Some Model-Based and Distance-Based Clustering Methods for Characterization of Regional Ecological Stressor-Response Patterns and Regional Environmental Quality Trends

We develop statistical methods for evaluation of regional variation of ecological stressor-response relationships, and regional variation in temporal profiles of water quality, for application to data from monitoring stations on bodies of water. To evaluate regional variation in regression relationships, we use model-based clustering procedures with class-specific regression models. Units for clustering are taken to be basins, or combinations of basins and ecoregions. We rely on a Bayesian formulation and sample the posterior distribution using a Markov chain Monte Carlo algorithm. Two general approaches to the label-switching problem are considered, each leading to procedures that we apply in data analyses. Two applications are presented. We explore some relationships among priors with a Dirichlet distribution for class probabilities. We compare two rank-based criteria for grouping stations according to similarities in temporal profiles. The two criteria are illustrated in a hierarchical cluster analysis based on measurements of a water quality variable.