On modeling multivariate abundance data with generalized linear latent variable models

The multivariate abundance data consist typically of multiple, correlated species encountered at a set of sites, together with records of additional covariates. When analysing such data, model-based approaches have been shown to outperform classical algorithmic-based dimension reduction methods. In this thesis we con-sider generalized linear latent variable models, which offer a general framework for the analysis of multivariate abundance data. In order to make the models more attractive among practitioners, new computationally efficient algorithms for the parameter estimation are developed by applying closed form approxima-tion methods, the variational approximation method and the Laplace approxima-tion method, for the marginal likelihood and by utilizing automatic differentia-tion tools when implementing the algorithms. The accuracy and computational efficiency of the methods are investigated and compared to existing methods through extensive simulation studies. The developed algorithms and additional tools implemented for model diagnosis, visualization and statistical inference are collected in R package gllvm. Several examples are provided to illustrate the use of the generalized linear latent variable models in ordination and when studying the between-species correlations and the effects of environmental variables, trait variables and their interactions on ecological communities.