Preserving correlation while modelling diameter distributions

Abstract

The construction of diameter-distribution models sometimes calls for the simultaneous prediction of population parameters from hierarchical data. Appropriate data for such models have characteristics that should be preserved or accommodated: clustering and contemporaneous correlations. Fitting techniques for such data must allow for these characteristics. Using a case study, I compare two techniques — seemingly-unrelated regression (SUR) and principal components analysis (PCA) — whilst using mixed-effects models. I adapt and apply a metric that focuses on volume prediction, which is a key application for diameter distributions. The results suggest that using mixed-effects models provides useful insights into environmental variation, and that SUR is more convenient and produces a slightly better fit than PCA. Both techniques are acceptable with regard to regression assumptions.