Mar 7, 2014

General models for resource use or other compositional count data using the Dirichlet-multinomial distribution

Perry De Valpine, Alexandra N Harmon-Threatt


Many ecological studies investigate how organisms use resources, such as habitats or foods, in relation to availability or other variables. Related statistical problems include analysis of proportions of species or genotypes in a community or population. These require statistical modeling of compositional count data: data on relative proportions of each category collected as counts. Common methods for analyzing compositional count data lack one or more important considerations. Some methods lack explicit accommodation of count data, dealing instead with proportions. Others do not handle between-sample heterogeneity for overdispersed data. Yet others do not allow general types of relationships between explanatory variables and resource use. All three components have been combined in a Bayesian framework, but for frequentist hypothesis tests and AIC model selection, maximum-likelihood estimation is needed. Here we propose the Dirichlet-multinomial distribution to accommodate overdispersed compositional count data. This approach can be used flexibly in combination with explanatory models, but the only correlations among compositional proportions that it can accommodate are the negative correlations due to the fact that proportions...Continue Reading

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