Generalized Linear Latent Variable Models for Multivariate Count and Biomass Data in Ecology
- 714 Downloads
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.
Supplementary materials accompanying this paper appear on-line.
KeywordsBiomass Laplace approximation Ordination Overdispersed count Species interactions
We thank the Associate Editor and the referees for their helpful comments. We also thank Dr Manoj Kumar and Dr Riitta Nissinen for providing us the plant-microbial diversity data. JN and ST were supported by the Academy of Finland grants 251965 and 283323.
- Blanchet, F. (2014). HMSC: Hierachical modelling of species community. R package version 0.6-2.Google Scholar
- Burnham, K. and Anderson, D. (2002). Model selection and multimodel inference: Al practical information-theoretic approach. Springer.Google Scholar
- Dunn, P. K. and Smyth, G. K. (1996). Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5:236–244.Google Scholar
- Hui, F. K. C., Warton, D., Ormerod, J., Haapaniemi, V., and Taskinen, S. (2016). Variational Approximations for Generalized Linear Latent Variable Models. Journal of Computational and Graphical Statistics. In press.Google Scholar
- Jorgensen, B. (1997). The Theory of Dispersion Models. Chapman & Hall.Google Scholar
- Kristensen, K., Nielsen, A., Berg, C., Skaug, H., and Bell, B. (2016). Tmb: Automatic differentiation and laplace approximation. Journal of Statistical Software, Articles, 70(5):1–21.Google Scholar