Generalized Linear Latent Variable Models for Multivariate Count and Biomass Data in Ecology

• Published in: Journal of agricultural, biological, and environmental statistics Vol. 22; no. 4; pp. 498 - 522
• Main Authors: Niku, Jenni, Warton, David I., Hui, Francis K. C., Taskinen, Sara
• Format: Journal Article
• Language: English
• Published: New York Springer 01.12.2017; Springer US; Springer Nature B.V
• Subjects: Agriculture; Analysis; Approximation; Approximation method; Arctic region; Bacteria; Biomass; Biostatistics; Computer simulation; Coral reef ecosystems; Coral reefs; data collection; Ecological monitoring; Ecological studies; Economic models; environmental factors; Estimates; Europe; Health Sciences; Inference; linear models; Mathematics and Statistics; Medicine; Modelling; Monitoring/Environmental Analysis; Multivariate analysis; Ordination; ordination techniques; Reefs; Species; Statistics; Statistics for Life Sciences; Arctic region; Europe; Biomass; Overdispersed count; Species interactions; Ordination; Laplace approximation
• DOI: 10.1007/s13253-017-0304-7
• ISSN: 1085-7117

In this paper we consider generalized linear latent variable models that can handle overdispersed counts and continuous but non-negative data. Such data are common in ecological studies when modelling multivariate abundances or biomass. By extending the standard generalized linear modelling framework to include latent variables, we can account for any covariation between species not accounted for by the predictors, notably species interactions and correlations driven by missing covariates. We show how estimation and inference for the considered models can be performed efficiently using the Laplace approximation method and use simulations to study the finite-sample properties of the resulting estimates. In the overdispersed count data case, the Laplace-approximated estimates perform similarly to the estimates based on variational approximation method, which is another method that provides a closed form approximation of the likelihood. In the biomass data case, we show that ignoring the correlation between taxa affects the regression estimates unfavourably. To illustrate how our methods can be used in unconstrained ordination and in making inference on environmental variables, we apply them to two ecological datasets: abundances of bacterial species in three arctic locations in Europe and abundances of coral reef species in Indonesia.