling 5 (2005), 173–185
The role of perturbation in compositional data analysis
J. Aitchison
Rosemount, Carrick Castle,
Lochgoilhead, Argyll, PA24 8AF
UK
eMail:
john.aitchison@btinternet.com
K.W. Ng
Department of Statistics and Actuarial Science
University of Hong Kong
China
Abstract:
In standard multivariate statistical analysis, common hypotheses of interest
concern changes in mean vectors and subvectors. In compositional data
analysis it is now well established that compositional change is most
readily described in terms of the simplicial operation of perturbation
and that subcompositions replace the marginal concept of subvectors.
Against the background of two motivating experimental studies in the
food industry, involving the compositions of cow's milk and chicken
carcasses, this paper emphasizes the importance of recognizing this
fundamental operation of change in the associated simplex sample space.
Well-defined hypotheses about the nature of any compositional effect can
be expressed, for example, in terms of perturbation values and
subcompositional stability and testing procedures developed. These
procedures are applied to lattices of such hypotheses in the two
practical situations. We identify the two problems as being the
counterpart of the analysis of paired comparison or split plot
experiments and of separate sample comparative experiments in the
jargon of standard multivariate analysis.
Keywords:
COMPOSITIONAL PAIRED COMPARISONS; GROUP OPERATIONS IN THE SIMPLEX;
LOGISTIC-NORMAL DISTRIBUTIONS; SUBCOMPOSITIONAL STABILITY
Downloads:
Example
data as text file
back