Regression Tree and Clustering for Distributions, and Homogeneous Structure of Population Characteristics

Scientists often collect samples on characteristics of different observation units and wonder whether those characteristics have similar distributional structure. We consider methods to find homogeneous subpopulations in a multidimensional space using regression tree and clustering methods for distributions of a population characteristic. We present a new methodology to estimate a standardized measure of distance between clusters of distributions and for hierarchical testing to find the minimal homogeneous or near-homogeneous tree structure. In addition, we introduce hierarchical clustering with adjacency constraints, which is useful for clustering georeferenced distributions. We conduct simulation studies to compare clustering performance with three measures: Modified Jensen–Shannon divergence (MJS), Earth Mover’s distance and Cramér–von Mises distance to validate the proposed testing procedure for homogeneity. As a motivational example, we introduce georeferenced yellowfin tuna fork length data collected from the catch of purse-seine vessels that operated in the eastern Pacific Ocean. Hierarchical clustering, with and without spatial adjacency constraints, and regression tree methods were applied to the density estimates of length. While the results from the two methods showed some similarities, hierarchical clustering with spatial adjacency produced a more flexible partition structure, without requiring additional covariate information. Clustering with MJS produced more stable results than clustering with the other measures.