Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data

Klein, Nadja; Kneib, Thomas; Lang, Stefan

doi:10.1080/01621459.2014.912955

Cited by 65 publications

(77 citation statements)

References 36 publications

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“…We analysed hummingbird visits at artificial and planted flowers, and the number of pollen tubes observed per style with mixed Bayesian, generalized additive models for location, scale and shape [35] implemented in BAYESX [36]. This method allowed us to (i) take into account the hierarchical data structure, (ii) incorporate the spatial dependency of neighbouring flowers (serial autocorrelation), (iii) model the nonlinear effect of distance to forest via a non-parametric function for distance and to (iv) model the detected zero-inflation and/or overdispersion in the dependent variable.…”

Section: (A) Pollinator Movementmentioning

confidence: 99%

Corridors restore animal-mediated pollination in fragmented tropical forest landscapes

et al. 2016

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Tropical biodiversity and associated ecosystem functions have become heavily eroded through habitat loss. Animal-mediated pollination is required in more than 94% of higher tropical plant species and 75% of the world's leading food crops, but it remains unclear if corridors avert deforestation-driven pollination breakdown in fragmented tropical landscapes. Here, we used manipulative resource experiments and field observations to show that corridors functionally connect neotropical forest fragments for forest-associated hummingbirds and increase pollen transfer. Further, corridors boosted forest-associated pollinator availability in fragments by 14.3 times compared with unconnected equivalents, increasing overall pollination success. Plants in patches without corridors showed pollination rates equal to bagged control flowers, indicating pollination failure in isolated fragments. This indicates, for the first time, that corridors benefit tropical forest ecosystems beyond boosting local species richness, by functionally connecting mutualistic network partners. We conclude that small-scale adjustments to landscape configuration safeguard native pollinators and associated pollination services in tropical forest landscapes.

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Section: (A) Pollinator Movementmentioning

confidence: 99%

Corridors restore animal-mediated pollination in fragmented tropical forest landscapes

et al. 2016

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“…. ,✓ iK ) > plugged in, should at least approximately be standard normally distributed if the correct model has been specified (Dunn and Smyth 1996;Klein et al 2015b). Resulting residuals can be assessed graphically in terms of quantile-quantile-plots.…”

Section: Diagnosticsmentioning

confidence: 99%

“…Note that for numerical reasons it is oftentimes better to replace the Hessian by the expected Fisher information with weights W kk = diag(E(@ 2`( ; y, X)/@⌘ k @⌘ > k )), see Klein et al (2015b). Moreover, to achieve convergence, algorithms for posterior mode usually initialize the parameter vectors ✓ k .…”

Section: Posterior Modementioning

confidence: 99%

“…This is specifically the case in more complex models, e.g., with response distributions outside the exponential family or when multiple predictors contain several smooth e↵ects (Klein, Kneib, and Lang 2015b). In addition, extensions such as variable selection, non-standard priors for hyper-parameters, or multilevel models are easily included.…”

Section: Introductionmentioning

confidence: 99%

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BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond)

Umlauf

Klein

Zeileis

2018

Journal of Computational and Graphical Statistics

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107

131

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Achim Zeileis Universität InnsbruckAbstract Bayesian analysis provides a convenient setting for the estimation of complex generalized additive regression models (GAMs). Since computational power has tremendously increased in the past decade it is now possible to tackle complicated inferential problems, e.g., with Markov chain Monte Carlo simulation, on virtually any modern computer. This is one of the reasons why Bayesian methods have become increasingly popular, leading to a number of highly specialized and optimized estimation engines and with attention shifting from conditional mean models to probabilistic distributional models capturing location, scale, shape (and other aspects) of the response distribution. In order to embed many different approaches suggested in literature and software, a unified modeling architecture for distributional GAMs is established that exploits the general structure of these models and encompasses many di↵erent response distributions, estimation techniques (posterior mode or posterior mean), and model terms (fixed, random, smooth, spatial, . . . ). It is shown that within this framework implementing algorithms for complex regression problems, as well as the integration of already existing software, is relatively straightforward. The usefulness is emphasized with two complex and computationally demanding application case studies: a large daily precipitation climatology based on more than 1.2 million observations from more than 50 meteorological stations, as well as a Cox model for continuous time with space-time interactions on a data set with over five thousand "individuals".

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“…Some Bayesian overdispersion methods are discussed in the collection assembled by ; for example, Basu and Mukhopadhyay (2000) consider generalizing the link function of a GLM to a mixture distribution and Dey and Ravishanker (2000) propose generalized exponential families for the outcome. More recently, Klein et al (2015) proposed a Bayesian approach to generalized additive models under the Zero-Inflated Negative Binomial model to estimate complicated regression functions.…”

Section: Introductionmentioning

confidence: 99%

An Extension of Generalized Linear Models to Finite Mixture Outcome Distributions

Raim

Neerchal

Morel

2018

Journal of Computational and Graphical Statistics

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Finite mixture distributions arise in sampling a heterogeneous population. Data drawn from such a population will exhibit extra variability relative to any single subpopulation. Statistical models based on finite mixtures can assist in the analysis of categorical and count outcomes when standard generalized linear models (GLMs) cannot adequately account for variability observed in the data. We propose an extension of GLM where the response is assumed to follow a finite mixture distribution, while the regression of interest is linked to the mixture's mean. This approach may be preferred over a finite mixture of regressions when the population mean is the quantity of interest; here, only a single regression function must be specified and interpreted in the analysis. A technical challenge is that the mean of a finite mixture is a composite parameter which does not appear explicitly in the density. The proposed model is completely likelihood-based and maintains the link to the regression through a certain random effects structure. We consider typical GLM cases where means are either real-valued, constrained to be positive, or constrained to be on the unit interval. The resulting model is applied to two example datasets through a Bayesian analysis: one with success/failure outcomes and one with count outcomes. Supporting the extra variation is seen to improve residual plots and to appropriately widen prediction intervals.

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Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data

Cited by 65 publications

References 36 publications

Corridors restore animal-mediated pollination in fragmented tropical forest landscapes

Corridors restore animal-mediated pollination in fragmented tropical forest landscapes

BAMLSS: Bayesian Additive Models for Location, Scale, and Shape (and Beyond)

An Extension of Generalized Linear Models to Finite Mixture Outcome Distributions

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