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Fitting Linear Mixed-Effects Models Using lme4

Published on Oct 7, 2015in Journal of Statistical Software 22.74
· DOI :10.18637/jss.v067.i01
Douglas M. Bates30
Estimated H-index: 30
Martin Mächler15
Estimated H-index: 15
+ 1 AuthorsSteven C. Walker10
Estimated H-index: 10
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.
  • References (33)
  • Citations (11050)
Published on Jan 1, 2016
C. G. Khatri1
Estimated H-index: 1
C. Radhakrishna Rao1
Estimated H-index: 1
involving an unknown function ?5 of a single variable t. Conditions under which the unknown functions in these two types of equations are polynomials of an assigned degree are given. The third, on the characterization of normal and gamma distributions, extends the earlier work of the authors (Rao, 1967 and Khatri and Rao, 1968*). We consider two sets of functions Li9 ..., Lq and Mlf ..., Mp of independent random variables Xl9 .... Xn with the condition
132 Citations
Published on Apr 1, 2014in Computing in Economics and Finance
Kyle Klein6
Estimated H-index: 6
(University of California, Santa Barbara),
Julian Neira1
Estimated H-index: 1
(University of California, Santa Barbara)
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. F...
17 Citations Source Cite
Published on Jan 25, 2014in Journal of Statistical Software 22.74
Adam Loy6
Estimated H-index: 6
Heike Hofmann25
Estimated H-index: 25
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 targetin...
14 Citations Source Cite
Published on Jan 1, 2014in MSOR connections
R Core Team1
Estimated H-index: 1
113k Citations
Published on Oct 1, 2013in Psychometrika 2.09
Yeojin Chung5
Estimated H-index: 5
(Kookmin University),
Sophia Rabe-Hesketh52
Estimated H-index: 52
(University of California, Berkeley)
+ 2 AuthorsJingchen Liu13
Estimated H-index: 13
(Columbia University)
Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zero variances are implausible a priori, we propose a maximum penalized likelihood approach to avoid such boundary estimates. This approach is equivalent to estimating variance parameters by their posterior mode, given a weakly informative prior distribution. By choosing the penalty from the log-gamma family with shape param...
76 Citations Source Cite
Published on Oct 28, 1997
A. C. Davison36
Estimated H-index: 36
(Rutgers University),
D. V. Hinkley6
Estimated H-index: 6
This book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; a...
4,777 Citations
Published on Jun 1, 2013in Methods in Ecology and Evolution 6.36
Benjamin M. Bolker46
Estimated H-index: 46
(McMaster University),
Beth Gardner24
Estimated H-index: 24
(Patuxent Wildlife Research Center)
+ 19 AuthorsPerry de Valpine21
Estimated H-index: 21
(University of California, Berkeley)
1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from ...
58 Citations Source Cite
Published on Jan 1, 2012in arXiv: Programming Languages
Jeff Bezanson3
Estimated H-index: 3
(Massachusetts Institute of Technology),
Stefan Karpinski4
Estimated H-index: 4
+ 1 AuthorsAlan Edelman35
Estimated H-index: 35
(Massachusetts Institute of Technology)
Dynamic languages have become popular for scientic computing. They are generally considered highly productive, but lacking in performance. This paper presents Julia, a new dynamic language for technical computing, designed for performance from the beginning by adapting and extending modern programming language techniques. A design based on generic functions and a rich type system simultaneously enables an expressive programming model and successful type inference, leading to good performance for...
201 Citations
Published on Jan 1, 2012in R Journal 1.37
Rense Nieuwenhuis7
Estimated H-index: 7
H.F. te Grotenhuis2
Estimated H-index: 2
Ben Pelzer12
Estimated H-index: 12
influence.ME provides tools for de- tecting influential data in mixed effects mod- els. The application of these models has become common practice, but the development of diag- nostic tools has lagged behind. influence.ME calculates standardized measures of influential data for the point estimates of generalized mixed effects models, such as DFBETAS, Cook's dis- tance, as well as percentile change and a test for changing levels of significance. influence.ME calculates these measures of influence...
104 Citations Source Cite
Published on Aug 24, 2011in Journal of Statistical Software 22.74
John C. Nash8
Estimated H-index: 8
(University of Ottawa),
Ravi Varadhan23
Estimated H-index: 23
R users can often solve optimization tasks easily using the tools in the optim function in the stats package provided by default on R installations. However, there are many other optimization and nonlinear modelling tools in R or in easily installed add-on packages. These present users with a bewildering array of choices. optimx is a wrapper to consolidate many of these choices for the optimization of functions that are mostly smooth with parameters at most bounds-constrained. We attempt to prov...
102 Citations Source Cite
Cited By11050
Julia Freytag1
Estimated H-index: 1
(Humboldt University of Berlin),
Fabian Stroben1
Estimated H-index: 1
(Humboldt University of Berlin)
+ 2 AuthorsJuliane E. Kämmer6
Estimated H-index: 6
(Humboldt University of Berlin)
Background Training in teamwork behaviour improves technical resuscitation performance. However, its effect on patient outcome is less clear, partly because teamwork behaviour is difficult to measure. Furthermore, it is unknown who should evaluate it. In clinical practice, experts are obliged to participate in resuscitation efforts and are thus unavailable to assess teamwork quality. Consequently, we sought to determine if raters with little clinical experience and experts provide comparable eva...
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Published on Apr 15, 2019in BMC Bioinformatics 2.21
Yun Zhang (J. Craig Venter Institute), Gautam Bandyopadhyay45
Estimated H-index: 45
(University of Rochester)
+ 2 AuthorsXing Qiu19
Estimated H-index: 19
(University of Rochester)
Background For many practical hypothesis testing (H-T) applications, the data are correlated and/or with heterogeneous variance structure. The regression t-test for weighted linear mixed-effects regression (LMER) is a legitimate choice because it accounts for complex covariance structure; however, high computational costs and occasional convergence issues make it impractical for analyzing high-throughput data. In this paper, we propose computationally efficient parametric and semiparametric test...
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Published on Mar 11, 2019in Scientific Reports 4.12
Mahdi Ghanbari , Viviana Klose + 1 AuthorsPaul D. Cotter60
Estimated H-index: 60
In this study, shotgun metagenomics was employed to monitor the effect of oxytetracycline, administered at a therapeutic dose, on the dynamics of the microbiota and resistome in the feces of weaned pigs. Sixteen weaning pigs were assigned to one of two treatments including standard starter diet for 21 days or antibiotic-supplemented diet (10 g oxytetracycline/100 kg body weight/day) for 7 days, followed by 14 days of standard starter diet. Feces were collected from the pigs on days 0, 8, and 21 ...
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Published on Feb 15, 2019in Mbio 6.69
Rachael E. Antwis9
Estimated H-index: 9
(University of Salford),
Katie L. Edwards6
Estimated H-index: 6
(Smithsonian Conservation Biology Institute)
+ 2 AuthorsSusanne Shultz28
Estimated H-index: 28
(University of Manchester)
Background: Host microbiomes play a role in hormone production and subsequent fertility in humans, but this is less well understood in non-model organisms. This is of particular relevance to species in zoo-based conservation breeding programmes, as relationships between host microbiome composition and reproductive output may allow for the development of microbial augmentation strategies to improve success. Here, we characterise faecal bacterial communities of breeding and non-breeding eastern bl...
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Published on Jan 3, 2019in Parasites & Vectors 3.16
Vetle Malmer Stigum2
Estimated H-index: 2
(University of Oslo),
Ryanne I. Jaarsma1
Estimated H-index: 1
+ 2 AuthorsAtle Mysterud58
Estimated H-index: 58
(University of Antwerp)
The geographical expansion of the tick Ixodes ricinus in northern Europe is a serious concern for animal and human health. The pathogen Anaplasma phagocytophilum is transmitted by ticks and causes emergences of tick-borne fever (anaplasmosis) in livestock. The transmission dynamics of the different ecotypes of A. phagocytophilum in the ecosystems is only partly determined. Red deer and roe deer contribute to circulation of different ecotypes of A. phagocytophilum in continental Europe, while the...
1 Citations Source Cite
Published on Apr 25, 2019in Scientific Reports 4.12
Christian Maltecca20
Estimated H-index: 20
(North Carolina State University),
Duc Lu6
Estimated H-index: 6
(North Carolina State University)
+ 4 AuthorsF. Tiezzi8
Estimated H-index: 8
(North Carolina State University)
In this paper, we evaluated the power of microbiome measures taken at three time points over the growth test period (weaning, 15 and 22 weeks) to foretell growth and carcass traits in 1039 individuals of a line of crossbred pigs. We measured prediction accuracy as the correlation between actual and predicted phenotypes in a five-fold cross-validation setting. Phenotypic traits measured included live weight measures and carcass composition obtained during the trial as well as at slaughter. We emp...
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Published on Mar 12, 2019in Environmental Evidence
Biljana Macura7
Estimated H-index: 7
(Stockholm Environment Institute),
Pär Byström29
Estimated H-index: 29
(Umeå University)
+ 3 AuthorsJosianne Støttrup21
Estimated H-index: 21
(Technical University of Denmark)
Background Shallow nearshore marine ecosystems are changing at an increasing rate due to a range of human activities such as urbanisation and commercial development. As a result, an increasing number of structural modifications occur in coastal nursery and spawning habitats of fish. Concomitant to this increase, there have been declines in many coastal fish populations and changes in the composition of fish communities. As requested by Swedish stakeholders, this review aimed to synthesise scient...
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Published on Mar 19, 2019in Nature Communications 12.35
Megan Murgatroyd4
Estimated H-index: 4
(University of Cape Town),
Stephen M. Redpath (University of Cape Town)+ 3 AuthorsArjun Amar22
Estimated H-index: 22
(University of Cape Town)
Identifying patterns of wildlife crime is a major conservation challenge. Here, we test whether deaths or disappearances of a protected species, the hen harrier, are associated with grouse moors, which are areas managed for the production of red grouse for recreational shooting. Using data from 58 satellite tracked hen harriers, we show high rates of unexpected tag failure and low first year survival compared to other harrier populations. The likelihood of harriers dying or disappearing increase...
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