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

Compositional data are multivariate observations subject to the constraints that the vector elements are non-negative 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 state-space 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 log-linear 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.



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