MCMC methods for multi-response generalized linear mixed models

By J. Hadfield. 2010

4,914 citations recorded by the source corpus.

Generalized linear mixed models provide a flexible framework for modeling a range of data, although with non-Gaussian response variables the likelihood cannot be obtained in closed form. Markov chain Monte Carlo methods solve this problem by sampling from a series of simpler conditional distributions that can be evaluated. The R package MCMCglmm implements such an algorithm for a range of model fitting problems. More than one response variable can be analyzed simultaneously, and these variables are allowed to follow Gaussian, Poisson, multi(bi)nominal, exponential, zero-inflated and censored distributions. A range of variance structures are permitted for the random effects, including interactions with categorical or continuous variables (i.e., random regression), and more complicated variance structures that arise through shared ancestry, either through a pedigree or through a phylogeny. Missing values are permitted in the response variable(s) and data can be known up to some level of measurement error as in meta-analysis. All simu- lation is done in C/ C++ using the CSparse library for sparse linear systems.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/488d4dd459fe05da4f0443a62be3dafd342ba9d6

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Citations in the corpus

C:N:P stoichiometry of Artemisia species and close relatives across northern China: unravelling effects of climate, soil and taxonomy (2015, methodology): “age (Hadfield 2010), to describe the posterior distributions of model”
Transgenerational plasticity in marine sticklebacks: maternal effects mediate impacts of a warming ocean (2014, methodology): “We fitted animal models as multivariate generalized linear mixed models with body size in both temperatures as Gaussian response variables using the MCMCglMM package (Hadfield 2010) of the R statistical environment (R Development Core Team 2011).”
Synthetic analyses of phenotypic selection in natural populations: lessons, limitations and future directions (2012, methodology): “We were unable to incorporate phylogeny into the meta-analysis (e.g., see Hadfield and Nakagawa 2010) because of the widely heterogeneous taxa in our dataset.”
Testing for the presence of coping styles in a wild mammal (2013, methodology): “genetic, maternal, or early environment) responsible for the association between two traits (Hadfield 2010).”
Meta‐analysis of variation: ecological and evolutionary applications and beyond (2015, methodology): “REMA was conducted in the R package metafor (Viechtbauer 2010), while MLMA was undertaken using the R package MCMCglmm (Hadfield 2010).”
Plant intraspecific variation modulates nutrient cycling through its below ground rhizospheric microbiome (2019, methodology): “To do so, we ran Bayesian generalized linear mixed models (GLMM), using the MCMCglmm package for r (Hadfield, 2010), with fungal PCPS1 or bacterial PCPS1 as dependent variables in two separate models.”
Latitudinal shift in thermal niche breadth results from thermal release during a climate‐mediated range expansion (2015, methodology): “Models were run in the MCMCglmm package for R 3.0.2 (Hadfield, 2010; R Core Team, 2012).”
Phylogenetic Regression for Binary Dependent Variables (2014, methodology): “…(i) phylogenetic logistic regression, implemented in a MATLAB program named PLogReg (Ives and Garland 2010), (ii) generalized linear mixed models with frequentist estimation, PGLMM (Ives and Helmus 2011), and (iii) generalized linear mixed models with Bayesian estimation, MCMCglmm (Hadfield 2010).”
Don't poke the bear: using tracking data to quantify behavioural syndromes in elusive wildlife (2019, methodology): “clearcut and bog selection as response variables using the R package ‘MCMCglmm’ (Hadfield, 2010).”
PyMC: Bayesian Stochastic Modelling in Python (2010, methodology): “Other packages include Hierarchical Bayes Compiler (Daumé III 2007) and a number of R (R Development Core Team 2010) packages, for example MCMCglmm (Hadfield 2010) and MCMCpack (Martin, Quinn, and Park 2009).”
brms: An R Package for Bayesian Multilevel Models Using Stan (2017, methodology): “2015) and MCMCglmm (Hadfield 2010), which are possibly the most general and widely applied R packages for MLMs, as well as rstanarm (Gabry and Goodrich 2016) and rethinking (McElreath 2016), which are both based on Stan.”