Abstract
Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in R software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation.
Highlights
High-dimensional multivariate abundance data, which consist of records of a large number of interacting species at a set of units or sites, are routinely collected in ecological studies
A number of approaches have been proposed in the literature to overcome such issues, with two of the more prominent ones being the variational approximation method to approximate the likelihood in the case of binary, ordinal and overdispersed count data [19], and the Laplace approximation method for responses from the exponential family of distributions [20], which has recently been adapted for overdispersed count and biomass data in ecology [21]; Note that the Laplace approximation can be considered as a special case of adaptive quadrature with only one quadrature point
We propose a framework for faster fitting of Generalized linear latent variable models (GLLVM) using either Laplace approximation method or the variational approximation method
Summary
High-dimensional multivariate abundance data, which consist of records (e.g. species counts, presence-absence records, and biomass) of a large number of interacting species at a set of units or sites, are routinely collected in ecological studies. A number of approaches have been proposed in the literature to overcome such issues, with two of the more prominent ones being the variational approximation method to approximate the likelihood in the case of binary, ordinal and overdispersed count data [19], and the Laplace approximation method for responses from the exponential family of distributions [20], which has recently been adapted for overdispersed count and biomass data in ecology [21]; Note that the Laplace approximation can be considered as a special case of adaptive quadrature with only one quadrature point Both estimation methods provide a closed form approximation to the marginal log-likelihood that can be maximized efficiently.
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