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. Bates26
Estimated H-index: 26
,
Martin Mächler13
Estimated H-index: 13
+ 1 AuthorsSteven C. Walker9
Estimated H-index: 9
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.
  • References (33)
  • Citations (9970)
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References33
Published on Sep 15, 2006
Timothy A. Davis22
Estimated H-index: 22
Preface 1. Introduction 2. Basic algorithms 3. Solving triangular systems 4. Cholesky factorization 5. Orthogonal methods 6. LU factorization 7. Fill-reducing orderings 8. Solving sparse linear systems 9. CSparse 10. Sparse matrices in MATLAB Appendix: Basics of the C programming language Bibliography Index.
701 Citations
Published on Jan 1, 2012in R Journal 1.37
Rense Nieuwenhuis6
Estimated H-index: 6
,
H.F. te Grotenhuis4
Estimated H-index: 4
,
Ben Pelzer10
Estimated H-index: 10
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...
103 Citations Source Cite
Published on Apr 2, 2002
Josae C. Pinheiro1
Estimated H-index: 1
,
Douglas M. Bates26
Estimated H-index: 26
Linear Mixed-Effects * Theory and Computational Methods for LME Models * Structure of Grouped Data * Fitting LME Models * Extending the Basic LME Model * Nonlinear Mixed-Effects * Theory and Computational Methods for NLME Models * Fitting NLME Models
7,879 Citations
Published on Feb 22, 2007in Journal of Statistical Software 22.74
Harold Doran1
Estimated H-index: 1
,
Douglas M. Bates26
Estimated H-index: 26
+ 1 AuthorsMaritza Dowling1
Estimated H-index: 1
Traditional Rasch estimation of the item and student parameters via marginal maximum likelihood, joint maximum likelihood or conditional maximum likelihood, assume individuals in clustered settings are uncorrelated and items within a test that share a grouping structure are also uncorrelated. These assumptions are often violated, particularly in educational testing situations, in which students are grouped into classrooms and many test items share a common grouping structure, such as a content s...
102 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...
99 Citations Source Cite
Published on Feb 1, 2005in Annals of Statistics 2.52
Andrew Gelman68
Estimated H-index: 68
(University of Chicago)
Analysis of variance (ANOVA) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (e.g., split-plot designs), it is not always easy to set up an appropriate ANOVA. We propose a hierarchical analysis that automatically gives the correct ANOVA comparisons even in complex scenarios. The inferences for all means and variances are performed under a model with a separate batch of effects for each row of the ANOVA table. We connect to classi...
316 Citations Source Cite
Published on Sep 1, 1996in Statistics and Computing 1.85
José C. Pinheiro3
Estimated H-index: 3
(University of Wisconsin-Madison),
Douglas M. Bates26
Estimated H-index: 26
(University of Wisconsin-Madison)
The estimation of variance-covariance matrices through optimization of an objective function, such as a log-likelihood function, is usually a difficult numerical problem. Since the estimates should be positive semi-definite matrices, we must use constrained optimization, or employ a parametrization that enforces this condition. We describe here five different parametrizations for variance-covariance matrices that ensure positive definiteness, thus leaving the estimation problem unconstrained. We...
240 Citations Source Cite
Published on Dec 18, 2006
Andrew Gelman68
Estimated H-index: 68
(Columbia University),
Yu-Sung Su9
Estimated H-index: 9
Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied r...
5,349 Citations
Published on Sep 1, 1997in Biometrics 1.52
Michael G. Kenward52
Estimated H-index: 52
,
James H. Roger8
Estimated H-index: 8
Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distr...
2,380 Citations Source Cite
Published on Sep 1, 1982in Biometrics 1.52
Charles R. Henderson38
Estimated H-index: 38
The model generally considered in analysis of covariance has all levels of classification factors and interactions fixed, and also covariate regression coefficients fixed. Mixed models are more appropriate in most applications. A summary of estimation and hypothesis testing for analysis of covariance in the mixed model, including the case of random regression coefficients, is presented. Higher-level covariate regressions (i.e., regressions in which, for all levels of a factor or interaction, all...
150 Citations Source Cite
  • References (33)
  • Citations (9970)
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Cited By9970
Published on Aug 1, 2015in Behavioral Ecology and Sociobiology 2.47
Chi-Hang Yuen5
Estimated H-index: 5
(University of the Witwatersrand),
Neville Pillay22
Estimated H-index: 22
(University of the Witwatersrand)
+ 2 AuthorsCarsten Schradin27
Estimated H-index: 27
The development and persistence of personality in nature are counterintuitivebecause,in heterogeneous environ- ments, personality is expected to limit the degree of behav- ioural flexibility. Recent work has shown that personality and behavioural flexibility might be linked, but their interaction is not well understood and could be elucidated by studying a socially flexible species. Using well-established tests, we measured the personality traits of activity, boldness, explora- tion and aggressi...
11 Citations Source Cite
Published on Jun 1, 2017in Functional Ecology 5.49
Martin I. Lind11
Estimated H-index: 11
(Uppsala University),
Hwei-yen Chen4
Estimated H-index: 4
(Uppsala University)
+ 6 AuthorsAlexei A. Maklakov18
Estimated H-index: 18
(University of East Anglia)
Summary Life-history theory predicts a trade-off between early-life fitness and life span. While the focus traditionally has been on the fecundity-life span trade-off, there are strong reasons to expect trade-offs with growth rate and/or development time. We investigated the roles of growth rate and development time in the evolution of life span in two independent selection experiments in the outcrossing nematode Caenorhabditis remanei. First, we found that selection under heat-shock leads to th...
7 Citations Source Cite
Published on Dec 17, 2013
Ken Aho6
Estimated H-index: 6
FOUNDATIONS Philosophical and Historical Foundations Introduction Nature of Science Scientific Principles Scientific Method Scientific Hypotheses Logic Variability and Uncertainty in Investigations Science and Statistics Statistics and Biology Introduction to Probability Introduction: Models for Random Variables Classical Probability Conditional Probability Odds Combinatorial Analysis Bayes Rule Probability Density Functions Introduction Introductory Examples of pdfs Other Important Distribution...
23 Citations
Published on Oct 1, 2015in Physiology & Behavior 2.52
Wolfgang Goymann30
Estimated H-index: 30
(Max Planck Society),
Camila Patricia Villavicencio5
Estimated H-index: 5
(Max Planck Society),
Beate A. Apfelbeck8
Estimated H-index: 8
(Max Planck Society)
In this study, we describe an approach based on an individual's hormonal reactive scope to study short-term effects of hormones on behavior. The control of territorial aggression has been traditionally linked to testosterone. Males of some vertebrate species show an increase in testosterone during territorial interactions and implantation studies suggest that such an increase in testosterone enhances the intensity and persistence of aggression. Here, we tested whether a short-term maximum releas...
14 Citations Source Cite
Published on Oct 1, 2016in arXiv: Methodology
Tanner Sorensen3
Estimated H-index: 3
,
Sven Hohenstein7
Estimated H-index: 7
,
Shravan Vasishth21
Estimated H-index: 21
With the arrival of the R packages nlme and lme4, linear mixed models (LMMs) have come to be widely used in experimentally-driven areas like psychology, linguistics, and cognitive science. This tutorial provides a practical introduction to fitting LMMs in a Bayesian framework using the probabilistic programming language Stan. We choose Stan (rather than WinBUGS or JAGS) because it provides an elegant and scalable framework for fitting models in most of the standard applications of LMMs. We ease ...
35 Citations Source Cite
Published on Jan 1, 2016in Journal of Arid Environments 1.99
Natasha N. Woods2
Estimated H-index: 2
(Ohio State University),
Maria N. Miriti10
Estimated H-index: 10
(Ohio State University)
Abstract We present results from a study that examines species-specific facilitation of germination in an arid perennial community. This system suffered 64% adult mortality and the local extinction of two common species as a consequence of drought that occurred between 1999 and 2004. Ambrosia dumosa , Larrea tridentata , and Tetracoccus hallii are included as candidate benefactor species based on their high abundance and broad distribution at the study site. Using complementary field and greenho...
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Published on Dec 1, 2016in G3: Genes, Genomes, Genetics 2.74
Robert M. Griffin4
Estimated H-index: 4
(Uppsala University),
Holger Schielzeth25
Estimated H-index: 25
(Bielefeld University),
Urban Friberg18
Estimated H-index: 18
(Linköping University)
Theory makes several predictions concerning differences in genetic variation between the X chromosome and the autosomes due to male X hemizygosity. The X chromosome should: (i) typically show relatively less standing genetic variation than the autosomes, (ii) exhibit more variation in males compared to females because of dosage compensation, and (iii) potentially be enriched with sex-specific genetic variation. Here, we address each of these predictions for lifespan and aging in Drosophila melan...
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Published on Aug 1, 2015in Molecular Breeding 2.08
Brandon Schlautman6
Estimated H-index: 6
(University of Wisconsin-Madison),
Giovanny Covarrubias-Pazaran5
Estimated H-index: 5
(University of Wisconsin-Madison)
+ 10 AuthorsShawn A. Steffan17
Estimated H-index: 17
(University of Wisconsin-Madison)
Since its domestication 200 years ago, breeding of the American cranberry (Vaccinium macrocarpon) has relied on phenotypic selection because applicable resources for molecular improvement strategies such as marker-assisted selection (MAS) remain limited. To enable MAS in cranberry, the first high-density SSR linkage map with 541 markers representing all 12 cranberry chromosomes was constructed for the CNJ02-1 progeny from a cross of elite cultivars, CNJ97-105-4 and NJ98-23. The population was ph...
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Published on Oct 1, 2015in Journal of contextual behavioral science
Kevin Haworth3
Estimated H-index: 3
(University of Wisconsin–Milwaukee),
Jonathan W. Kanter29
Estimated H-index: 29
(University of Washington)
+ 3 AuthorsRobert J. Kohlenberg25
Estimated H-index: 25
(University of Washington)
Abstract A therapeutic model of social connection derived from Functional Analytic Psychotherapy (FAP) that applies to both the client’s outside-of-therapy relationships and the psychotherapeutic relationship is explored in two studies. The model integrates established behavioral principles with existing research on the reciprocal process of self-disclosure and responsiveness that occurs during development of intimate relationships to highlight a promising therapeutic process. In this process, s...
49 Citations Source Cite
Published on Jan 1, 2017in Animal Production Science 1.37
Joshua N Philp3
Estimated H-index: 3
(University of Sydney),
Adam M. Komarek7
Estimated H-index: 7
(University of Sydney)
+ 1 AuthorsWilliam Bellotti (University of Sydney)
Small mixed farming systems in developing economies often rely on compensatory growth to recover livestock weight lost during seasonal feed shortages; however, deficit feed management may continue to affect the capacity of livestock to efficiently use feeds even after adequate feeding has resumed. Accordingly, we compared the difference in liveweight gain and feed utilisation over time in Tan weaner sheep in western China, during a period of ad libitum compensatory feeding after alternative feed...
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