Homogeneity pursuit and variable selection in regression models for multivariate abundance data.

When building regression models for multivariate abundance data in ecology, it is important to allow for the fact that the species are correlated with each other. Moreover, there is often evidence species exhibit some degree of homogeneity in their responses to each environmental predictor, and that most species are informed by only a subset of predictors. We propose a generalized estimating equation (GEE) approach for simultaneous homogeneity pursuit (ie, grouping species with similar coefficient values while allowing differing groups for different covariates) and variable selection in regression models for multivariate abundance data. Using GEEs allows us to straightforwardly account for between-response correlations through a (reduced-rank) working correlation matrix. We augment the GEE with both adaptive fused lasso- and adaptive lasso-type penalties, which aim to cluster the species-specific coefficients within each covariate and encourage differing levels of sparsity across the covariates, respectively. Numerical studies demonstrate the strong finite sample performance of the proposed method relative to several existing approaches for modeling multivariate abundance data. Applying the proposed method to presence-absence records collected along the Great Barrier Reef in Australia reveals both a substantial degree of homogeneity and sparsity in species-environmental relationships. We show this leads to a more parsimonious model for understanding the environmental drivers of seabed biodiversity, and results in stronger out-of-sample predictive performance relative to methods that do not accommodate such features.

The use of generalized linear mixed models to investigate postmortem lipids in textiles.

Human remains are oftentimes located with textile materials, making them a ubiquitous source of physical evidence. Human remains are also frequently discovered in outdoor environments, increasing the exposure to scavenging activity and soft-tissue decomposition. In such cases, postmortem interval (PMI) estimations can be challenging for investigators when attempting to use traditional methods for reconstructive purposes. Lipid analysis is an emerging area of research in forensic taphonomy, with recent works demonstrating success with the detection and monitoring of lipids over time. In this work, generalized linear mixed models (GLMMs) were utilized to perform rigorous statistical analyses on 30 lipid outcomes in combination with accumulated-degree-days (ADD). The results of this study were consistent with recent works, indicating oleic and palmitic acids to be the most suitable lipids in textiles to target for future use as soft-tissue biomarkers of human decomposition. Interspecies differences between humans and pigs were also addressed in this work.