Fitting Linear Mixed-Effects Models Using lme4
07 Oct 2015-Journal of Statistical Software (Foundation for Open Access Statistics)-Vol. 67, Iss: 1, pp 1-48
TL;DR: In this article, a model is described in an lmer call by a formula, in this case including both fixed-and random-effects terms, and the formula and data together determine a numerical representation of the model from which the profiled deviance or the profeatured REML criterion can be evaluated as a function of some of model parameters.
Abstract: Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.
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TL;DR: The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects, and implementing the Satterthwaite's method for approximating degrees of freedom for the t and F tests.
Abstract: One of the frequent questions by users of the mixed model function lmer of the lme4 package has been: How can I get p values for the F and t tests for objects returned by lmer? The lmerTest package extends the 'lmerMod' class of the lme4 package, by overloading the anova and summary functions by providing p values for tests for fixed effects. We have implemented the Satterthwaite's method for approximating degrees of freedom for the t and F tests. We have also implemented the construction of Type I - III ANOVA tables. Furthermore, one may also obtain the summary as well as the anova table using the Kenward-Roger approximation for denominator degrees of freedom (based on the KRmodcomp function from the pbkrtest package). Some other convenient mixed model analysis tools such as a step method, that performs backward elimination of nonsignificant effects - both random and fixed, calculation of population means and multiple comparison tests together with plot facilities are provided by the package as well.
12,305 citations
TL;DR: The glmmTMB package fits many types of GLMMs and extensions, including models with continuously distributed responses, but here the authors focus on count responses and its ability to estimate the Conway-Maxwell-Poisson distribution parameterized by the mean is unique.
Abstract: Count data can be analyzed using generalized linear mixed models when observations are correlated in ways that require random effects However, count data are often zero-inflated, containing more zeros than would be expected from the typical error distributions We present a new package, glmmTMB, and compare it to other R packages that fit zero-inflated mixed models The glmmTMB package fits many types of GLMMs and extensions, including models with continuously distributed responses, but here we focus on count responses glmmTMB is faster than glmmADMB, MCMCglmm, and brms, and more flexible than INLA and mgcv for zero-inflated modeling One unique feature of glmmTMB (among packages that fit zero-inflated mixed models) is its ability to estimate the Conway-Maxwell-Poisson distribution parameterized by the mean Overall, its most appealing features for new users may be the combination of speed, flexibility, and its interface’s similarity to lme4
4,497 citations
Cites methods from "Fitting Linear Mixed-Effects Models..."
..., formula syntax) on the lme4 package — one of the most widely used R packages for fitting GLMMs (Bates et al., 2015)....
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...We based glmmTMB’s interface (e.g., formula syntax) on the lme4 package — one of the most widely used R packages for fitting GLMMs (Bates et al., 2015)....
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TL;DR: The brms package implements Bayesian multilevel models in R using the probabilistic programming language Stan, allowing users to fit linear, robust linear, binomial, Poisson, survival, ordinal, zero-inflated, hurdle, and even non-linear models all in a multileVEL context.
Abstract: The brms package implements Bayesian multilevel models in R using the probabilistic programming language Stan. A wide range of distributions and link functions are supported, allowing users to fit - among others - linear, robust linear, binomial, Poisson, survival, ordinal, zero-inflated, hurdle, and even non-linear models all in a multilevel context. Further modeling options include autocorrelation of the response variable, user defined covariance structures, censored data, as well as meta-analytic standard errors. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their beliefs. In addition, model fit can easily be assessed and compared with the Watanabe-Akaike information criterion and leave-one-out cross-validation.
4,353 citations
Cites methods from "Fitting Linear Mixed-Effects Models..."
...These are lme4 (Bates et al. 2015) and MCMCglmm (HadĄeld 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....
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Boston Children's Hospital1, Harvard University2, University of Oxford3, Northeastern University4, Universidad San Francisco de Quito5, University of Southampton6, Institute for Health Metrics and Evaluation7, Pasteur Institute8, University of Paris9, Institute for Scientific Interchange10, Beijing Normal University11, Royal Veterinary College12
TL;DR: Real-time mobility data from Wuhan and detailed case data including travel history are used to elucidate the role of case importation in transmission in cities across China and to ascertain the impact of control measures.
Abstract: The ongoing coronavirus disease 2019 (COVID-19) outbreak expanded rapidly throughout China. Major behavioral, clinical, and state interventions were undertaken to mitigate the epidemic and prevent the persistence of the virus in human populations in China and worldwide. It remains unclear how these unprecedented interventions, including travel restrictions, affected COVID-19 spread in China. We used real-time mobility data from Wuhan and detailed case data including travel history to elucidate the role of case importation in transmission in cities across China and to ascertain the impact of control measures. Early on, the spatial distribution of COVID-19 cases in China was explained well by human mobility data. After the implementation of control measures, this correlation dropped and growth rates became negative in most locations, although shifts in the demographics of reported cases were still indicative of local chains of transmission outside of Wuhan. This study shows that the drastic control measures implemented in China substantially mitigated the spread of COVID-19.
2,362 citations
TL;DR: This analysis estimates a seasonal decline of 76%, and mid-summer decline of 82% in flying insect biomass over the 27 years of study, and shows that this decline is apparent regardless of habitat type, while changes in weather, land use, and habitat characteristics cannot explain this overall decline.
Abstract: Global declines in insects have sparked wide interest among scientists, politicians, and the general public. Loss of insect diversity and abundance is expected to provoke cascading effects on food webs and to jeopardize ecosystem services. Our understanding of the extent and underlying causes of this decline is based on the abundance of single species or taxonomic groups only, rather than changes in insect biomass which is more relevant for ecological functioning. Here, we used a standardized protocol to measure total insect biomass using Malaise traps, deployed over 27 years in 63 nature protection areas in Germany (96 unique location-year combinations) to infer on the status and trend of local entomofauna. Our analysis estimates a seasonal decline of 76%, and mid-summer decline of 82% in flying insect biomass over the 27 years of study. We show that this decline is apparent regardless of habitat type, while changes in weather, land use, and habitat characteristics cannot explain this overall decline. This yet unrecognized loss of insect biomass must be taken into account in evaluating declines in abundance of species depending on insects as a food source, and ecosystem functioning in the European landscape.
2,065 citations
References
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TL;DR: The tools implemented in HLMdiag for both residual and influence analysis are discussed, including those targeting all aspects and levels of continuous response hierarchical linear models with strictly nested dependence structures fit using the lmer() function in the lme4 package.
Abstract: Over the last twenty years there have been numerous developments in diagnostic pro- cedures for hierarchical linear models; however, these procedures are not widely imple- mented in statistical software packages, and those packages that do contain a complete framework for model assessment are not open source. The lack of availability of diagnostic procedures for hierarchical linear models has limited their adoption in statistical practice. The R package HLMdiag provides diagnostic tools targeting all aspects and levels of continuous response hierarchical linear models with strictly nested dependence structures fit using the lmer() function in the lme4 package. In this paper we discuss the tools implemented in HLMdiag for both residual and influence analysis.
51 citations
"Fitting Linear Mixed-Effects Models..." refers background in this paper
...ME (Loy and Hofmann 2014; Nieuwenhuis, Te Grotenhuis, and Pelzer 2012)....
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TL;DR: This work describes an implementation of the Nelder-Mead simplex method in parallel using a distributed memory and describes how the algorithm can be implemented with only two MPI commands.
Abstract: The Nelder-Mead simplex method is an optimization routine that works well with irregular objective functions. For a function of $$n$$ parameters, it compares the objective function at the $$n+1$$ vertices of a simplex and updates the worst vertex through simplex search steps. However, a standard serial implementation can be prohibitively expensive for optimizations over a large number of parameters. We describe an implementation of the Nelder-Mead method in parallel using a distributed memory. For $$p$$ processors, each processor is assigned $$(n+1)/p$$ vertices at each iteration. Each processor then updates its worst local vertices, communicates the results, and a new simplex is formed with the vertices from all processors. We also describe how the algorithm can be implemented with only two MPI commands. In simulations, our implementation exhibits large speedups and is scalable to large problem sizes.
35 citations
"Fitting Linear Mixed-Effects Models..." refers background in this paper
...There is most likely further room for improvement in the nonlinear optimization module; for example, some speed-up could be gained by using parallel implementations of derivative-free optimizers that evaluated several trial points at once (Klein and Neira 2013)....
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