0000000001299609
AUTHOR
David I. Warton
Efficient estimation of generalized linear latent variable models.
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 estim…
Model‐based approaches to unconstrained ordination
Summary Unconstrained ordination is commonly used in ecology to visualize multivariate data, in particular, to visualize the main trends between different sites in terms of their species composition or relative abundance. Methods of unconstrained ordination currently used, such as non-metric multidimensional scaling, are algorithm-based techniques developed and implemented without directly accommodating the statistical properties of the data at hand. Failure to account for these key data properties can lead to misleading results. A model-based approach to unconstrained ordination can address this issue, and in this study, two types of models for ordination are proposed based on finite mixtu…
Analyzing environmental‐trait interactions in ecological communities with fourth‐corner latent variable models
In ecological community studies it is often of interest to study the effect of species related trait variables on abundances or presence-absences. Specifically, the interest may lay in the interactions between environmental and trait variables. An increasingly popular approach for studying such interactions is to use the so-called fourth-corner model, which explicitly posits a regression model where the mean response of each species is a function of interactions between covariate and trait predictors (among other terms). On the other hand, many of the fourth-corner models currently applied in the literature are too simplistic to properly account for variation in environmental and trait resp…
Extending Joint Models in Community Ecology : A Response to Beissinger et al.
The joint modelling of many variables in community ecology is a new and technically challenging area with many opportunities for future developments. The possibility of extending joint models to deal with imperfect detection has been highlighted by Beissinger et al. as an important problem worthy of further investigation [1]. We agree, and previously pointed to this potential extension as an outstanding question [2], alongside models that can estimate phylogenetic repulsion or attraction, nonlinearity in the response to latent variables, and spatial or temporal correlation, because further developments in all these directions are needed.
smatr 3 - an R package for estimation and inference about allometric lines
Summary 1. The Standardised Major Axis Tests and Routines (SMATR) software provides tools for estimation and inference about allometric lines, currently widely used in ecology and evolution. 2. This paper describes some significant improvements to the functionality of the package, now available on R in smatr version 3. 3. New inclusions in the package include sma and ma functions that accept formula input and perform the key inference tasks; multiple comparisons; graphical methods for visualising data and checking (S)MA assumptions; robust (S)MA estimation and inference tools.
gllvm: Fast analysis of multivariate abundance data with generalized linear latent variable models inr
The work of J.N. was supported by the Wihuri Foundation. The work of S.T. was supported by the CRoNoS COST Action IC1408.F.K.C.H. was also supported by an ANU cross disciplinary grant.
gllvm : Fast analysis of multivariate abundance data with generalized linear latent variable models in R
1.There has been rapid development in tools for multivariate analysis based on fully specified statistical models or “joint models”. One approach attracting a lot of attention is generalized linear latent variable models (GLLVMs). However, software for fitting these models is typically slow and not practical for large datsets. 2.The R package gllvm offers relatively fast methods to fit GLLVMs via maximum likelihood, along with tools for model checking, visualization and inference. 3.The main advantage of the package over other implementations is speed e.g. being two orders of magnitude faster, and capable of handling thousands of response variables. These advances come from using variationa…
So Many Variables: Joint Modeling in Community Ecology
Technological advances have enabled a new class of multivariate models for ecology, with the potential now to specify a statistical model for abundances jointly across many taxa, to simultaneously explore interactions across taxa and the response of abundance to environmental variables. Joint models can be used for several purposes of interest to ecologists, including estimating patterns of residual correlation across taxa, ordination, multivariate inference about environmental effects and environment-by-trait interactions, accounting for missing predictors, and improving predictions in situations where one can leverage knowledge of some species to predict others. We demonstrate this by exa…
Robust estimation and inference for bivariate line-fitting in allometry.
In allometry, bivariate techniques related to principal component analysis are often used in place of linear regression, and primary interest is in making inferences about the slope. We demonstrate that the current inferential methods are not robust to bivariate contamination, and consider four robust alternatives to the current methods -- a novel sandwich estimator approach, using robust covariance matrices derived via an influence function approach, Huber's M-estimator and the fast-and-robust bootstrap. Simulations demonstrate that Huber's M-estimators are highly efficient and robust against bivariate contamination, and when combined with the fast-and-robust bootstrap, we can make accurat…
Variational Approximations for Generalized Linear Latent Variable Models
Generalized linear latent variable models (GLLVMs) are a powerful class of models for understanding the relationships among multiple, correlated responses. Estimation, however, presents a major challenge, as the marginal likelihood does not possess a closed form for nonnormal responses. We propose a variational approximation (VA) method for estimating GLLVMs. For the common cases of binary, ordinal, and overdispersed count data, we derive fully closed-form approximations to the marginal log-likelihood function in each case. Compared to other methods such as the expectation-maximization algorithm, estimation using VA is fast and straightforward to implement. Predictions of the latent variabl…
Variational Approximations for Generalized Linear Latent Variable Models
Generalized linear latent variable models (GLLVMs) are a powerful class of models for understanding the relationships among multiple, correlated responses. Estimation, however, presents a major challenge, as the marginal likelihood does not possess a closed form for nonnormal responses. We propose a variational approximation (VA) method for estimating GLLVMs. For the common cases of binary, ordinal, and overdispersed count data, we derive fully closed-form approximations to the marginal log-likelihood function in each case. Compared to other methods such as the expectation-maximization algorithm, estimation using VA is fast and straightforward to implement. Predictions of the latent variabl…