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

Niku, Jenni; Warton, David I.; Hui, Francis K. C.; Taskinen, Sara

doi:10.1007/s13253-017-0304-7

Cited by 60 publications

(77 citation statements)

References 37 publications

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“…Parameter estimation of HCMs can be challenging and time consuming because they rely on iterative algorithms though updating methods to overcome these issues are becoming available (Niku et al. , Gomez et al. ).…”

Section: Resultsmentioning

confidence: 99%

Analyzing community structure subject to incomplete sampling: hierarchical community model vs. canonical ordinations

Yamaura

Blanchet

Higa

2019

Ecology

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Citation: Yamaura, Y., F. G. Blanchet, and M. Higa. 2019. Analyzing community structure subject to incomplete sampling: hierarchical community model vs. canonical ordinations. Ecology 100(8):Abstract. Recently developing hierarchical community models (HCMs) accounting for incomplete sampling are promising approaches to understand community organization. However, pros and cons of incorporating incomplete sampling in the analysis and related design issues remain unknown. In this study, we compared HCM and canonical redundancy analysis (RDA) carried out with 10 different dissimilarity coefficients to evaluate how each approach restores true community abundance data sampled with imperfect detection. We conducted simulation experiments with varying numbers of sampling sites, visits, mean detectability and mean abundance. Performance of HCM was measured by estimates of "expected" (mean) abundance (k ij ) and realized abundance (N ij : direct estimate of site-and species-specific abundance). We also compared HCM and different types of RDA (normal, partial, and weighted), all performed with the same ten different dissimilarity coefficients, with unequal number of visits to sampling sites. In addition, we applied the models to a virtual survey carried out on the Barro Colorado Island tree plot data for which we know true community abundance. Simulation experiments showed thatN ij yielded by HCM best restored the underlying abundance of constituent species among 12 abundance estimates by HCM and RDA regardless if the sampling was equal or unequal. Mean abundance predominantly affected the performance of HCM and RDA whilek ij yielded by HCM had comparable performance to percentage difference and Gower dissimilarity coefficients of RDA. Relative performance of RDA types depended on the combination of dissimilarity coefficients and the distribution of sampling effort. Best performance ofN ij followed byk ij , percentage difference and Gower dissimilarity were also observed for the analysis of tree plot data, and graphical plots (triplots) based onk ij rather thanN ij clearly separated the effects of two environmental covariates on the abundance of constituent species. Under our conditions of model evaluation and the method, we concluded that, in terms of assessing the environmental dependence of abundance, HCMs and RDA can have comparable performance if we can choose appropriate dissimilarity coefficients for RDA. However, since HCMs provide straightforward biological interpretations of parameter estimates and flexibility of the analysis, HCMs would be useful in many situations as well as conventional canonical ordinations.

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Section: Resultsmentioning

confidence: 99%

Analyzing community structure subject to incomplete sampling: hierarchical community model vs. canonical ordinations

Yamaura

Blanchet

Higa

2019

Ecology

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“…Some of the models also anticipate the growing challenges of Big Data for ecology (Hampton et al, ). Generalized linear latent variable models, for example, include latent variables instead of random effects to capture residual correlation, which considerably reduces the size of the variance—covariance matrix (Niku, Warton, Hui, & Taskinen, ; Warton, Blanchet, et al, ). In hierarchical modeling of species communities (Ovaskainen et al, ), this approach is coupled with a fourth corner model (including species traits, Legendre, Galzin, & Harmelin‐Vivien, ) and phylogenetic relationships to create a flexible and comprehensive framework for community data analysis.…”

Section: Discussionmentioning

confidence: 99%

Should ecologists prefer model‐ over distance‐based multivariate methods?

Jupke

Schäfer

2020

Ecology and Evolution

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Ecological data sets often record the abundance of species, together with a set of explanatory variables. Multivariate statistical methods are optimal to analyze such data and are thus frequently used in ecology for exploration, visualization, and inference. Most approaches are based on pairwise distance matrices instead of the sites‐by‐species matrix, which stands in stark contrast to univariate statistics, where data models, assuming specific distributions, are the norm. However, through advances in statistical theory and computational power, models for multivariate data have gained traction. Systematic simulation‐based performance evaluations of these methods are important as guides for practitioners but still lacking. Here, we compare two model‐based methods, multivariate generalized linear models (MvGLMs) and constrained quadratic ordination (CQO), with two distance‐based methods, distance‐based redundancy analysis (dbRDA) and canonical correspondence analysis (CCA). We studied the performance of the methods to discriminate between causal variables and noise variables for 190 simulated data sets covering different sample sizes and data distributions. MvGLM and dbRDA differentiated accurately between causal and noise variables. The former had the lowest false‐positive rate (0.008), while the latter had the lowest false‐negative rate (0.027). CQO and CCA had the highest false‐negative rate (0.291) and false‐positive rate (0.256), respectively, where these error rates were typically high for data sets with linear responses. Our study shows that both model‐ and distance‐based methods have their place in the ecologist's statistical toolbox. MvGLM and dbRDA are reliable for analyzing species–environment relations, whereas both CQO and CCA exhibited considerable flaws, especially with linear environmental gradients.

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“…Additionally, the computational methods proposed in this article may not be feasible in such settings, and instead we may need to combine OFAL with faster, approximate likelihood‐based estimation methods (Hui et al., ; Niku et al., ). Such research into more computationally efficient approaches will also be beneficial if we wanted to include more tuning parameters in the OFAL penalty, for example, the mixing parameter

α

discussed in Section .…”

Section: Discussionmentioning

confidence: 99%

Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO

2018

Self Cite

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Generalized linear latent variable models (GLLVMs) offer a general framework for flexibly analyzing data involving multiple responses. When fitting such models, two of the major challenges are selecting the order, that is, the number of factors, and an appropriate structure for the loading matrix, typically a sparse structure. Motivated by the application of GLLVMs to study marine species assemblages in the Southern Ocean, we propose the Ordered Factor LASSO or OFAL penalty for order selection and achieving sparsity in GLLVMs. The OFAL penalty is the first penalty developed specifically for order selection in latent variable models, and achieves this by using a hierarchically structured group LASSO type penalty to shrink entire columns of the loading matrix to zero, while ensuring that non-zero loadings are concentrated on the lower-order factors. Simultaneously, individual element sparsity is achieved through the use of an adaptive LASSO. In conjunction with using an information criterion which promotes aggressive shrinkage, simulation shows that the OFAL penalty performs strongly compared with standard methods and penalties for order selection, achieving sparsity, and prediction in GLLVMs. Applying the OFAL penalty to the Southern Ocean marine species dataset suggests the available environmental predictors explain roughly half of the total covariation between species, thus leading to a smaller number of latent variables and increased sparsity in the loading matrix compared to a model without any covariates.

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

Cited by 60 publications

References 37 publications

Analyzing community structure subject to incomplete sampling: hierarchical community model vs. canonical ordinations

Analyzing community structure subject to incomplete sampling: hierarchical community model vs. canonical ordinations

Should ecologists prefer model‐ over distance‐based multivariate methods?

Order Selection and Sparsity in Latent Variable Models via the Ordered Factor LASSO

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