A Finite Mixture Approach for Identification of Geographic Regions with Distinctive Ecological Stressor-Response Relationships

We study a model-based clustering procedure that aims to identify geographic regions with distinctive relationships among ecological and environmental variables. We use a finite mixture model with a distinct linear regression model for each mixture component, relating a measure of environmental quality to multiple regressors. Component-specific values of regression coefficients are allowed, for a common set of regressors. We implement Bayesian inference jointly for the true partition and component regression parameters. We assume a known, prior classification of measurement locations into “clustering units,” where measurement locations belong to the same mixture component if they belong to the same clustering unit. A Metropolis algorithm, derived from a well-known Gibbs sampler, is used to sample the posterior distribution. Our approach to the label switching problem relies on constraints on cluster membership, selected based on statistics and graphical displays that do not depend upon cluster indexing. Our approach is applied to data representing streams and rivers in the state of Ohio, equating clustering units to river basins. The results appear to be interpretable given geographic features of possible ecological significance.