Abstract #300695

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JSM 2003 Abstract #300695
Activity Number: 81
Type: Contributed
Date/Time: Monday, August 4, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics & the Environment
Abstract - #300695
Title: Random Effects Graphical Models and the Analysis of Compositional Data
Author(s): Devin S. Johnson*+ and Jennifer A. Hoeting
Companies: Colorado State University and Colorado State University
Address: Department of Statistics, Fort Collins, CO, 80523-0001,
Keywords: compositional data ; hierachical models ; graphical models ; MCMC ; log-linear models ; stream invertebrates
Abstract:

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 stream invertebrate functional groups.

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