


Models for the Analysis of Discrete Compositional
Data:
An Application of Random Effects Graphical Models 
Devin
Johnson
Department of Statistics
Colorado State University
Friday, 01 August 2003
3:00 PM
E202 Engineering Building
ABSTRACT
Compositional data are multivariate observations subject to
the constraints that the vector elements are nonnegative and
sum to one. Current models for compositional data are
undefined when there are elements of an observation with a value
of zero. This can occur frequently when compositions are constructed
from count data. A statespace model has been proposed in the
past to alleviate this problem. However, the model is limited
to the analysis of one categorical variable at a time. Conversely,
graphical loglinear models have been used for many years
to model cell probabilities for multiway contingency tables.
These models, however, are limited to one sample, or one observation
in the case of compositional analysis. Using a Bayesian hierarchical
model, the class of graphical models can be expanded to
include the analysis of compositional data. In addition, this
hierarchical graphical model allows parsimonious modeling of
multiway compositions, by providing a cell independence structure
which holds with probability 1 for all compositional observations.
Use of this model is demonstrated with compositional data
on fish species richness. Functional group composition at each
sampled stream site is modeled with several local and
watershed covariates. A graphical model is constructed to illustrate
the dependence relationships between these environmental variables
and fish species richness in two categorical traits.
Key Words:
Compositional data, Bayesian hierarchical model, graphical models, MCMC,
species richness.


