Evaluating significance in linear mixed-effects models in R

Mixed-effects models are being used ever more frequently in the analysis of experimental data. However, in the lme4 package in R the standards for evaluating significance of fixed effects in these models (i.e., obtaining p -values) are somewhat vague. There are good reasons for this, but as research...

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Veröffentlicht in:	Behavior research methods Jg. 49; H. 4; S. 1494 - 1502
1. Verfasser:	Luke, Steven G.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.08.2017
Schlagworte:	Behavioral Science and Psychology Cognitive Psychology Humans Linear Models Psychology Sample Size Statistics as Topic Type 1 error lme4 Linear mixed-effects models Statistics values p-values
ISSN:	1554-3528, 1554-3528
Online-Zugang:	Volltext
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Abstract	Mixed-effects models are being used ever more frequently in the analysis of experimental data. However, in the lme4 package in R the standards for evaluating significance of fixed effects in these models (i.e., obtaining p -values) are somewhat vague. There are good reasons for this, but as researchers who are using these models are required in many cases to report p -values, some method for evaluating the significance of the model output is needed. This paper reports the results of simulations showing that the two most common methods for evaluating significance, using likelihood ratio tests and applying the z distribution to the Wald t values from the model output ( t -as- z ), are somewhat anti-conservative, especially for smaller sample sizes. Other methods for evaluating significance, including parametric bootstrapping and the Kenward-Roger and Satterthwaite approximations for degrees of freedom, were also evaluated. The results of these simulations suggest that Type 1 error rates are closest to .05 when models are fitted using REML and p -values are derived using the Kenward-Roger or Satterthwaite approximations, as these approximations both produced acceptable Type 1 error rates even for smaller samples.
AbstractList	Mixed-effects models are being used ever more frequently in the analysis of experimental data. However, in the lme4 package in R the standards for evaluating significance of fixed effects in these models (i.e., obtaining p-values) are somewhat vague. There are good reasons for this, but as researchers who are using these models are required in many cases to report p-values, some method for evaluating the significance of the model output is needed. This paper reports the results of simulations showing that the two most common methods for evaluating significance, using likelihood ratio tests and applying the z distribution to the Wald t values from the model output (t-as-z), are somewhat anti-conservative, especially for smaller sample sizes. Other methods for evaluating significance, including parametric bootstrapping and the Kenward-Roger and Satterthwaite approximations for degrees of freedom, were also evaluated. The results of these simulations suggest that Type 1 error rates are closest to .05 when models are fitted using REML and p-values are derived using the Kenward-Roger or Satterthwaite approximations, as these approximations both produced acceptable Type 1 error rates even for smaller samples. Mixed-effects models are being used ever more frequently in the analysis of experimental data. However, in the lme4 package in R the standards for evaluating significance of fixed effects in these models (i.e., obtaining p -values) are somewhat vague. There are good reasons for this, but as researchers who are using these models are required in many cases to report p -values, some method for evaluating the significance of the model output is needed. This paper reports the results of simulations showing that the two most common methods for evaluating significance, using likelihood ratio tests and applying the z distribution to the Wald t values from the model output ( t -as- z ), are somewhat anti-conservative, especially for smaller sample sizes. Other methods for evaluating significance, including parametric bootstrapping and the Kenward-Roger and Satterthwaite approximations for degrees of freedom, were also evaluated. The results of these simulations suggest that Type 1 error rates are closest to .05 when models are fitted using REML and p -values are derived using the Kenward-Roger or Satterthwaite approximations, as these approximations both produced acceptable Type 1 error rates even for smaller samples.
Author	Luke, Steven G.
Author_xml	– sequence: 1 givenname: Steven G. surname: Luke fullname: Luke, Steven G. email: steven_luke@byu.edu organization: Department of Psychology, Brigham Young University
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/27620283$$D View this record in MEDLINE/PubMed
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References	Barr, Levy, Scheepers, Tily (CR2) 2013; 68 CR4 CR6 CR5 CR8 CR7 CR9 Satterthwaite (CR12) 1941; 6 Schaalje, McBride, Fellingham (CR13) 2002; 7 CR14 Bates, Mächler, Bolker, Walker (CR3) 2015; 67 CR11 Stroup (CR15) 2015; 107 Westfall, Kenny, Judd (CR16) 2014; 143 (CR10) 2015 Baayen, Davidson, Bates (CR1) 2008; 59 DJ Barr (809_CR2) 2013; 68 FE Satterthwaite (809_CR12) 1941; 6 809_CR11 J Westfall (809_CR16) 2014; 143 R Core Team (809_CR10) 2015 D Bates (809_CR3) 2015; 67 GB Schaalje (809_CR13) 2002; 7 WW Stroup (809_CR15) 2015; 107 809_CR4 809_CR9 RH Baayen (809_CR1) 2008; 59 809_CR14 809_CR6 809_CR5 809_CR8 809_CR7
References_xml	– volume: 6 start-page: 309 issue: 5 year: 1941 end-page: 316 ident: CR12 article-title: Synthesis of variance publication-title: Psychometrika doi: 10.1007/BF02288586 – year: 2015 ident: CR10 publication-title: R: A Language and Environment for Statistical Computing (Version 3.2.2) – volume: 67 start-page: 1 issue: 1 year: 2015 end-page: 48 ident: CR3 article-title: Fitting linear mixed-effects models using lme4 publication-title: Journal of Statistical Software doi: 10.18637/jss.v067.i01 – volume: 107 start-page: 811 issue: 2 year: 2015 end-page: 827 ident: CR15 article-title: Rethinking the analysis of non-normal data in plant and soil science publication-title: Agronomy Journal doi: 10.2134/agronj2013.0342 – ident: CR4 – ident: CR14 – volume: 7 start-page: 512 issue: 4 year: 2002 end-page: 524 ident: CR13 article-title: Adequacy of approximations to distributions of test statistics in complex mixed linear models publication-title: Journal of Agricultural, Biological, and Environmental Statistics doi: 10.1198/108571102726 – volume: 59 start-page: 390 issue: 4 year: 2008 end-page: 412 ident: CR1 article-title: Mixed-effects modeling with crossed random effects for subjects and items publication-title: Journal of Memory and Language doi: 10.1016/j.jml.2007.12.005 – volume: 68 start-page: 255 issue: 3 year: 2013 end-page: 278 ident: CR2 article-title: Random effects structure for confirmatory hypothesis testing: Keep it maximal publication-title: Journal of Memory and Language doi: 10.1016/j.jml.2012.11.001 – ident: CR11 – ident: CR9 – ident: CR6 – ident: CR5 – ident: CR7 – ident: CR8 – volume: 143 start-page: 2020 issue: 5 year: 2014 ident: CR16 article-title: Statistical power and optimal design in experiments in which samples of participants respond to samples of stimuli publication-title: Journal of Experimental Psychology: General doi: 10.1037/xge0000014 – ident: 809_CR4 – ident: 809_CR14 – ident: 809_CR6 – ident: 809_CR7 doi: 10.2307/2533558 – volume: 7 start-page: 512 issue: 4 year: 2002 ident: 809_CR13 publication-title: Journal of Agricultural, Biological, and Environmental Statistics doi: 10.1198/108571102726 – volume: 59 start-page: 390 issue: 4 year: 2008 ident: 809_CR1 publication-title: Journal of Memory and Language doi: 10.1016/j.jml.2007.12.005 – volume: 6 start-page: 309 issue: 5 year: 1941 ident: 809_CR12 publication-title: Psychometrika doi: 10.1007/BF02288586 – ident: 809_CR5 doi: 10.1214/ss/1009213286 – volume: 67 start-page: 1 issue: 1 year: 2015 ident: 809_CR3 publication-title: Journal of Statistical Software doi: 10.18637/jss.v067.i01 – volume: 68 start-page: 255 issue: 3 year: 2013 ident: 809_CR2 publication-title: Journal of Memory and Language doi: 10.1016/j.jml.2012.11.001 – volume-title: R: A Language and Environment for Statistical Computing (Version 3.2.2) year: 2015 ident: 809_CR10 – volume: 143 start-page: 2020 issue: 5 year: 2014 ident: 809_CR16 publication-title: Journal of Experimental Psychology: General doi: 10.1037/xge0000014 – volume: 107 start-page: 811 issue: 2 year: 2015 ident: 809_CR15 publication-title: Agronomy Journal doi: 10.2134/agronj2013.0342 – ident: 809_CR9 doi: 10.1007/978-1-4419-0318-1 – ident: 809_CR8 – ident: 809_CR11
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SubjectTerms	Behavioral Science and Psychology Cognitive Psychology Humans Linear Models Psychology Sample Size Statistics as Topic
Title	Evaluating significance in linear mixed-effects models in R
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