├── vignettes ├── .gitignore ├── sims │ ├── ext_sims_2.csv │ └── binomial.csv ├── r-references.bib ├── bibliography.bib ├── appendix3a_binomial.Rmd └── appendix1c_sensitivity.Rmd ├── inst ├── paper │ ├── 01.AMPSS_LMEM_cache │ │ ├── html │ │ │ ├── sim_beafc272da0ce5a03f1702bf7552cad5.rdb │ │ │ ├── sim_beafc272da0ce5a03f1702bf7552cad5.rdx │ │ │ ├── sim_beafc272da0ce5a03f1702bf7552cad5.RData │ │ │ └── __packages │ │ └── latex │ │ │ └── __packages │ ├── images │ │ ├── orcid.png │ │ ├── sim-items-1.pdf │ │ ├── sim-items-1.png │ │ ├── sim-subjects-1.pdf │ │ └── sim-subjects-1.png │ ├── 01.AMPSS_LMEM.docx │ ├── 01.AMPSS_LMEM.pdf │ ├── Makefile │ ├── r-references.bib │ └── bibliography.bib ├── app │ ├── main_tab.R │ ├── R │ │ ├── plot_funcs.R │ │ ├── data_funcs.R │ │ ├── lmer_funcs.R │ │ └── misc_funcs.R │ ├── comp_tab.R │ ├── power_tab.R │ ├── www │ │ └── custom.css │ └── intro_tab.R ├── CITATION └── appendices │ ├── appendix3a_binomial.Rmd │ └── appendix1c_sensitivity.Rmd ├── NAMESPACE ├── .gitignore ├── .Rbuildignore ├── docs ├── articles │ ├── appendix3a_binomial_files │ │ ├── figure-html │ │ │ └── unnamed-chunk-2-1.png │ │ ├── header-attrs-2.7 │ │ │ └── header-attrs.js │ │ └── accessible-code-block-0.0.1 │ │ │ └── empty-anchor.js │ ├── appendix1a_example_code_files │ │ ├── figure-html │ │ │ └── unnamed-chunk-8-1.png │ │ ├── header-attrs-2.7 │ │ │ └── header-attrs.js │ │ └── accessible-code-block-0.0.1 │ │ │ └── empty-anchor.js │ ├── appendix1b_example_code_files │ │ ├── figure-html │ │ │ └── unnamed-chunk-7-1.png │ │ ├── header-attrs-2.7 │ │ │ └── header-attrs.js │ │ └── accessible-code-block-0.0.1 │ │ │ └── empty-anchor.js │ ├── appendix1c_sensitivity_files │ │ ├── figure-html │ │ │ ├── unnamed-chunk-12-1.png │ │ │ ├── unnamed-chunk-6-1.png │ │ │ └── unnamed-chunk-9-1.png │ │ ├── header-attrs-2.7 │ │ │ └── header-attrs.js │ │ └── accessible-code-block-0.0.1 │ │ │ └── empty-anchor.js │ ├── appendix2_extended_example_files │ │ ├── figure-html │ │ │ ├── unnamed-chunk-3-1.png │ │ │ ├── unnamed-chunk-4-1.png │ │ │ ├── unnamed-chunk-9-1.png │ │ │ ├── unnamed-chunk-10-1.png │ │ │ └── unnamed-chunk-11-1.png │ │ ├── header-attrs-2.7 │ │ │ └── header-attrs.js │ │ └── accessible-code-block-0.0.1 │ │ │ └── empty-anchor.js │ ├── appendix3b_extended_binomial_files │ │ ├── figure-html │ │ │ ├── prob-vs-logit-1.png │ │ │ └── unnamed-chunk-2-1.png │ │ ├── header-attrs-2.7 │ │ │ └── header-attrs.js │ │ └── accessible-code-block-0.0.1 │ │ │ └── empty-anchor.js │ ├── paper_files │ │ ├── header-attrs-2.7 │ │ │ └── header-attrs.js │ │ └── accessible-code-block-0.0.1 │ │ │ └── empty-anchor.js │ └── index.html ├── pkgdown.yml ├── link.svg ├── bootstrap-toc.css ├── docsearch.js ├── pkgdown.js ├── bootstrap-toc.js ├── 404.html ├── reference │ ├── app.html │ ├── paper.html │ ├── index.html │ └── appendix.html ├── authors.html ├── pkgdown.css └── index.html ├── _pkgdown.yml ├── man ├── app.Rd ├── paper.Rd └── appendix.Rd ├── lmem_sim.Rproj ├── DESCRIPTION ├── R └── functions.R └── README.md /vignettes/.gitignore: -------------------------------------------------------------------------------- 1 | *.html 2 | *.R 3 | -------------------------------------------------------------------------------- /inst/paper/01.AMPSS_LMEM_cache/html/sim_beafc272da0ce5a03f1702bf7552cad5.rdb: -------------------------------------------------------------------------------- 1 | -------------------------------------------------------------------------------- /inst/paper/images/orcid.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/debruine/lmem_sim/HEAD/inst/paper/images/orcid.png -------------------------------------------------------------------------------- /inst/paper/01.AMPSS_LMEM.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/debruine/lmem_sim/HEAD/inst/paper/01.AMPSS_LMEM.docx 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/docs/articles/appendix3b_extended_binomial_files/figure-html/unnamed-chunk-2-1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/debruine/lmem_sim/HEAD/docs/articles/appendix3b_extended_binomial_files/figure-html/unnamed-chunk-2-1.png -------------------------------------------------------------------------------- /inst/paper/01.AMPSS_LMEM_cache/latex/__packages: -------------------------------------------------------------------------------- 1 | base 2 | papaja 3 | tidyverse 4 | ggplot2 5 | tibble 6 | tidyr 7 | readr 8 | purrr 9 | dplyr 10 | stringr 11 | forcats 12 | Matrix 13 | lme4 14 | lmerTest 15 | -------------------------------------------------------------------------------- /inst/paper/Makefile: -------------------------------------------------------------------------------- 1 | 01.AMPSS_LMEM.pdf : 01.AMPSS_LMEM.Rmd r-references.bib 2 | Rscript -e 'rmarkdown::render("01.AMPSS_LMEM.Rmd", papaja::apa6_pdf())' 3 | 4 | manuscript_code.R : 01.AMPSS_LMEM.Rmd 5 | Rscript -e 'knitr::purl("01.AMPSS_LMEM.Rmd", "manuscript_code.R")' 6 | -------------------------------------------------------------------------------- /inst/paper/01.AMPSS_LMEM_cache/html/__packages: -------------------------------------------------------------------------------- 1 | base 2 | methods 3 | datasets 4 | utils 5 | grDevices 6 | graphics 7 | stats 8 | papaja 9 | tidyverse 10 | ggplot2 11 | tibble 12 | tidyr 13 | readr 14 | purrr 15 | dplyr 16 | stringr 17 | forcats 18 | Matrix 19 | lme4 20 | lmerTest 21 | -------------------------------------------------------------------------------- /_pkgdown.yml: -------------------------------------------------------------------------------- 1 | articles: 2 | - title: Articles 3 | navbar: ~ 4 | contents: 5 | - paper 6 | - appendix1a_example_code 7 | - appendix1b_example_code 8 | - appendix1c_sensitivity 9 | - appendix2_extended_example 10 | - appendix3a_binomial 11 | - appendix3b_extended_binomial 12 | 13 | -------------------------------------------------------------------------------- /man/app.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/functions.R 3 | \name{app} 4 | \alias{app} 5 | \title{Launch Shiny App} 6 | \usage{ 7 | app(...) 8 | } 9 | \arguments{ 10 | \item{...}{arguments to pass to shiny::runApp} 11 | } 12 | \description{ 13 | Launch a local copy of the shiny app that accompanies Simulating LMEM 14 | } 15 | -------------------------------------------------------------------------------- /man/paper.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/functions.R 3 | \name{paper} 4 | \alias{paper} 5 | \title{Open Simulating LMEM paper} 6 | \usage{ 7 | paper(type = c("pdf", "html", "Rmd")) 8 | } 9 | \arguments{ 10 | \item{type}{The type of manuscript to open (pdf, html, or Rmd)} 11 | } 12 | \description{ 13 | Open the manuscript 14 | } 15 | -------------------------------------------------------------------------------- /lmem_sim.Rproj: -------------------------------------------------------------------------------- 1 | Version: 1.0 2 | 3 | RestoreWorkspace: Default 4 | SaveWorkspace: Default 5 | AlwaysSaveHistory: Default 6 | 7 | EnableCodeIndexing: Yes 8 | UseSpacesForTab: Yes 9 | NumSpacesForTab: 2 10 | Encoding: UTF-8 11 | 12 | RnwWeave: Sweave 13 | LaTeX: pdfLaTeX 14 | 15 | BuildType: Package 16 | PackageUseDevtools: Yes 17 | PackageInstallArgs: --no-multiarch --with-keep.source 18 | -------------------------------------------------------------------------------- /man/appendix.Rd: -------------------------------------------------------------------------------- 1 | % Generated by roxygen2: do not edit by hand 2 | % Please edit documentation in R/functions.R 3 | \name{appendix} 4 | \alias{appendix} 5 | \title{Open Simulating LMEM appendices} 6 | \usage{ 7 | appendix(i = c("1a", "1b", "1c", "2", "3a", "3b"), filename = NULL) 8 | } 9 | \arguments{ 10 | \item{i}{Which appendix to open} 11 | 12 | \item{filename}{Where to save the appendix} 13 | } 14 | \description{ 15 | Open Simulating LMEM appendices 16 | } 17 | -------------------------------------------------------------------------------- /inst/app/main_tab.R: -------------------------------------------------------------------------------- 1 | ### main_tab ---- 2 | main_tab <- tabItem( 3 | tabName = "main_tab", 4 | fluidRow( 5 | box( 6 | title = "Overview", 7 | #title = "Output from broom.mixed::tidy(lmerMod)", 8 | width = 12, 9 | tableOutput("broom_output") 10 | ) 11 | ), 12 | fluidRow( 13 | box( 14 | title = "Output from summary(lmerMod)", 15 | width = 12, 16 | htmlOutput("lmer_output") 17 | ) 18 | ) 19 | ) 20 | 21 | -------------------------------------------------------------------------------- /docs/articles/paper_files/header-attrs-2.7/header-attrs.js: -------------------------------------------------------------------------------- 1 | // Pandoc 2.9 adds attributes on both header and div. We remove the former (to 2 | // be compatible with the behavior of Pandoc < 2.8). 3 | document.addEventListener('DOMContentLoaded', function(e) { 4 | var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); 5 | var i, h, a; 6 | for (i = 0; i < hs.length; i++) { 7 | h = hs[i]; 8 | if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 9 | a = h.attributes; 10 | while (a.length > 0) h.removeAttribute(a[0].name); 11 | } 12 | }); 13 | -------------------------------------------------------------------------------- /docs/articles/appendix1c_sensitivity_files/header-attrs-2.7/header-attrs.js: -------------------------------------------------------------------------------- 1 | // Pandoc 2.9 adds attributes on both header and div. We remove the former (to 2 | // be compatible with the behavior of Pandoc < 2.8). 3 | document.addEventListener('DOMContentLoaded', function(e) { 4 | var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); 5 | var i, h, a; 6 | for (i = 0; i < hs.length; i++) { 7 | h = hs[i]; 8 | if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 9 | a = h.attributes; 10 | while (a.length > 0) h.removeAttribute(a[0].name); 11 | } 12 | }); 13 | -------------------------------------------------------------------------------- /docs/articles/appendix3a_binomial_files/header-attrs-2.7/header-attrs.js: -------------------------------------------------------------------------------- 1 | // Pandoc 2.9 adds attributes on both header and div. We remove the former (to 2 | // be compatible with the behavior of Pandoc < 2.8). 3 | document.addEventListener('DOMContentLoaded', function(e) { 4 | var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); 5 | var i, h, a; 6 | for (i = 0; i < hs.length; i++) { 7 | h = hs[i]; 8 | if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 9 | a = h.attributes; 10 | while (a.length > 0) h.removeAttribute(a[0].name); 11 | } 12 | }); 13 | -------------------------------------------------------------------------------- /docs/articles/appendix1a_example_code_files/header-attrs-2.7/header-attrs.js: -------------------------------------------------------------------------------- 1 | // Pandoc 2.9 adds attributes on both header and div. We remove the former (to 2 | // be compatible with the behavior of Pandoc < 2.8). 3 | document.addEventListener('DOMContentLoaded', function(e) { 4 | var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); 5 | var i, h, a; 6 | for (i = 0; i < hs.length; i++) { 7 | h = hs[i]; 8 | if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 9 | a = h.attributes; 10 | while (a.length > 0) h.removeAttribute(a[0].name); 11 | } 12 | }); 13 | -------------------------------------------------------------------------------- /docs/articles/appendix1b_example_code_files/header-attrs-2.7/header-attrs.js: -------------------------------------------------------------------------------- 1 | // Pandoc 2.9 adds attributes on both header and div. We remove the former (to 2 | // be compatible with the behavior of Pandoc < 2.8). 3 | document.addEventListener('DOMContentLoaded', function(e) { 4 | var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); 5 | var i, h, a; 6 | for (i = 0; i < hs.length; i++) { 7 | h = hs[i]; 8 | if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 9 | a = h.attributes; 10 | while (a.length > 0) h.removeAttribute(a[0].name); 11 | } 12 | }); 13 | -------------------------------------------------------------------------------- /docs/articles/appendix2_extended_example_files/header-attrs-2.7/header-attrs.js: -------------------------------------------------------------------------------- 1 | // Pandoc 2.9 adds attributes on both header and div. We remove the former (to 2 | // be compatible with the behavior of Pandoc < 2.8). 3 | document.addEventListener('DOMContentLoaded', function(e) { 4 | var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); 5 | var i, h, a; 6 | for (i = 0; i < hs.length; i++) { 7 | h = hs[i]; 8 | if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 9 | a = h.attributes; 10 | while (a.length > 0) h.removeAttribute(a[0].name); 11 | } 12 | }); 13 | -------------------------------------------------------------------------------- /docs/articles/appendix3b_extended_binomial_files/header-attrs-2.7/header-attrs.js: -------------------------------------------------------------------------------- 1 | // Pandoc 2.9 adds attributes on both header and div. We remove the former (to 2 | // be compatible with the behavior of Pandoc < 2.8). 3 | document.addEventListener('DOMContentLoaded', function(e) { 4 | var hs = document.querySelectorAll("div.section[class*='level'] > :first-child"); 5 | var i, h, a; 6 | for (i = 0; i < hs.length; i++) { 7 | h = hs[i]; 8 | if (!/^h[1-6]$/i.test(h.tagName)) continue; // it should be a header h1-h6 9 | a = h.attributes; 10 | while (a.length > 0) h.removeAttribute(a[0].name); 11 | } 12 | }); 13 | -------------------------------------------------------------------------------- /docs/pkgdown.yml: -------------------------------------------------------------------------------- 1 | pandoc: '2.13' 2 | pkgdown: 1.6.1 3 | pkgdown_sha: ~ 4 | articles: 5 | appendix1a_example_code: appendix1a_example_code.html 6 | appendix1b_example_code: appendix1b_example_code.html 7 | appendix1c_sensitivity: appendix1c_sensitivity.html 8 | appendix2_extended_example: appendix2_extended_example.html 9 | appendix3a_binomial: appendix3a_binomial.html 10 | appendix3b_extended_binomial: appendix3b_extended_binomial.html 11 | appendix3b_treasurehunt: appendix3b_treasurehunt.html 12 | appendix3b_treasuremain: appendix3b_treasuremain.html 13 | paper: paper.html 14 | last_built: 2021-05-14T15:17Z 15 | 16 | -------------------------------------------------------------------------------- /inst/CITATION: -------------------------------------------------------------------------------- 1 | citHeader("To cite lmem.sim in publications use:") 2 | 3 | citEntry( 4 | entry = "Article", 5 | title = "Understanding mixed effects models through data simulation", 6 | author = "DeBruine, Lisa M. and Barr, Dale J.", 7 | doi = "10.1177/2515245920965119", 8 | journal = "Advances in Methods and Practices in Psychological Science", 9 | volume = "4", 10 | number = "1", 11 | pages = "2515245920965119", 12 | year = "2021", 13 | url = "https://debruine.github.io/lmem_sim/", 14 | textVersion = paste("DeBruine, L. M., & Barr, D. J. (2021). Understanding mixed effects models through data simulation. Advances in Methods and Practices in Psychological Science. https://doi.org/10.1177/2515245920965119") 15 | ) 16 | -------------------------------------------------------------------------------- /docs/articles/paper_files/accessible-code-block-0.0.1/empty-anchor.js: -------------------------------------------------------------------------------- 1 | // Hide empty tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> 2 | // v0.0.1 3 | // Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. 4 | 5 | document.addEventListener('DOMContentLoaded', function() { 6 | const codeList = document.getElementsByClassName("sourceCode"); 7 | for (var i = 0; i < codeList.length; i++) { 8 | var linkList = codeList[i].getElementsByTagName('a'); 9 | for (var j = 0; j < linkList.length; j++) { 10 | if (linkList[j].innerHTML === "") { 11 | linkList[j].setAttribute('aria-hidden', 'true'); 12 | } 13 | } 14 | } 15 | }); 16 | -------------------------------------------------------------------------------- /docs/articles/appendix3a_binomial_files/accessible-code-block-0.0.1/empty-anchor.js: -------------------------------------------------------------------------------- 1 | // Hide empty tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> 2 | // v0.0.1 3 | // Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. 4 | 5 | document.addEventListener('DOMContentLoaded', function() { 6 | const codeList = document.getElementsByClassName("sourceCode"); 7 | for (var i = 0; i < codeList.length; i++) { 8 | var linkList = codeList[i].getElementsByTagName('a'); 9 | for (var j = 0; j < linkList.length; j++) { 10 | if (linkList[j].innerHTML === "") { 11 | linkList[j].setAttribute('aria-hidden', 'true'); 12 | } 13 | } 14 | } 15 | }); 16 | -------------------------------------------------------------------------------- /docs/articles/appendix1a_example_code_files/accessible-code-block-0.0.1/empty-anchor.js: -------------------------------------------------------------------------------- 1 | // Hide empty tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> 2 | // v0.0.1 3 | // Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. 4 | 5 | document.addEventListener('DOMContentLoaded', function() { 6 | const codeList = document.getElementsByClassName("sourceCode"); 7 | for (var i = 0; i < codeList.length; i++) { 8 | var linkList = codeList[i].getElementsByTagName('a'); 9 | for (var j = 0; j < linkList.length; j++) { 10 | if (linkList[j].innerHTML === "") { 11 | linkList[j].setAttribute('aria-hidden', 'true'); 12 | } 13 | } 14 | } 15 | }); 16 | -------------------------------------------------------------------------------- /docs/articles/appendix1b_example_code_files/accessible-code-block-0.0.1/empty-anchor.js: -------------------------------------------------------------------------------- 1 | // Hide empty tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> 2 | // v0.0.1 3 | // Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. 4 | 5 | document.addEventListener('DOMContentLoaded', function() { 6 | const codeList = document.getElementsByClassName("sourceCode"); 7 | for (var i = 0; i < codeList.length; i++) { 8 | var linkList = codeList[i].getElementsByTagName('a'); 9 | for (var j = 0; j < linkList.length; j++) { 10 | if (linkList[j].innerHTML === "") { 11 | linkList[j].setAttribute('aria-hidden', 'true'); 12 | } 13 | } 14 | } 15 | }); 16 | -------------------------------------------------------------------------------- /docs/articles/appendix1c_sensitivity_files/accessible-code-block-0.0.1/empty-anchor.js: -------------------------------------------------------------------------------- 1 | // Hide empty tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> 2 | // v0.0.1 3 | // Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. 4 | 5 | document.addEventListener('DOMContentLoaded', function() { 6 | const codeList = document.getElementsByClassName("sourceCode"); 7 | for (var i = 0; i < codeList.length; i++) { 8 | var linkList = codeList[i].getElementsByTagName('a'); 9 | for (var j = 0; j < linkList.length; j++) { 10 | if (linkList[j].innerHTML === "") { 11 | linkList[j].setAttribute('aria-hidden', 'true'); 12 | } 13 | } 14 | } 15 | }); 16 | -------------------------------------------------------------------------------- /docs/articles/appendix2_extended_example_files/accessible-code-block-0.0.1/empty-anchor.js: -------------------------------------------------------------------------------- 1 | // Hide empty tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> 2 | // v0.0.1 3 | // Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. 4 | 5 | document.addEventListener('DOMContentLoaded', function() { 6 | const codeList = document.getElementsByClassName("sourceCode"); 7 | for (var i = 0; i < codeList.length; i++) { 8 | var linkList = codeList[i].getElementsByTagName('a'); 9 | for (var j = 0; j < linkList.length; j++) { 10 | if (linkList[j].innerHTML === "") { 11 | linkList[j].setAttribute('aria-hidden', 'true'); 12 | } 13 | } 14 | } 15 | }); 16 | -------------------------------------------------------------------------------- /docs/articles/appendix3b_extended_binomial_files/accessible-code-block-0.0.1/empty-anchor.js: -------------------------------------------------------------------------------- 1 | // Hide empty tag within highlighted CodeBlock for screen reader accessibility (see https://github.com/jgm/pandoc/issues/6352#issuecomment-626106786) --> 2 | // v0.0.1 3 | // Written by JooYoung Seo (jooyoung@psu.edu) and Atsushi Yasumoto on June 1st, 2020. 4 | 5 | document.addEventListener('DOMContentLoaded', function() { 6 | const codeList = document.getElementsByClassName("sourceCode"); 7 | for (var i = 0; i < codeList.length; i++) { 8 | var linkList = codeList[i].getElementsByTagName('a'); 9 | for (var j = 0; j < linkList.length; j++) { 10 | if (linkList[j].innerHTML === "") { 11 | linkList[j].setAttribute('aria-hidden', 'true'); 12 | } 13 | } 14 | } 15 | }); 16 | -------------------------------------------------------------------------------- /docs/link.svg: -------------------------------------------------------------------------------- 1 | 2 | 3 | 5 | 8 | 12 | 13 | -------------------------------------------------------------------------------- /DESCRIPTION: -------------------------------------------------------------------------------- 1 | Package: lmem.sim 2 | Title: Simulating for LMEM 3 | Version: 0.0.0.9001 4 | Date: 2021-05-14 5 | Authors@R: c( 6 | person( 7 | given = "Lisa", 8 | family = "DeBruine", 9 | role = c("aut", "cre"), 10 | email = "debruine@gmail.com", 11 | comment = c(ORCID = "0000-0002-7523-5539") 12 | ), 13 | person( 14 | given = "Dale", 15 | family = "Barr", 16 | role = c("aut"), 17 | email = "dale.barr@glasgow.ac.uk", 18 | comment = c(ORCID = "0000-0002-1121-4608") 19 | )) 20 | Description: Additional resources for Understanding mixed effects models through data simulation . 21 | Depends: 22 | R (>= 3.2.4) 23 | Imports: 24 | dplyr, 25 | tidyr, 26 | purrr, 27 | ggplot2, 28 | afex, 29 | lme4, 30 | broom.mixed, 31 | faux, 32 | lmerTest 33 | Suggests: 34 | knitr, 35 | rmarkdown, 36 | papaja, 37 | shiny, 38 | shinydashboard, 39 | shinyjs, 40 | MASS 41 | Remotes: 42 | crsh/papaja 43 | VignetteBuilder: knitr 44 | RoxygenNote: 7.1.1 45 | Encoding: UTF-8 46 | LazyData: true 47 | URL: https://github.com/debruine/lmem_sim 48 | BugReports: https://github.com/debruine/lmem_sim/issues 49 | License: CC BY 4.0 50 | -------------------------------------------------------------------------------- /R/functions.R: -------------------------------------------------------------------------------- 1 | #' Launch Shiny App 2 | #' 3 | #' Launch a local copy of the shiny app that accompanies Simulating LMEM 4 | #' 5 | #' @param ... arguments to pass to shiny::runApp 6 | #' 7 | #' @export 8 | #' 9 | app <- function(...) { 10 | appDir <- system.file("app", package = "lmem.sim") 11 | shiny::runApp(appDir, ...) 12 | } 13 | 14 | #' Open Simulating LMEM paper 15 | #' 16 | #' Open the manuscript 17 | #' 18 | #' @param type The type of manuscript to open (pdf, html, or Rmd) 19 | #' 20 | #' @export 21 | #' 22 | paper <- function(type = c("pdf", "html", "Rmd")) { 23 | type <- match.arg(type) 24 | filename <- paste0("paper/01.AMPSS_LMEM.", type) 25 | f <- system.file(filename, package = "lmem.sim") 26 | browseURL(f) 27 | } 28 | 29 | #' Open Simulating LMEM appendices 30 | #' 31 | #' @param i Which appendix to open 32 | #' @param filename Where to save the appendix 33 | #' 34 | #' @export 35 | #' 36 | appendix <- function(i = c("1a", "1b", "1c", "2", "3a", "3b"), filename = NULL) { 37 | i <- match.arg(i) 38 | dir <- system.file("appendices/", package = "lmem.sim") 39 | files <- list.files(dir, ".Rmd", full.names = TRUE) 40 | n <- grepl(paste0("appendix", i), files) 41 | f <- files[n][[1]] 42 | 43 | if (is.null(filename)) filename <- basename(f) 44 | 45 | file.copy(f, filename) 46 | utils::browseURL(filename) 47 | } 48 | 49 | -------------------------------------------------------------------------------- /vignettes/sims/ext_sims_2.csv: -------------------------------------------------------------------------------- 1 | effect,group,term,estimate,std.error,statistic,df,p.value 2 | fixed,NA,(Intercept),800.1520312010771,10.824044905189528,73.92356907328134,238.64763132142974,1.774890900354849e-166 3 | fixed,NA,X_e,-8.143875258984634,7.000678457746131,-1.1632980014920662,137.371432463037,0.24672530227557052 4 | fixed,NA,X_c,56.143812618290205,10.028565572437712,5.598389142769792,192.69299139929353,7.368755336570842e-8 5 | fixed,NA,X_e:X_c,82.39589560789746,10.032571144314398,8.212839403046985,144.45383938260895,1.1076255072625297e-13 6 | ran_pars,subj_id,sd__(Intercept),102.19878574854683,NA,NA,NA,NA 7 | ran_pars,subj_id,cor__(Intercept).X_e,0.31318827449875714,NA,NA,NA,NA 8 | ran_pars,subj_id,cor__(Intercept).X_c,0.34871622889073606,NA,NA,NA,NA 9 | ran_pars,subj_id,cor__(Intercept).X_e:X_c,0.11156080618878045,NA,NA,NA,NA 10 | ran_pars,subj_id,sd__X_e,45.25860205339935,NA,NA,NA,NA 11 | ran_pars,subj_id,cor__X_e.X_c,0.2823068424164505,NA,NA,NA,NA 12 | ran_pars,subj_id,cor__X_e.X_e:X_c,0.11842738071053396,NA,NA,NA,NA 13 | ran_pars,subj_id,sd__X_c,85.14224221245728,NA,NA,NA,NA 14 | ran_pars,subj_id,cor__X_c.X_e:X_c,0.011528766388017453,NA,NA,NA,NA 15 | ran_pars,subj_id,sd__X_e:X_c,81.17459208550507,NA,NA,NA,NA 16 | ran_pars,item_id,sd__(Intercept),79.3118684387006,NA,NA,NA,NA 17 | ran_pars,item_id,cor__(Intercept).X_e,0.01632039800618323,NA,NA,NA,NA 18 | ran_pars,item_id,cor__(Intercept).X_c,0.38445920912737014,NA,NA,NA,NA 19 | ran_pars,item_id,cor__(Intercept).X_e:X_c,0.04121436179741903,NA,NA,NA,NA 20 | ran_pars,item_id,sd__X_e,55.34865518730321,NA,NA,NA,NA 21 | ran_pars,item_id,cor__X_e.X_c,0.1406742082999369,NA,NA,NA,NA 22 | ran_pars,item_id,cor__X_e.X_e:X_c,0.11506623132043559,NA,NA,NA,NA 23 | ran_pars,item_id,sd__X_c,74.96203248090238,NA,NA,NA,NA 24 | ran_pars,item_id,cor__X_c.X_e:X_c,0.17201202047210634,NA,NA,NA,NA 25 | ran_pars,item_id,sd__X_e:X_c,59.307404873047425,NA,NA,NA,NA 26 | ran_pars,Residual,sd__Observation,201.6563569439757,NA,NA,NA,NA 27 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Understanding mixed effects models through data simulation 2 | 3 | *Lisa M. DeBruine & Dale J. Barr* 4 | 5 | This repository contains all materials needed to reproduce the manuscript, as well as supplemental scripts and shiny apps. 6 | 7 | **Abstract** Experimental designs that sample both subjects and stimuli from a larger population need to account for random effects of both subjects and stimuli using mixed effects models. However, much of this research is analyzed using ANOVA on aggregated responses because researchers are not confident specifying and interpreting mixed effects models. The tutorial will explain how to simulate data with random effects structure and analyse the data using linear mixed effects regression (with the lme4 R package), with a focus on interpreting the output in light of the simulated parameters. Data simulation can not only enhance understanding of how these models work, but also enables researchers to perform power calculations for complex designs. 8 | 9 | 10 | * [AMPPS paper](https://doi.org/10.1177/2515245920965119) 11 | * [PsyArXiv preprint](https://psyarxiv.com/xp5cy) 12 | * [Example code](https://debruine.github.io/lmem_sim/articles/) 13 | * Shiny App [Simulating LMEM](https://shiny.psy.gla.ac.uk/lmem_sim/) 14 | * Shiny App [Crossed Random Effects](https://shiny.psy.gla.ac.uk/Dale/crossed/) 15 | 16 | ## Installation 17 | 18 | You can install the development version of a package that include all the packages you'll need for the examples, plus a local version of the shiny app, from [GitHub](https://github.com/debruine/lmem_sim) with: 19 | 20 | ``` r 21 | devtools::install_github("debruine/lmem_sim") 22 | ``` 23 | 24 | Here are some functions included in the app: 25 | 26 | ``` r 27 | lmem.sim::paper() # open the pdf version of the paper 28 | lmem.sim::paper("html") # open the html version of the paper 29 | lmem.sim::appendix("1a") # open appendix 1a 30 | lmem.sim::app() # start the app 31 | citation("lmem.sim") # get the citation 32 | ``` 33 | 34 | -------------------------------------------------------------------------------- /inst/app/R/plot_funcs.R: -------------------------------------------------------------------------------- 1 | plot_dat <- function(dat, b0 = 0, view = c("violin", "boxplot"), grp = "") { 2 | min_RT <- min(dat$RT) 3 | max_RT <- max(dat$RT) 4 | 5 | # aggregate over subjects or stimuli if grp is set 6 | if (grp == "subj") { 7 | dat <- dat %>% 8 | group_by(subj_id, category) %>% 9 | summarise(RT = mean(RT)) 10 | } else if (grp == "item") { 11 | dat <- dat %>% 12 | group_by(item_id, category) %>% 13 | summarise(RT = mean(RT)) 14 | } 15 | 16 | plot <- ggplot(dat, aes(category, RT, color = category)) + 17 | geom_hline(yintercept = b0) + 18 | xlab("Stimulus Type") + 19 | ylab("Rating") + 20 | scale_color_discrete(name = "Stimulus Type") + 21 | coord_cartesian(ylim = c(min_RT, max_RT)) + 22 | theme(legend.position="bottom") 23 | 24 | if ("violin" %in% view) { 25 | plot <- plot + geom_violin(alpha = 0.5, show.legend = FALSE) 26 | } 27 | 28 | if ("boxplot" %in% view) { 29 | plot <- plot + geom_boxplot(width = 0.2, show.legend = FALSE, 30 | position = position_dodge(width = 0.9)) 31 | } 32 | 33 | return(plot) 34 | } 35 | 36 | plot_power_lmer <- function(dat) { 37 | dat %>% 38 | filter(type == "power", analysis == "lmer") %>% 39 | mutate(analysis = recode(analysis, 40 | "lmer" = "LMER")) %>% 41 | filter(type == "power") %>% 42 | ggplot(aes(es)) + 43 | geom_density() + 44 | xlab("Effect Size (raw estimate)") + 45 | ggtitle("LMER") 46 | } 47 | 48 | plot_power_anova <- function(dat) { 49 | dat %>% 50 | filter(type == "power", analysis != "lmer") %>% 51 | mutate(analysis = recode(analysis, 52 | "anova_subj" = "By-Subjects ANOVA", 53 | "anova_item" = "By-Items ANOVA")) %>% 54 | ggplot(aes(es, color = analysis)) + 55 | geom_density(show.legend = TRUE) + 56 | xlab("Effect Size (Cohen's d)") + 57 | theme(legend.position="bottom") + 58 | ggtitle("ANOVAs") 59 | } -------------------------------------------------------------------------------- /inst/app/comp_tab.R: -------------------------------------------------------------------------------- 1 | ### comp_tab ---- 2 | comp_tab <- tabItem( 3 | tabName = "comp_tab", 4 | h3("Compare ANOVAs and LMER for an individual simulation"), 5 | fluidRow( 6 | box( 7 | title = "Descriptives", 8 | width = 8, 9 | tableOutput("descr_table") 10 | ), 11 | box( 12 | title = "Plot Type", 13 | width = 4, 14 | checkboxGroupInput( 15 | "dat_plot_view", 16 | "View:", 17 | c("violin" = "violin", 18 | "boxplot" = "boxplot"), 19 | selected = c("violin", "boxplot") 20 | ) 21 | ) 22 | ), 23 | fluidRow( 24 | column( 25 | width = 8, 26 | box( 27 | title = "By-Item ANOVA", 28 | width = NULL, 29 | tableOutput("item_coef") 30 | ) 31 | ), 32 | column( 33 | width = 4, 34 | box( 35 | title = "Aggregated by Items", 36 | width = NULL, 37 | plotOutput(outputId = "dat_item_plot", height = "auto") 38 | ) 39 | ) 40 | ), 41 | fluidRow( 42 | column( 43 | width = 8, 44 | box( 45 | title = "By-Subjects ANOVA", 46 | width = NULL, 47 | tableOutput("subj_coef") 48 | ) 49 | ), 50 | column( 51 | width = 4, 52 | box( 53 | title = "Aggregated by Subject", 54 | width = NULL, 55 | plotOutput(outputId = "dat_subj_plot", height = "auto") 56 | ) 57 | ) 58 | ), 59 | fluidRow( 60 | column( 61 | width = 8, 62 | box( 63 | title = "LMER", 64 | width = NULL, 65 | p("The p-value for the main effect in LMER will be near-identical to the by-stimuli ANOVA if the random slope for the main effect is set to zero (i.e., where between-subject variation in the effect of stimulus type is 0)."), 66 | tableOutput("lmer_coef") 67 | ) 68 | ), 69 | column( 70 | width = 4, 71 | box( 72 | title = "Not Aggregated", 73 | width = NULL, 74 | plotOutput(outputId = "dat_plot", height = "auto") 75 | ) 76 | ) 77 | ) 78 | ) 79 | -------------------------------------------------------------------------------- /docs/bootstrap-toc.css: -------------------------------------------------------------------------------- 1 | /*! 2 | * Bootstrap Table of Contents v0.4.1 (http://afeld.github.io/bootstrap-toc/) 3 | * Copyright 2015 Aidan Feldman 4 | * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */ 5 | 6 | /* modified from https://github.com/twbs/bootstrap/blob/94b4076dd2efba9af71f0b18d4ee4b163aa9e0dd/docs/assets/css/src/docs.css#L548-L601 */ 7 | 8 | /* All levels of nav */ 9 | nav[data-toggle='toc'] .nav > li > a { 10 | display: block; 11 | padding: 4px 20px; 12 | font-size: 13px; 13 | font-weight: 500; 14 | color: #767676; 15 | } 16 | nav[data-toggle='toc'] .nav > li > a:hover, 17 | nav[data-toggle='toc'] .nav > li > a:focus { 18 | padding-left: 19px; 19 | color: #563d7c; 20 | text-decoration: none; 21 | background-color: transparent; 22 | border-left: 1px solid #563d7c; 23 | } 24 | nav[data-toggle='toc'] .nav > .active > a, 25 | nav[data-toggle='toc'] .nav > .active:hover > a, 26 | nav[data-toggle='toc'] .nav > .active:focus > a { 27 | padding-left: 18px; 28 | font-weight: bold; 29 | color: #563d7c; 30 | background-color: transparent; 31 | border-left: 2px solid #563d7c; 32 | } 33 | 34 | /* Nav: second level (shown on .active) */ 35 | nav[data-toggle='toc'] .nav .nav { 36 | display: none; /* Hide by default, but at >768px, show it */ 37 | padding-bottom: 10px; 38 | } 39 | nav[data-toggle='toc'] .nav .nav > li > a { 40 | padding-top: 1px; 41 | padding-bottom: 1px; 42 | padding-left: 30px; 43 | font-size: 12px; 44 | font-weight: normal; 45 | } 46 | nav[data-toggle='toc'] .nav .nav > li > a:hover, 47 | nav[data-toggle='toc'] .nav .nav > li > a:focus { 48 | padding-left: 29px; 49 | } 50 | nav[data-toggle='toc'] .nav .nav > .active > a, 51 | nav[data-toggle='toc'] .nav .nav > .active:hover > a, 52 | nav[data-toggle='toc'] .nav .nav > .active:focus > a { 53 | padding-left: 28px; 54 | font-weight: 500; 55 | } 56 | 57 | /* from https://github.com/twbs/bootstrap/blob/e38f066d8c203c3e032da0ff23cd2d6098ee2dd6/docs/assets/css/src/docs.css#L631-L634 */ 58 | nav[data-toggle='toc'] .nav > .active > ul { 59 | display: block; 60 | } 61 | -------------------------------------------------------------------------------- /inst/app/power_tab.R: -------------------------------------------------------------------------------- 1 | ### power_tab ---- 2 | power_tab <- tabItem( 3 | tabName = "power_tab", 4 | h3("Compare False Positive Rate and Power"), 5 | p("This function will run the number of simulations with the parameters you've set and report the proportion of runs that gave a significant effect of condition (given the alpha you set). It will also report the false positive rate for the same simulations with the main effect of condition set to 0. If you set the main effect of condition to 0, then power will be equal to the false positive rate."), 6 | fluidRow( 7 | column( 8 | width = 4, 9 | actionButton("calc_power", "Calculate"), 10 | sliderInput("n_reps", "Number of Simulations to Run:", 11 | min = 10, max = 100, value = 10, step = 10), 12 | sliderInput("alpha", "(Justify Your) Alpha", 13 | min = .005, max = .100, value = 0.05, step = 0.005) 14 | ), 15 | column( 16 | width = 8, 17 | title = "False Positive/Power Calculations", 18 | tableOutput("power_table") 19 | ) 20 | ), 21 | p("It is not an error that the false positive rate for the by-subjects ANOVA is very high. With this type of within-subjects, between-items design, you can get very high false positive rates if items have some variation in their mean DV (i.e., where faces tend to vary in expressiveness). For this type of design (no between-subject factors), the by-items ANOVA will have a closer-to-nominal false positive rate, but will have a more inflated false positive rate for designs with between-subject factors where subjects have some random variation in their mean repsonses."), 22 | p("If you set the Item Intercept SD to 0, you will see that the by-subjects ANOVA has a false positive rate closer to the nominal alpha (defaults to 0.05). However, this models a very unrealistic situation where the variation in expressiveness of faces is 0."), 23 | h4("Simulated Effect Size Distribution"), 24 | fluidRow( 25 | column( 26 | width = 6, 27 | plotOutput(outputId = "power_plot_anova", height = "auto") 28 | ), 29 | column( 30 | width = 6, 31 | plotOutput(outputId = "power_plot_lmer", height = "auto") 32 | ) 33 | ) 34 | ) 35 | -------------------------------------------------------------------------------- /docs/docsearch.js: -------------------------------------------------------------------------------- 1 | $(function() { 2 | 3 | // register a handler to move the focus to the search bar 4 | // upon pressing shift + "/" (i.e. "?") 5 | $(document).on('keydown', function(e) { 6 | if (e.shiftKey && e.keyCode == 191) { 7 | e.preventDefault(); 8 | $("#search-input").focus(); 9 | } 10 | }); 11 | 12 | $(document).ready(function() { 13 | // do keyword highlighting 14 | /* modified from https://jsfiddle.net/julmot/bL6bb5oo/ */ 15 | var mark = function() { 16 | 17 | var referrer = document.URL ; 18 | var paramKey = "q" ; 19 | 20 | if (referrer.indexOf("?") !== -1) { 21 | var qs = referrer.substr(referrer.indexOf('?') + 1); 22 | var qs_noanchor = qs.split('#')[0]; 23 | var qsa = qs_noanchor.split('&'); 24 | var keyword = ""; 25 | 26 | for (var i = 0; i < qsa.length; i++) { 27 | var currentParam = qsa[i].split('='); 28 | 29 | if (currentParam.length !== 2) { 30 | continue; 31 | } 32 | 33 | if (currentParam[0] == paramKey) { 34 | keyword = decodeURIComponent(currentParam[1].replace(/\+/g, "%20")); 35 | } 36 | } 37 | 38 | if (keyword !== "") { 39 | $(".contents").unmark({ 40 | done: function() { 41 | $(".contents").mark(keyword); 42 | } 43 | }); 44 | } 45 | } 46 | }; 47 | 48 | mark(); 49 | }); 50 | }); 51 | 52 | /* Search term highlighting ------------------------------*/ 53 | 54 | function matchedWords(hit) { 55 | var words = []; 56 | 57 | var hierarchy = hit._highlightResult.hierarchy; 58 | // loop to fetch from lvl0, lvl1, etc. 59 | for (var idx in hierarchy) { 60 | words = words.concat(hierarchy[idx].matchedWords); 61 | } 62 | 63 | var content = hit._highlightResult.content; 64 | if (content) { 65 | words = words.concat(content.matchedWords); 66 | } 67 | 68 | // return unique words 69 | var words_uniq = [...new Set(words)]; 70 | return words_uniq; 71 | } 72 | 73 | function updateHitURL(hit) { 74 | 75 | var words = matchedWords(hit); 76 | var url = ""; 77 | 78 | if (hit.anchor) { 79 | url = hit.url_without_anchor + '?q=' + escape(words.join(" ")) + '#' + hit.anchor; 80 | } else { 81 | url = hit.url + '?q=' + escape(words.join(" ")); 82 | } 83 | 84 | return url; 85 | } 86 | -------------------------------------------------------------------------------- /inst/app/R/data_funcs.R: -------------------------------------------------------------------------------- 1 | sim_dat <- function(...) { 2 | trials <- sim_trials(...) 3 | dat_code(trials, ...) 4 | } 5 | 6 | sim_trials <- function( 7 | n_subj = 100, # number of subjects 8 | n_ingroup = 25, # number of ingroup stimuli 9 | n_outgroup = 25, # number of outgroup stimuli 10 | omega_0 = 80, # by-item random intercept sd 11 | tau_0 = 100, # by-subject random intercept sd 12 | tau_1 = 40, # by-subject random slope sd 13 | rho = 0.2, # correlation between intercept and slope 14 | sigma = 200, ...) { # residual (standard deviation) 15 | 16 | # simulate a sample of items 17 | items <- data.frame( 18 | item_id = seq_len(n_ingroup + n_outgroup), 19 | category = rep(c("ingroup", "outgroup"), c(n_ingroup, n_outgroup)), 20 | X_i = rep(c(-0.5, 0.5), c(n_ingroup, n_outgroup)), 21 | O_0i = rnorm(n = n_ingroup + n_outgroup, mean = 0, sd = omega_0) 22 | ) 23 | 24 | # simulate a sample of subjects 25 | subjects <- rnorm_multi( 26 | n = n_subj, mu = 0, sd = c(tau_0, tau_1), r = rho, 27 | varnames = c("T_0s", "T_1s") 28 | ) 29 | subjects$subj_id <- 1:n_subj 30 | 31 | # cross subject and item IDs 32 | crossing(subjects, items) %>% 33 | mutate(e_si = rnorm(nrow(.), mean = 0, sd = sigma)) 34 | } 35 | 36 | 37 | dat_code <- function(trials, beta_0, beta_1 = 0, ...) { 38 | mutate(trials, 39 | RT = beta_0 + O_0i + T_0s + (beta_1 + T_1s) * X_i + e_si, 40 | RT_null = beta_0 + O_0i + T_0s + ( 0 + T_1s) * X_i + e_si 41 | ) 42 | } 43 | 44 | 45 | descr <- function(dat) { 46 | subj_table <- dat %>% 47 | group_by(subj_id, category) %>% 48 | summarise(RT = mean(RT)) %>% 49 | ungroup() %>% 50 | group_by(category) %>% 51 | summarise(sd = sd(RT), n = n()) %>% 52 | ungroup() %>% 53 | unite(cell, category, sep = " ") %>% 54 | spread(cell, sd) %>% 55 | mutate(`grouped by` = "subjects", stat = "sd") 56 | 57 | item_table <- dat %>% 58 | group_by(item_id, category) %>% 59 | summarise(RT = mean(RT)) %>% 60 | ungroup() %>% 61 | group_by(category) %>% 62 | summarise(sd = sd(RT), n = n()*2) %>% # x2 because 2 groups of stim 63 | ungroup() %>% 64 | unite(cell, category, sep = " ") %>% 65 | spread(cell, sd) %>% 66 | mutate(`grouped by` = "items", stat = "sd") 67 | 68 | all_table <- dat %>% 69 | group_by(category) %>% 70 | summarise(sd = sd(RT), n = n()) %>% 71 | ungroup() %>% 72 | unite(cell, category, sep = " ") %>% 73 | spread(cell, sd) %>% 74 | mutate(`grouped by` = "all", stat = "sd") 75 | 76 | all_table_RT <- dat %>% 77 | group_by(category) %>% 78 | summarise(RT = mean(RT), n = n()) %>% 79 | ungroup() %>% 80 | unite(cell, category, sep = " ") %>% 81 | spread(cell, RT) %>% 82 | mutate(`grouped by` = "", stat = "mean") 83 | 84 | bind_rows( 85 | all_table_RT, 86 | all_table, 87 | subj_table, 88 | item_table 89 | ) %>% 90 | select(`grouped by`, n, stat, ingroup, outgroup) 91 | } 92 | -------------------------------------------------------------------------------- /docs/pkgdown.js: -------------------------------------------------------------------------------- 1 | /* http://gregfranko.com/blog/jquery-best-practices/ */ 2 | (function($) { 3 | $(function() { 4 | 5 | $('.navbar-fixed-top').headroom(); 6 | 7 | $('body').css('padding-top', $('.navbar').height() + 10); 8 | $(window).resize(function(){ 9 | $('body').css('padding-top', $('.navbar').height() + 10); 10 | }); 11 | 12 | $('[data-toggle="tooltip"]').tooltip(); 13 | 14 | var cur_path = paths(location.pathname); 15 | var links = $("#navbar ul li a"); 16 | var max_length = -1; 17 | var pos = -1; 18 | for (var i = 0; i < links.length; i++) { 19 | if (links[i].getAttribute("href") === "#") 20 | continue; 21 | // Ignore external links 22 | if (links[i].host !== location.host) 23 | continue; 24 | 25 | var nav_path = paths(links[i].pathname); 26 | 27 | var length = prefix_length(nav_path, cur_path); 28 | if (length > max_length) { 29 | max_length = length; 30 | pos = i; 31 | } 32 | } 33 | 34 | // Add class to parent
  • , and enclosing
  • if in dropdown 35 | if (pos >= 0) { 36 | var menu_anchor = $(links[pos]); 37 | menu_anchor.parent().addClass("active"); 38 | menu_anchor.closest("li.dropdown").addClass("active"); 39 | } 40 | }); 41 | 42 | function paths(pathname) { 43 | var pieces = pathname.split("/"); 44 | pieces.shift(); // always starts with / 45 | 46 | var end = pieces[pieces.length - 1]; 47 | if (end === "index.html" || end === "") 48 | pieces.pop(); 49 | return(pieces); 50 | } 51 | 52 | // Returns -1 if not found 53 | function prefix_length(needle, haystack) { 54 | if (needle.length > haystack.length) 55 | return(-1); 56 | 57 | // Special case for length-0 haystack, since for loop won't run 58 | if (haystack.length === 0) { 59 | return(needle.length === 0 ? 0 : -1); 60 | } 61 | 62 | for (var i = 0; i < haystack.length; i++) { 63 | if (needle[i] != haystack[i]) 64 | return(i); 65 | } 66 | 67 | return(haystack.length); 68 | } 69 | 70 | /* Clipboard --------------------------*/ 71 | 72 | function changeTooltipMessage(element, msg) { 73 | var tooltipOriginalTitle=element.getAttribute('data-original-title'); 74 | element.setAttribute('data-original-title', msg); 75 | $(element).tooltip('show'); 76 | element.setAttribute('data-original-title', tooltipOriginalTitle); 77 | } 78 | 79 | if(ClipboardJS.isSupported()) { 80 | $(document).ready(function() { 81 | var copyButton = ""; 82 | 83 | $(".examples, div.sourceCode").addClass("hasCopyButton"); 84 | 85 | // Insert copy buttons: 86 | $(copyButton).prependTo(".hasCopyButton"); 87 | 88 | // Initialize tooltips: 89 | $('.btn-copy-ex').tooltip({container: 'body'}); 90 | 91 | // Initialize clipboard: 92 | var clipboardBtnCopies = new ClipboardJS('[data-clipboard-copy]', { 93 | text: function(trigger) { 94 | return trigger.parentNode.textContent; 95 | } 96 | }); 97 | 98 | clipboardBtnCopies.on('success', function(e) { 99 | changeTooltipMessage(e.trigger, 'Copied!'); 100 | e.clearSelection(); 101 | }); 102 | 103 | clipboardBtnCopies.on('error', function() { 104 | changeTooltipMessage(e.trigger,'Press Ctrl+C or Command+C to copy'); 105 | }); 106 | }); 107 | } 108 | })(window.jQuery || window.$) 109 | -------------------------------------------------------------------------------- /inst/app/R/lmer_funcs.R: -------------------------------------------------------------------------------- 1 | sim_lmer <- function(dat_sim) { 2 | mod_sim <- lmer(RT ~ X_i + (1 | item_id) + (1 + X_i | subj_id), 3 | dat_sim, REML = TRUE) 4 | 5 | return(mod_sim) 6 | } 7 | 8 | sim_subj_anova <- function(dat) { 9 | dat_sub <- dat %>% 10 | group_by(subj_id, category, X_i) %>% 11 | summarise(RT = mean(RT)) 12 | 13 | mod <- afex::aov_4(RT ~ (X_i | subj_id), 14 | factorize = FALSE, 15 | data = dat_sub) 16 | 17 | mod.sum <- anova(mod) 18 | 19 | # within cohen's d 20 | x <- filter(dat_sub, category == "ingroup") %>% pull(RT) 21 | y <- filter(dat_sub, category == "outgroup") %>% pull(RT) 22 | mod.sum$d <- cohen_d(x, y, TRUE) 23 | 24 | return(mod.sum) 25 | } 26 | 27 | sim_item_anova <- function(dat) { 28 | dat_item <- dat %>% 29 | group_by(item_id, category, X_i) %>% 30 | summarise(RT = mean(RT)) 31 | 32 | mod <- afex::aov_4(RT ~ X_i + (1 | item_id), 33 | factorize = FALSE, 34 | data = dat_item) 35 | 36 | mod.sum <- anova(mod) 37 | 38 | # between cohen's d 39 | x <- filter(dat_item, category == "ingroup") %>% pull(RT) 40 | y <- filter(dat_item, category == "outgroup") %>% pull(RT) 41 | mod.sum$d <- cohen_d(x, y, FALSE) 42 | 43 | return(mod.sum) 44 | } 45 | 46 | sim_power <- function(rep = 0, ...) { 47 | dat <- sim_dat(...) 48 | dots <- list(...) 49 | 50 | # run models to calculate power 51 | mod.lmer <- sim_lmer(dat) 52 | mod.subj <- sim_subj_anova(dat) 53 | mod.item<- sim_item_anova(dat) 54 | 55 | if (dots$beta_1 != 0) { 56 | # run models for null effect to calculate false positives 57 | dat$RT <- dat$RT_null 58 | 59 | mod.lmer.null <- sim_lmer(dat) 60 | mod.subj.null <- sim_subj_anova(dat) 61 | mod.item.null <- sim_item_anova(dat) 62 | } 63 | 64 | # get output into tables 65 | table.lmer <- summary(mod.lmer)$coefficients %>% 66 | as_tibble(rownames = "effect") %>% 67 | filter(effect != "(Intercept)") %>% 68 | select(effect, es = Estimate, p = 6) %>% 69 | mutate(analysis = "lmer", type = "power") 70 | 71 | table.subj <- mod.subj %>% 72 | as_tibble(rownames = "effect") %>% 73 | select(effect, es = d, p = 7) %>% 74 | mutate(analysis = "anova_subj", type = "power") 75 | 76 | table.item <- mod.item %>% 77 | as_tibble(rownames = "effect") %>% 78 | select(effect, es = d, p = 7) %>% 79 | mutate(analysis = "anova_item", type = "power") 80 | 81 | if (dots$beta_1 == 0) { 82 | # avoid duplicate models if effect is null 83 | table.lmer.null <- mutate(table.lmer, type = "false positive") 84 | table.subj.null <- mutate(table.subj, type = "false positive") 85 | table.item.null <- mutate(table.item, type = "false positive") 86 | } else { 87 | table.lmer.null <- summary(mod.lmer.null)$coefficients %>% 88 | as_tibble(rownames = "effect") %>% 89 | filter(effect != "(Intercept)") %>% 90 | select(effect, es = Estimate, p = 6) %>% 91 | mutate(analysis = "lmer", type = "false positive") 92 | 93 | table.subj.null <- mod.subj.null %>% 94 | as_tibble(rownames = "effect") %>% 95 | select(effect, es = ges, p = 7) %>% 96 | mutate(analysis = "anova_subj", type = "false positive") 97 | 98 | table.item.null <- mod.item.null %>% 99 | as_tibble(rownames = "effect") %>% 100 | select(effect, es = ges, p = 7) %>% 101 | mutate(analysis = "anova_item", type = "false positive") 102 | } 103 | 104 | bind_rows(table.lmer, table.subj, table.item, 105 | table.lmer.null, table.subj.null, table.item.null) %>% 106 | mutate(rep = rep) 107 | } 108 | -------------------------------------------------------------------------------- /vignettes/r-references.bib: -------------------------------------------------------------------------------- 1 | @Manual{R-base, 2 | title = {R: A Language and Environment for Statistical Computing}, 3 | author = {{R Core Team}}, 4 | organization = {R Foundation for Statistical Computing}, 5 | address = {Vienna, Austria}, 6 | year = {2018}, 7 | url = {https://www.R-project.org/}, 8 | } 9 | @Manual{R-broom.mixed, 10 | title = {broom.mixed: Tidying Methods for Mixed Models}, 11 | author = {Ben Bolker and David Robinson}, 12 | year = {2019}, 13 | note = {R package version 0.2.4}, 14 | url = {https://CRAN.R-project.org/package=broom.mixed}, 15 | } 16 | @Manual{R-dplyr, 17 | title = {dplyr: A Grammar of Data Manipulation}, 18 | author = {Hadley Wickham and Romain François and Lionel Henry and Kirill Müller}, 19 | year = {2019}, 20 | note = {R package version 0.8.1}, 21 | url = {https://CRAN.R-project.org/package=dplyr}, 22 | } 23 | @Manual{R-forcats, 24 | title = {forcats: Tools for Working with Categorical Variables (Factors)}, 25 | author = {Hadley Wickham}, 26 | year = {2019}, 27 | note = {R package version 0.4.0}, 28 | url = {https://CRAN.R-project.org/package=forcats}, 29 | } 30 | @Book{R-ggplot2, 31 | author = {Hadley Wickham}, 32 | title = {ggplot2: Elegant Graphics for Data Analysis}, 33 | publisher = {Springer-Verlag New York}, 34 | year = {2016}, 35 | isbn = {978-3-319-24277-4}, 36 | url = {https://ggplot2.tidyverse.org}, 37 | } 38 | @Article{R-lme4, 39 | title = {Fitting Linear Mixed-Effects Models Using {lme4}}, 40 | author = {Douglas Bates and Martin M{\"a}chler and Ben Bolker and Steve Walker}, 41 | journal = {Journal of Statistical Software}, 42 | year = {2015}, 43 | volume = {67}, 44 | number = {1}, 45 | pages = {1--48}, 46 | doi = {10.18637/jss.v067.i01}, 47 | } 48 | @Article{R-lmerTest, 49 | title = {{lmerTest} Package: Tests in Linear Mixed Effects Models}, 50 | author = {Alexandra Kuznetsova and Per B. Brockhoff and Rune H. B. Christensen}, 51 | journal = {Journal of Statistical Software}, 52 | year = {2017}, 53 | volume = {82}, 54 | number = {13}, 55 | pages = {1--26}, 56 | doi = {10.18637/jss.v082.i13}, 57 | } 58 | @Manual{R-Matrix, 59 | title = {Matrix: Sparse and Dense Matrix Classes and Methods}, 60 | author = {Douglas Bates and Martin Maechler}, 61 | year = {2018}, 62 | note = {R package version 1.2-15}, 63 | url = {https://CRAN.R-project.org/package=Matrix}, 64 | } 65 | @Manual{R-papaja, 66 | author = {Frederik Aust and Marius Barth}, 67 | title = {{papaja}: {Create} {APA} manuscripts with {R Markdown}}, 68 | year = {2018}, 69 | note = {R package version 0.1.0.9842}, 70 | url = {https://github.com/crsh/papaja}, 71 | } 72 | @Manual{R-purrr, 73 | title = {purrr: Functional Programming Tools}, 74 | author = {Lionel Henry and Hadley Wickham}, 75 | year = {2019}, 76 | note = {R package version 0.3.2}, 77 | url = {https://CRAN.R-project.org/package=purrr}, 78 | } 79 | @Manual{R-readr, 80 | title = {readr: Read Rectangular Text Data}, 81 | author = {Hadley Wickham and Jim Hester and Romain Francois}, 82 | year = {2018}, 83 | note = {R package version 1.3.1}, 84 | url = {https://CRAN.R-project.org/package=readr}, 85 | } 86 | @Manual{R-stringr, 87 | title = {stringr: Simple, Consistent Wrappers for Common String Operations}, 88 | author = {Hadley Wickham}, 89 | year = {2019}, 90 | note = {R package version 1.4.0}, 91 | url = {https://CRAN.R-project.org/package=stringr}, 92 | } 93 | @Manual{R-tibble, 94 | title = {tibble: Simple Data Frames}, 95 | author = {Kirill Müller and Hadley Wickham}, 96 | year = {2019}, 97 | note = {R package version 2.1.1}, 98 | url = {https://CRAN.R-project.org/package=tibble}, 99 | } 100 | @Manual{R-tidyr, 101 | title = {tidyr: Easily Tidy Data with 'spread()' and 'gather()' Functions}, 102 | author = {Hadley Wickham and Lionel Henry}, 103 | year = {2019}, 104 | note = {R package version 0.8.3}, 105 | url = {https://CRAN.R-project.org/package=tidyr}, 106 | } 107 | @Manual{R-tidyverse, 108 | title = {tidyverse: Easily Install and Load the 'Tidyverse'}, 109 | author = {Hadley Wickham}, 110 | year = {2017}, 111 | note = {R package version 1.2.1}, 112 | url = {https://CRAN.R-project.org/package=tidyverse}, 113 | } 114 | @Manual{R-afex, 115 | title = {afex: Analysis of Factorial Experiments}, 116 | author = {Henrik Singmann and Ben Bolker and Jake Westfall and Frederik Aust}, 117 | year = {2019}, 118 | note = {R package version 0.23-0}, 119 | url = {https://CRAN.R-project.org/package=afex}, 120 | } 121 | 122 | @Manual{R-faux, 123 | title = {faux: Simulation for Factorial Designs}, 124 | author = {Lisa DeBruine}, 125 | doi = {10.5281/zenodo.2669586}, 126 | publisher = {Zenodo}, 127 | year = {2020}, 128 | month = {August}, 129 | note = {R package version 0.0.1.2}, 130 | url = {https://debruine.github.io/faux/}, 131 | } 132 | -------------------------------------------------------------------------------- /inst/paper/r-references.bib: -------------------------------------------------------------------------------- 1 | @Manual{R-base, 2 | title = {R: A Language and Environment for Statistical Computing}, 3 | author = {{R Core Team}}, 4 | organization = {R Foundation for Statistical Computing}, 5 | address = {Vienna, Austria}, 6 | year = {2018}, 7 | url = {https://www.R-project.org/}, 8 | } 9 | @Manual{R-broom.mixed, 10 | title = {broom.mixed: Tidying Methods for Mixed Models}, 11 | author = {Ben Bolker and David Robinson}, 12 | year = {2019}, 13 | note = {R package version 0.2.4}, 14 | url = {https://CRAN.R-project.org/package=broom.mixed}, 15 | } 16 | @Manual{R-dplyr, 17 | title = {dplyr: A Grammar of Data Manipulation}, 18 | author = {Hadley Wickham and Romain François and Lionel Henry and Kirill Müller}, 19 | year = {2019}, 20 | note = {R package version 0.8.1}, 21 | url = {https://CRAN.R-project.org/package=dplyr}, 22 | } 23 | @Manual{R-forcats, 24 | title = {forcats: Tools for Working with Categorical Variables (Factors)}, 25 | author = {Hadley Wickham}, 26 | year = {2019}, 27 | note = {R package version 0.4.0}, 28 | url = {https://CRAN.R-project.org/package=forcats}, 29 | } 30 | @Book{R-ggplot2, 31 | author = {Hadley Wickham}, 32 | title = {ggplot2: Elegant Graphics for Data Analysis}, 33 | publisher = {Springer-Verlag New York}, 34 | year = {2016}, 35 | isbn = {978-3-319-24277-4}, 36 | url = {https://ggplot2.tidyverse.org}, 37 | } 38 | @Article{R-lme4, 39 | title = {Fitting Linear Mixed-Effects Models Using {lme4}}, 40 | author = {Douglas Bates and Martin M{\"a}chler and Ben Bolker and Steve Walker}, 41 | journal = {Journal of Statistical Software}, 42 | year = {2015}, 43 | volume = {67}, 44 | number = {1}, 45 | pages = {1--48}, 46 | doi = {10.18637/jss.v067.i01}, 47 | } 48 | @Article{R-lmerTest, 49 | title = {{lmerTest} Package: Tests in Linear Mixed Effects Models}, 50 | author = {Alexandra Kuznetsova and Per B. Brockhoff and Rune H. B. Christensen}, 51 | journal = {Journal of Statistical Software}, 52 | year = {2017}, 53 | volume = {82}, 54 | number = {13}, 55 | pages = {1--26}, 56 | doi = {10.18637/jss.v082.i13}, 57 | } 58 | @Manual{R-Matrix, 59 | title = {Matrix: Sparse and Dense Matrix Classes and Methods}, 60 | author = {Douglas Bates and Martin Maechler}, 61 | year = {2018}, 62 | note = {R package version 1.2-15}, 63 | url = {https://CRAN.R-project.org/package=Matrix}, 64 | } 65 | @Manual{R-papaja, 66 | author = {Frederik Aust and Marius Barth}, 67 | title = {{papaja}: {Create} {APA} manuscripts with {R Markdown}}, 68 | year = {2018}, 69 | note = {R package version 0.1.0.9842}, 70 | url = {https://github.com/crsh/papaja}, 71 | } 72 | @Manual{R-purrr, 73 | title = {purrr: Functional Programming Tools}, 74 | author = {Lionel Henry and Hadley Wickham}, 75 | year = {2019}, 76 | note = {R package version 0.3.2}, 77 | url = {https://CRAN.R-project.org/package=purrr}, 78 | } 79 | @Manual{R-readr, 80 | title = {readr: Read Rectangular Text Data}, 81 | author = {Hadley Wickham and Jim Hester and Romain Francois}, 82 | year = {2018}, 83 | note = {R package version 1.3.1}, 84 | url = {https://CRAN.R-project.org/package=readr}, 85 | } 86 | @Manual{R-stringr, 87 | title = {stringr: Simple, Consistent Wrappers for Common String Operations}, 88 | author = {Hadley Wickham}, 89 | year = {2019}, 90 | note = {R package version 1.4.0}, 91 | url = {https://CRAN.R-project.org/package=stringr}, 92 | } 93 | @Manual{R-tibble, 94 | title = {tibble: Simple Data Frames}, 95 | author = {Kirill Müller and Hadley Wickham}, 96 | year = {2019}, 97 | note = {R package version 2.1.1}, 98 | url = {https://CRAN.R-project.org/package=tibble}, 99 | } 100 | @Manual{R-tidyr, 101 | title = {tidyr: Easily Tidy Data with 'spread()' and 'gather()' Functions}, 102 | author = {Hadley Wickham and Lionel Henry}, 103 | year = {2019}, 104 | note = {R package version 0.8.3}, 105 | url = {https://CRAN.R-project.org/package=tidyr}, 106 | } 107 | @Manual{R-tidyverse, 108 | title = {tidyverse: Easily Install and Load the 'Tidyverse'}, 109 | author = {Hadley Wickham}, 110 | year = {2017}, 111 | note = {R package version 1.2.1}, 112 | url = {https://CRAN.R-project.org/package=tidyverse}, 113 | } 114 | @Manual{R-afex, 115 | title = {afex: Analysis of Factorial Experiments}, 116 | author = {Henrik Singmann and Ben Bolker and Jake Westfall and Frederik Aust}, 117 | year = {2019}, 118 | note = {R package version 0.23-0}, 119 | url = {https://CRAN.R-project.org/package=afex}, 120 | } 121 | 122 | @Manual{R-faux, 123 | title = {faux: Simulation for Factorial Designs}, 124 | author = {Lisa DeBruine}, 125 | doi = {10.5281/zenodo.2669586}, 126 | publisher = {Zenodo}, 127 | year = {2020}, 128 | month = {August}, 129 | note = {R package version 0.0.1.2}, 130 | url = {https://debruine.github.io/faux/}, 131 | } 132 | -------------------------------------------------------------------------------- /inst/app/www/custom.css: -------------------------------------------------------------------------------- 1 | .sidebar .box { 2 | background-color: inherit; 3 | } 4 | 5 | .sidebar .box-title { 6 | color: white; 7 | } 8 | 9 | pre.shiny-text-output { 10 | white-space: pre-wrap; /* css-3 */ 11 | white-space: -moz-pre-wrap; /* Mozilla, since 1999 */ 12 | white-space: -pre-wrap; /* Opera 4-6 */ 13 | white-space: -o-pre-wrap; /* Opera 7 */ 14 | word-wrap: break-word; /* Internet Explorer 5.5+ */ 15 | } 16 | 17 | p { font-size: 120%; } 18 | 19 | #broom_output table tbody tr td:nth-child(3) { color: white; } 20 | ul.sidebar-menu label { width: 100%; padding: 1px 5px; } 21 | 22 | label[for="n_subj"] { background-color: inherit; } 23 | label[for="n_ingroup"] { background-color: inherit; } 24 | label[for="n_outgroup"] { background-color: inherit; } 25 | #broom_output table tbody tr:nth-child(1) td:nth-child(3) { background-color: #E50F45; } 26 | #broom_output table tbody tr:nth-child(2) td:nth-child(3) { background-color: #E76839; } 27 | #broom_output table tbody tr:nth-child(3) td:nth-child(3) { background-color: #B29700; } 28 | #broom_output table tbody tr:nth-child(4) td:nth-child(3) { background-color: #086F50; } 29 | #broom_output table tbody tr:nth-child(5) td:nth-child(3) { background-color: #015FA1; } 30 | #broom_output table tbody tr:nth-child(6) td:nth-child(3) { background-color: #702981; } 31 | #broom_output table tbody tr:nth-child(7) td:nth-child(3) { background-color: #C20FA7; } 32 | 33 | label[for="beta_0"] + span.irs span.irs-bar, 34 | label[for="beta_0"] + span.irs span.irs-bar-edge, 35 | label[for="beta_0_"] + span.irs span.irs-bar, 36 | label[for="beta_0_"] + span.irs span.irs-bar-edge 37 | { 38 | background-color: #E50F45; 39 | border-color: #E50F45; 40 | } 41 | 42 | label[for="beta_1"] + span.irs span.irs-bar, 43 | label[for="beta_1"] + span.irs span.irs-bar-edge, 44 | label[for="beta_1_"] + span.irs span.irs-bar, 45 | label[for="beta_1_"] + span.irs span.irs-bar-edge 46 | { 47 | background-color: #E76839; 48 | border-color: #E76839; 49 | } 50 | 51 | label[for="tau_0"] + span.irs span.irs-bar, 52 | label[for="tau_0"] + span.irs span.irs-bar-edge, 53 | label[for="tau_0_"] + span.irs span.irs-bar, 54 | label[for="tau_0_"] + span.irs span.irs-bar-edge 55 | { 56 | background-color: #B29700; 57 | border-color: #B29700; 58 | } 59 | 60 | label[for="tau_1"] + span.irs span.irs-bar, 61 | label[for="tau_1"] + span.irs span.irs-bar-edge, 62 | label[for="tau_1_"] + span.irs span.irs-bar, 63 | label[for="tau_1_"] + span.irs span.irs-bar-edge 64 | { 65 | background-color: #086F50; 66 | border-color: #086F50; 67 | } 68 | 69 | label[for="rho"] + span.irs span.irs-bar, 70 | label[for="rho"] + span.irs span.irs-bar-edge, 71 | label[for="rho_"] + span.irs span.irs-bar, 72 | label[for="rho_"] + span.irs span.irs-bar-edge 73 | { 74 | background-color: #015FA1; 75 | border-color: #015FA1; 76 | } 77 | 78 | label[for="omega_0"] + span.irs span.irs-bar, 79 | label[for="omega_0"] + span.irs span.irs-bar-edge, 80 | label[for="omega_0_"] + span.irs span.irs-bar, 81 | label[for="omega_0_"] + span.irs span.irs-bar-edge { 82 | background-color: #702981; 83 | border-color: #702981; 84 | } 85 | 86 | label[for="sigma"] + span.irs span.irs-bar, 87 | label[for="sigma"] + span.irs span.irs-bar-edge, 88 | label[for="sigma_"] + span.irs span.irs-bar, 89 | label[for="sigma_"] + span.irs span.irs-bar-edge { 90 | background-color: #C20FA7; 91 | border-color: #C20FA7; 92 | } 93 | 94 | label[for="n_subj"] + span.irs span.irs-bar, 95 | label[for="n_subj"] + span.irs span.irs-bar-edge, 96 | label[for="n_subj_"] + span.irs span.irs-bar, 97 | label[for="n_subj_"] + span.irs span.irs-bar-edge { 98 | background-color: #F5AABF; 99 | border-color: #F5AABF; 100 | } 101 | 102 | label[for="n_ingroup"] + span.irs span.irs-bar, 103 | label[for="n_ingroup"] + span.irs span.irs-bar-edge, 104 | label[for="n_ingroup_"] + span.irs span.irs-bar, 105 | label[for="n_ingroup_"] + span.irs span.irs-bar-edge, 106 | label[for="n_outgroup"] + span.irs span.irs-bar, 107 | label[for="n_outgroup"] + span.irs span.irs-bar-edge, 108 | label[for="n_outgroup_"] + span.irs span.irs-bar, 109 | label[for="n_outgroup_"] + span.irs span.irs-bar-edge{ 110 | background-color: #64D2E0; 111 | border-color: #64D2E0; 112 | } 113 | 114 | #resim, #reset { display: inline-block; width: 40%;} 115 | 116 | 117 | .RT, .beta_0, .beta_1, .T0s, .T1s, .rho, .O0i, .err, .X1, .n_subj, .n_item { 118 | background-color: transparent; 119 | color: black; 120 | border-bottom: 2px solid transparent; 121 | border-radius: 0; 122 | } 123 | .beta_0 { border-color: #E50F45; } 124 | .beta_1 { border-color: #E76839; } 125 | .T0s { border-color: #B29700; } 126 | .T1s { border-color: #086F50; } 127 | .rho { border-color: #3B5CA7; } 128 | .O0i { border-color: #702981; } 129 | .err { border-color: #C20FA7; } 130 | .n_subj { border-color: #F5AABF; } 131 | .n_item { border-color: #64D2E0; } 132 | 133 | #lmer_output { 134 | font-family: Courier, sans-serif; 135 | } -------------------------------------------------------------------------------- /docs/bootstrap-toc.js: -------------------------------------------------------------------------------- 1 | /*! 2 | * Bootstrap Table of Contents v0.4.1 (http://afeld.github.io/bootstrap-toc/) 3 | * Copyright 2015 Aidan Feldman 4 | * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */ 5 | (function() { 6 | 'use strict'; 7 | 8 | window.Toc = { 9 | helpers: { 10 | // return all matching elements in the set, or their descendants 11 | findOrFilter: function($el, selector) { 12 | // http://danielnouri.org/notes/2011/03/14/a-jquery-find-that-also-finds-the-root-element/ 13 | // http://stackoverflow.com/a/12731439/358804 14 | var $descendants = $el.find(selector); 15 | return $el.filter(selector).add($descendants).filter(':not([data-toc-skip])'); 16 | }, 17 | 18 | generateUniqueIdBase: function(el) { 19 | var text = $(el).text(); 20 | var anchor = text.trim().toLowerCase().replace(/[^A-Za-z0-9]+/g, '-'); 21 | return anchor || el.tagName.toLowerCase(); 22 | }, 23 | 24 | generateUniqueId: function(el) { 25 | var anchorBase = this.generateUniqueIdBase(el); 26 | for (var i = 0; ; i++) { 27 | var anchor = anchorBase; 28 | if (i > 0) { 29 | // add suffix 30 | anchor += '-' + i; 31 | } 32 | // check if ID already exists 33 | if (!document.getElementById(anchor)) { 34 | return anchor; 35 | } 36 | } 37 | }, 38 | 39 | generateAnchor: function(el) { 40 | if (el.id) { 41 | return el.id; 42 | } else { 43 | var anchor = this.generateUniqueId(el); 44 | el.id = anchor; 45 | return anchor; 46 | } 47 | }, 48 | 49 | createNavList: function() { 50 | return $(''); 51 | }, 52 | 53 | createChildNavList: function($parent) { 54 | var $childList = this.createNavList(); 55 | $parent.append($childList); 56 | return $childList; 57 | }, 58 | 59 | generateNavEl: function(anchor, text) { 60 | var $a = $(''); 61 | $a.attr('href', '#' + anchor); 62 | $a.text(text); 63 | var $li = $('
  • '); 64 | $li.append($a); 65 | return $li; 66 | }, 67 | 68 | generateNavItem: function(headingEl) { 69 | var anchor = this.generateAnchor(headingEl); 70 | var $heading = $(headingEl); 71 | var text = $heading.data('toc-text') || $heading.text(); 72 | return this.generateNavEl(anchor, text); 73 | }, 74 | 75 | // Find the first heading level (`

    `, then `

    `, etc.) that has more than one element. Defaults to 1 (for `

    `). 76 | getTopLevel: function($scope) { 77 | for (var i = 1; i <= 6; i++) { 78 | var $headings = this.findOrFilter($scope, 'h' + i); 79 | if ($headings.length > 1) { 80 | return i; 81 | } 82 | } 83 | 84 | return 1; 85 | }, 86 | 87 | // returns the elements for the top level, and the next below it 88 | getHeadings: function($scope, topLevel) { 89 | var topSelector = 'h' + topLevel; 90 | 91 | var secondaryLevel = topLevel + 1; 92 | var secondarySelector = 'h' + secondaryLevel; 93 | 94 | return this.findOrFilter($scope, topSelector + ',' + secondarySelector); 95 | }, 96 | 97 | getNavLevel: function(el) { 98 | return parseInt(el.tagName.charAt(1), 10); 99 | }, 100 | 101 | populateNav: function($topContext, topLevel, $headings) { 102 | var $context = $topContext; 103 | var $prevNav; 104 | 105 | var helpers = this; 106 | $headings.each(function(i, el) { 107 | var $newNav = helpers.generateNavItem(el); 108 | var navLevel = helpers.getNavLevel(el); 109 | 110 | // determine the proper $context 111 | if (navLevel === topLevel) { 112 | // use top level 113 | $context = $topContext; 114 | } else if ($prevNav && $context === $topContext) { 115 | // create a new level of the tree and switch to it 116 | $context = helpers.createChildNavList($prevNav); 117 | } // else use the current $context 118 | 119 | $context.append($newNav); 120 | 121 | $prevNav = $newNav; 122 | }); 123 | }, 124 | 125 | parseOps: function(arg) { 126 | var opts; 127 | if (arg.jquery) { 128 | opts = { 129 | $nav: arg 130 | }; 131 | } else { 132 | opts = arg; 133 | } 134 | opts.$scope = opts.$scope || $(document.body); 135 | return opts; 136 | } 137 | }, 138 | 139 | // accepts a jQuery object, or an options object 140 | init: function(opts) { 141 | opts = this.helpers.parseOps(opts); 142 | 143 | // ensure that the data attribute is in place for styling 144 | opts.$nav.attr('data-toggle', 'toc'); 145 | 146 | var $topContext = this.helpers.createChildNavList(opts.$nav); 147 | var topLevel = this.helpers.getTopLevel(opts.$scope); 148 | var $headings = this.helpers.getHeadings(opts.$scope, topLevel); 149 | this.helpers.populateNav($topContext, topLevel, $headings); 150 | } 151 | }; 152 | 153 | $(function() { 154 | $('nav[data-toggle="toc"]').each(function(i, el) { 155 | var $nav = $(el); 156 | Toc.init($nav); 157 | }); 158 | }); 159 | })(); 160 | -------------------------------------------------------------------------------- /inst/paper/bibliography.bib: -------------------------------------------------------------------------------- 1 | @article{matuschek_et_al_2017, 2 | title={Balancing Type {I} error and power in linear mixed models}, 3 | author={Matuschek, Hannes and Kliegl, Reinhold and Vasishth, Shravan and Baayen, Harald and Bates, Douglas}, 4 | journal={Journal of Memory and Language}, 5 | volume={94}, 6 | pages={305--315}, 7 | year={2017}, 8 | publisher={Elsevier} 9 | } 10 | } 11 | 12 | @article{barr_2013, 13 | title={Random effects structure for testing interactions in linear mixed-effects models}, 14 | author={Barr, Dale J}, 15 | journal={{Frontiers in Psychology}}, 16 | volume={4}, 17 | pages={328}, 18 | year={2013} 19 | } 20 | 21 | @article{baayen_davidson_bates_2008, 22 | author = {Baayen, R. H. and Davidson, D. J. and Bates, D. M.}, 23 | journal = {Journal of Memory and Language}, 24 | pages = {390--412}, 25 | title = {Mixed-effects modeling with crossed random effects for subjects and items}, 26 | volume = {59}, 27 | year = {2008} 28 | } 29 | 30 | @incollection{barr_2018, 31 | title={{Generalizing over encounters: Statistical and theoretical considerations}}, 32 | author={Barr, Dale J}, 33 | year={2018}, 34 | editor={S.-A. Rueschemeyer and M. G. Gaskell}, 35 | booktitle={Oxford Handbook of Psycholinguistics}, 36 | publisher={Oxford University Press} 37 | } 38 | 39 | @article{barr_et_al_2013, 40 | title={{Random effects structure for confirmatory hypothesis testing: Keep it maximal}}, 41 | author={Barr, Dale J and Levy, Roger and Scheepers, Christoph and Tily, Harry J}, 42 | journal={{Journal of Memory and Language}}, 43 | volume={68}, 44 | number={3}, 45 | pages={255--278}, 46 | year={2013} 47 | } 48 | 49 | @article{bedny_aguirre_thompson-schill_2007, 50 | title={Item analysis in functional magnetic resonance imaging}, 51 | author={Bedny, Marina and Aguirre, Geoffrey K and Thompson-Schill, Sharon L}, 52 | journal={Neuroimage}, 53 | volume={35}, 54 | number={3}, 55 | pages={1093--1102}, 56 | year={2007}, 57 | publisher={Elsevier} 58 | } 59 | 60 | 61 | @article{judd_westfall_kenny_2012, 62 | title={{Treating stimuli as a random factor in social psychology: A new and comprehensive solution to a pervasive but largely ignored problem.}}, 63 | author={Judd, Charles M and Westfall, Jacob and Kenny, David A}, 64 | journal={{Journal of Personality and Social Psychology}}, 65 | volume={103}, 66 | pages={54}, 67 | year={2012} 68 | } 69 | 70 | 71 | @article{locker_hoffman_bovaird_2007, 72 | author = {Locker, Lawrence and Hoffman, Lesa and Bovaird, James}, 73 | journal = {Behavior Research Methods}, 74 | pages = {723--730}, 75 | title = {On the use of multilevel modeling as an alternative to items analysis in psycholinguistic research}, 76 | volume = {39}, 77 | year = {2007} 78 | } 79 | 80 | 81 | @article{clark_1973, 82 | title={{The language-as-fixed-effect fallacy: A critique of language statistics in psychological research}}, 83 | author={Clark, Herbert H}, 84 | journal={{Journal of Verbal Learning and Verbal Behavior}}, 85 | volume={12}, 86 | pages={335--359}, 87 | year={1973}, 88 | publisher={Elsevier} 89 | } 90 | 91 | @article{coleman_1964, 92 | title={Generalizing to a language population}, 93 | author={Coleman, Edmund B}, 94 | journal={Psychological Reports}, 95 | volume={14}, 96 | pages={219--226}, 97 | year={1964} 98 | } 99 | 100 | @article{forster_dickinson_1976, 101 | author = {Forster, K. and Dickinson, R.}, 102 | journal = {{Journal of Verbal Learning and Verbal Behavior}}, 103 | pages = {135--142}, 104 | title = {More on the language-as-fixed-effect fallacy: Monte Carlo estimates of error rates for {$F_1$,$F_2$},{$F'$}, and min {$F'$}}, 105 | volume = {15}, 106 | year = {1976} 107 | } 108 | 109 | @article{luke-2017, 110 | title={Evaluating significance in linear mixed-effects models in R}, 111 | author={Luke, Steven G}, 112 | journal={{Behavior Research Methods}}, 113 | volume={49}, 114 | number={4}, 115 | pages={1494--1502}, 116 | year={2017}, 117 | publisher={Springer} 118 | } 119 | 120 | @article{westfall_yarkoni_2016, 121 | title={{Fixing the stimulus-as-fixed-effect fallacy in task fMRI}}, 122 | author={Westfall, Jacob and Nichols, Thomas E and Yarkoni, Tal}, 123 | journal={{Wellcome Open Research}}, 124 | volume={1}, 125 | year={2016}, 126 | publisher={The Wellcome Trust} 127 | } 128 | 129 | @article{westfall_2014, 130 | author = {Westfall, Jacob and Kenny, David A. and Judd, Charles M.}, 131 | title = {Statistical power and optimal design in experiments in which samples of participants respond to samples of stimuli}, 132 | journal = {Journal of Experimental Psychology: General}, 133 | volume = {143}, 134 | number = {5}, 135 | pages = {2020-2045}, 136 | year = {2014}, 137 | doi = {} 138 | } 139 | 140 | @article{yarkoni-GC, 141 | title={The generalizability crisis}, 142 | author={Yarkoni, Tal}, 143 | year={2019}, 144 | publisher={PsyArXiv}, 145 | URL = {https://psyarxiv.com/jqw35} 146 | } 147 | 148 | @article{TOSTtutorial, 149 | author = {Daniël Lakens and Anne M. Scheel and Peder M. Isager}, 150 | title = {Equivalence Testing for Psychological Research: A Tutorial}, 151 | journal = {Advances in Methods and Practices in Psychological Science}, 152 | volume = {1}, 153 | number = {2}, 154 | pages = {259--269}, 155 | year = {2018}, 156 | doi = {10.1177/2515245918770963}, 157 | URL = { https://doi.org/10.1177/2515245918770963 } 158 | } 159 | 160 | @book{wickham-advr, 161 | title={{Advanced R}}, 162 | author={Wickham, Hadley}, 163 | year={2019}, 164 | publisher={CRC press}, 165 | URL = {http://adv-r.had.co.nz/} 166 | } -------------------------------------------------------------------------------- /vignettes/bibliography.bib: -------------------------------------------------------------------------------- 1 | @article{matuschek_et_al_2017, 2 | title={Balancing Type {I} error and power in linear mixed models}, 3 | author={Matuschek, Hannes and Kliegl, Reinhold and Vasishth, Shravan and Baayen, Harald and Bates, Douglas}, 4 | journal={Journal of Memory and Language}, 5 | volume={94}, 6 | pages={305--315}, 7 | year={2017}, 8 | publisher={Elsevier} 9 | } 10 | } 11 | 12 | @article{barr_2013, 13 | title={Random effects structure for testing interactions in linear mixed-effects models}, 14 | author={Barr, Dale J}, 15 | journal={{Frontiers in Psychology}}, 16 | volume={4}, 17 | pages={328}, 18 | year={2013} 19 | } 20 | 21 | @article{baayen_davidson_bates_2008, 22 | author = {Baayen, R. H. and Davidson, D. J. and Bates, D. M.}, 23 | journal = {Journal of Memory and Language}, 24 | pages = {390--412}, 25 | title = {Mixed-effects modeling with crossed random effects for subjects and items}, 26 | volume = {59}, 27 | year = {2008} 28 | } 29 | 30 | @incollection{barr_2018, 31 | title={{Generalizing over encounters: Statistical and theoretical considerations}}, 32 | author={Barr, Dale J}, 33 | year={2018}, 34 | editor={S.-A. Rueschemeyer and M. G. Gaskell}, 35 | booktitle={Oxford Handbook of Psycholinguistics}, 36 | publisher={Oxford University Press} 37 | } 38 | 39 | @article{barr_et_al_2013, 40 | title={{Random effects structure for confirmatory hypothesis testing: Keep it maximal}}, 41 | author={Barr, Dale J and Levy, Roger and Scheepers, Christoph and Tily, Harry J}, 42 | journal={{Journal of Memory and Language}}, 43 | volume={68}, 44 | number={3}, 45 | pages={255--278}, 46 | year={2013} 47 | } 48 | 49 | @article{bedny_aguirre_thompson-schill_2007, 50 | title={Item analysis in functional magnetic resonance imaging}, 51 | author={Bedny, Marina and Aguirre, Geoffrey K and Thompson-Schill, Sharon L}, 52 | journal={Neuroimage}, 53 | volume={35}, 54 | number={3}, 55 | pages={1093--1102}, 56 | year={2007}, 57 | publisher={Elsevier} 58 | } 59 | 60 | 61 | @article{judd_westfall_kenny_2012, 62 | title={{Treating stimuli as a random factor in social psychology: A new and comprehensive solution to a pervasive but largely ignored problem.}}, 63 | author={Judd, Charles M and Westfall, Jacob and Kenny, David A}, 64 | journal={{Journal of Personality and Social Psychology}}, 65 | volume={103}, 66 | pages={54}, 67 | year={2012} 68 | } 69 | 70 | 71 | @article{locker_hoffman_bovaird_2007, 72 | author = {Locker, Lawrence and Hoffman, Lesa and Bovaird, James}, 73 | journal = {Behavior Research Methods}, 74 | pages = {723--730}, 75 | title = {On the use of multilevel modeling as an alternative to items analysis in psycholinguistic research}, 76 | volume = {39}, 77 | year = {2007} 78 | } 79 | 80 | 81 | @article{clark_1973, 82 | title={{The language-as-fixed-effect fallacy: A critique of language statistics in psychological research}}, 83 | author={Clark, Herbert H}, 84 | journal={{Journal of Verbal Learning and Verbal Behavior}}, 85 | volume={12}, 86 | pages={335--359}, 87 | year={1973}, 88 | publisher={Elsevier} 89 | } 90 | 91 | @article{coleman_1964, 92 | title={Generalizing to a language population}, 93 | author={Coleman, Edmund B}, 94 | journal={Psychological Reports}, 95 | volume={14}, 96 | pages={219--226}, 97 | year={1964} 98 | } 99 | 100 | @article{forster_dickinson_1976, 101 | author = {Forster, K. and Dickinson, R.}, 102 | journal = {{Journal of Verbal Learning and Verbal Behavior}}, 103 | pages = {135--142}, 104 | title = {More on the language-as-fixed-effect fallacy: Monte Carlo estimates of error rates for {$F_1$,$F_2$},{$F'$}, and min {$F'$}}, 105 | volume = {15}, 106 | year = {1976} 107 | } 108 | 109 | @article{luke-2017, 110 | title={Evaluating significance in linear mixed-effects models in R}, 111 | author={Luke, Steven G}, 112 | journal={{Behavior Research Methods}}, 113 | volume={49}, 114 | number={4}, 115 | pages={1494--1502}, 116 | year={2017}, 117 | publisher={Springer} 118 | } 119 | 120 | @article{westfall_yarkoni_2016, 121 | title={{Fixing the stimulus-as-fixed-effect fallacy in task fMRI}}, 122 | author={Westfall, Jacob and Nichols, Thomas E and Yarkoni, Tal}, 123 | journal={{Wellcome Open Research}}, 124 | volume={1}, 125 | year={2016}, 126 | publisher={The Wellcome Trust} 127 | } 128 | 129 | @article{westfall_2014, 130 | author = {Westfall, Jacob and Kenny, David A. and Judd, Charles M.}, 131 | title = {Statistical power and optimal design in experiments in which samples of participants respond to samples of stimuli}, 132 | journal = {Journal of Experimental Psychology: General}, 133 | volume = {143}, 134 | number = {5}, 135 | pages = {2020-2045}, 136 | year = {2014}, 137 | doi = {} 138 | } 139 | 140 | @article{yarkoni-GC, 141 | title={The generalizability crisis}, 142 | author={Yarkoni, Tal}, 143 | year={2019}, 144 | publisher={PsyArXiv}, 145 | URL = {https://psyarxiv.com/jqw35} 146 | } 147 | 148 | @article{TOSTtutorial, 149 | author = {Daniël Lakens and Anne M. Scheel and Peder M. Isager}, 150 | title = {Equivalence Testing for Psychological Research: A Tutorial}, 151 | journal = {Advances in Methods and Practices in Psychological Science}, 152 | volume = {1}, 153 | number = {2}, 154 | pages = {259--269}, 155 | year = {2018}, 156 | doi = {10.1177/2515245918770963}, 157 | URL = { https://doi.org/10.1177/2515245918770963 } 158 | } 159 | 160 | @book{wickham-advr, 161 | title={{Advanced R}}, 162 | author={Wickham, Hadley}, 163 | year={2019}, 164 | publisher={CRC press}, 165 | URL = {http://adv-r.had.co.nz/} 166 | } -------------------------------------------------------------------------------- /inst/app/R/misc_funcs.R: -------------------------------------------------------------------------------- 1 | cohen_d <- function(x, y, paired = TRUE) { 2 | # https://t.co/GmRX4y7gCl 3 | # adapted from https://github.com/Lakens/anchor_based_methods_SESOI/blob/master/effect_size_d_paired_function.R 4 | 5 | m_diff <- mean(y-x) # mean difference 6 | sd1 <- sd(x) #standard deviation of measurement 1 7 | sd2 <- sd(y) #standard deviation of measurement 2 8 | s_diff <- sd(y-x) #standard deviation of the difference scores 9 | N <- length(x) #number of observations of measurement 1 10 | N2 <- length(y) #number of observations of measurement 2 11 | 12 | # design-specific pooled standard deviation and 13 | # bias correction (unb) 14 | if (paired) { 15 | s_av <- sqrt((sd1^2+sd2^2)/2) 16 | unb <- 1-(3/(4*(N-1)-1)) 17 | } else { 18 | ss_x <- sum((x - mean(x))^2) 19 | ss_y <- sum((y - mean(y))^2) 20 | Ns <- N + N2 - 2 21 | s_av <- sqrt((ss_x + ss_y)/Ns) 22 | unb <- 1-(3/(4*(N+N2)-9)) 23 | } 24 | 25 | #Cohen's d_av, using s_av as standardizer 26 | d_av <- m_diff/s_av 27 | d_av_unb <- unb*d_av 28 | 29 | d_av_unb 30 | } 31 | 32 | ## FAUX functions 33 | 34 | rnorm_multi <- function (n, vars = NULL, mu = 0, sd = 1, r = 0, varnames = NULL, 35 | empirical = FALSE, as.matrix = FALSE) { 36 | if (!is.numeric(n) || n%%1 > 0 || n < 1) { 37 | stop("n must be an integer > 0") 38 | } 39 | if (!(empirical %in% c(TRUE, FALSE))) { 40 | stop("empirical must be TRUE or FALSE") 41 | } 42 | if (is.null(vars)) { 43 | if (!is.null(varnames)) { 44 | vars <- length(varnames) 45 | } else if (length(mu) > 1) { 46 | vars <- length(mu) 47 | } else if (length(sd) > 1) { 48 | vars <- length(sd) 49 | } else if (is.matrix(r)) { 50 | vars <- ncol(r) 51 | } else { 52 | stop("The number of variables (vars) was not explicitly set and can't be guessed from the input.") 53 | } 54 | } 55 | if (length(mu) == 1) { 56 | mu <- rep(mu, vars) 57 | } else if (length(mu) != vars) { 58 | stop("the length of mu must be 1 or vars") 59 | } else { 60 | mu <- as.matrix(mu) %>% as.vector() 61 | } 62 | if (length(sd) == 1) { 63 | sd <- rep(sd, vars) 64 | } else if (length(sd) != vars) { 65 | stop("the length of sd must be 1 or vars") 66 | } else { 67 | sd <- as.matrix(sd) %>% as.vector() 68 | } 69 | if (n == 1 & empirical == TRUE) { 70 | warning("When n = 1 and empirical = TRUE, returned data are equal to mu") 71 | mvn <- mu 72 | cor_mat <- r 73 | } else { 74 | cor_mat <- cormat(r, vars) 75 | sigma <- (sd %*% t(sd)) * cor_mat 76 | err <- "The correlated variables could not be generated." 77 | if (empirical) err <- paste(err, "Try increasing the N or setting empirical = FALSE.") 78 | p <- length(mu) 79 | if (!all(dim(sigma) == c(p, p))) stop(err) 80 | eS <- eigen(sigma, symmetric = TRUE) 81 | ev <- eS$values 82 | if (!all(ev >= -0.000001 * abs(ev[1L]))) stop(paste(err)) 83 | X <- matrix(stats::rnorm(p * n), n) 84 | if (empirical) { 85 | X <- scale(X, TRUE, FALSE) 86 | X <- X %*% svd(X, nu = 0)$v 87 | X <- scale(X, FALSE, TRUE) 88 | } 89 | tryCatch({ 90 | X <- drop(mu) + eS$vectors %*% diag(sqrt(pmax(ev, 91 | 0)), p) %*% t(X) 92 | }, error = function(e) { 93 | stop(err) 94 | }) 95 | mvn <- t(X) 96 | } 97 | if (n == 1) mvn <- matrix(mvn, nrow = 1) 98 | if (length(varnames) == vars) { 99 | colnames(mvn) <- varnames 100 | } else if (!is.null(colnames(cor_mat))) { 101 | colnames(mvn) <- colnames(cor_mat) 102 | } else { 103 | colnames(mvn) <- make_id(ncol(mvn), "X") 104 | } 105 | if (as.matrix == TRUE) 106 | mvn 107 | else data.frame(mvn, check.names = FALSE) 108 | } 109 | 110 | cormat <- function (cors = 0, vars = 3) { 111 | if (is.numeric(cors) & length(cors) == 1) { 112 | if (cors >= -1 & cors <= 1) { 113 | cors = rep(cors, vars * (vars - 1)/2) 114 | } else { 115 | stop("cors must be between -1 and 1") 116 | } 117 | } 118 | if (vars == 1) { 119 | cor_mat <- matrix(1, nrow = 1) 120 | } else if (is.matrix(cors)) { 121 | if (!is.numeric(cors)) { 122 | stop("cors matrix not numeric") 123 | } else if (dim(cors)[1] != vars || dim(cors)[2] != vars) { 124 | stop("cors matrix wrong dimensions") 125 | } else if (sum(cors == t(cors)) != (nrow(cors)^2)) { 126 | stop("cors matrix not symmetric") 127 | } else { 128 | cor_mat <- cors 129 | } 130 | } else if (length(cors) == vars * vars) { 131 | cor_mat <- matrix(cors, vars) 132 | } else if (length(cors) == vars * (vars - 1)/2) { 133 | cor_mat <- cormat_from_triangle(cors) 134 | } 135 | if (!is_pos_def(cor_mat)) { 136 | stop("correlation matrix not positive definite") 137 | } 138 | return(cor_mat) 139 | } 140 | 141 | cormat_from_triangle <- function (cors) { 142 | vars <- ceiling(sqrt(2 * length(cors))) 143 | if (length(cors) != vars * (vars - 1)/2) 144 | stop("you don't have the right number of correlations") 145 | cor_mat <- matrix(nrow = vars, ncol = vars) 146 | upcounter = 1 147 | lowcounter = 1 148 | for (col in 1:vars) { 149 | for (row in 1:vars) { 150 | if (row == col) { 151 | cor_mat[row, col] = 1 152 | } else if (row > col) { 153 | cor_mat[row, col] = cors[lowcounter] 154 | lowcounter <- lowcounter + 1 155 | } 156 | } 157 | } 158 | for (row in 1:vars) { 159 | for (col in 1:vars) { 160 | if (row < col) { 161 | cor_mat[row, col] = cors[upcounter] 162 | upcounter <- upcounter + 1 163 | } 164 | } 165 | } 166 | cor_mat 167 | } 168 | 169 | is_pos_def <- function (cor_mat, tol = 0.00000001) { 170 | ev <- eigen(cor_mat, only.values = TRUE)$values 171 | sum(ev < tol) == 0 172 | } 173 | 174 | make_id <- function (n = 100, prefix = "S", digits = 0, suffix = "") 175 | { 176 | if (!is.numeric(n)) 177 | stop("n must be numeric") 178 | if (length(n) == 1) 179 | n <- 1:n 180 | max_digits <- as.character(n) %>% nchar() %>% max() %>% max(digits) 181 | max_decimal <- as.character(n) %>% sub("(^\\d*\\.|^\\d*$)", 182 | "", .) %>% nchar() %>% max() 183 | fmt <- paste0(prefix, "%0", max_digits, ".", max_decimal, 184 | "f", suffix) 185 | sprintf(fmt, n) 186 | } -------------------------------------------------------------------------------- /docs/404.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Page not found (404) • lmem.sim 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 55 | 56 | 57 | 58 | 59 | 60 | 61 |
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    Appendix 1c: Sensitivity Analysis
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    Appendix 2: Extended Examples
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    Appendix 3b: Extended Binomial Example
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    Launch Shiny App

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    Launch a local copy of the shiny app that accompanies Simulating LMEM

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    app(...)
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    Arguments

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    paper(type = c("pdf", "html", "Rmd"))
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    The type of manuscript to open (pdf, html, or Rmd)

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    Open Simulating LMEM paper

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    Developed by Lisa DeBruine, Dale Barr.

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    Site built with pkgdown 1.6.1.

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    205 | 206 | 207 | 208 | 209 | 210 | 211 | 212 | 213 | -------------------------------------------------------------------------------- /docs/authors.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Citation and Authors • lmem.sim 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 55 | 56 | 57 | 58 | 59 | 60 | 61 |
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    Citation

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    DeBruine, L. M., & Barr, D. J. (2021). Understanding mixed effects models through data simulation. Advances in Methods and Practices in Psychological Science. https://doi.org/10.1177/2515245920965119

    145 | 
    @Article{,
146 |   title = {Understanding mixed effects models through data simulation},
147 |   author = {{DeBruine} and Lisa M. and {Barr} and Dale J.},
148 |   doi = {10.1177/2515245920965119},
149 |   journal = {Advances in Methods and Practices in Psychological Science},
150 |   volume = {4},
151 |   number = {1},
152 |   pages = {2515245920965119},
153 |   year = {2021},
154 |   url = {https://debruine.github.io/lmem_sim/},
155 | }
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    Authors

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      Lisa DeBruine. Author, maintainer. 164 |

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      Dale Barr. Author. 168 |

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    Developed by Lisa DeBruine, Dale Barr.

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    Site built with pkgdown 1.6.1.

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    189 | 190 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | -------------------------------------------------------------------------------- /docs/reference/appendix.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Open Simulating LMEM appendices — appendix • lmem.sim 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | 52 | 56 | 57 | 58 | 59 | 60 | 61 | 62 |
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    Open Simulating LMEM appendices

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    Open Simulating LMEM appendices

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    appendix(i = c("1a", "1b", "1c", "2", "3a", "3b"), filename = NULL)
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    Arguments

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    i

    Which appendix to open

    filename

    Where to save the appendix

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    Developed by Lisa DeBruine, Dale Barr.

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    186 | 187 | 188 | 189 | 190 | 191 | 192 | 193 | 194 | -------------------------------------------------------------------------------- /vignettes/appendix3a_binomial.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: 'Appendix 3a: Binomial Example' 3 | subtitle: "Understanding mixed effects models through data simulation" 4 | author: "Lisa M. DeBruine & Dale J. Barr" 5 | output: rmarkdown::html_vignette 6 | vignette: > 7 | %\VignetteIndexEntry{Appendix 3a: Binomial Example} 8 | %\VignetteEngine{knitr::rmarkdown} 9 | %\VignetteEncoding{UTF-8} 10 | --- 11 | 12 | ```{r setup, include = FALSE} 13 | knitr::opts_chunk$set( 14 | echo = TRUE, 15 | warning = FALSE, 16 | message = FALSE, 17 | fig.width = 8, 18 | fig.height = 5, 19 | out.width = "100%" 20 | ) 21 | ``` 22 | 23 | [Download the .Rmd for this example](https://github.com/debruine/lmem_sim/blob/master/vignettes/appendix3a_binomial.Rmd) 24 | 25 | ## Simulating binomial data with crossed random factors 26 | 27 | To give an overview of the simulation task, we will simulate data from a design with crossed random factors of subjects and stimuli, fit a model to the simulated data, and then try to recover the parameter values we put in from the output. In this hypothetical study, subjects classify the emotional expressions of faces as quickly as possible, and we use accuracy (correct/incorrect) as the primary dependent variable. The faces are of two types: either from the subject's ingroup or from an outgroup. For simplicity, we further assume that each face appears only once in the stimulus set. The key question is whether there is any difference in classification accuracy across the type of face. 28 | 29 | The important parts of the design are: 30 | 31 | * Random factor 1: subjects (associated variables will be prefixed by T, $\tau$, or `tau`) 32 | * Random factor 2: faces (associated variables will be prefixed by O, $\omega$, or `omega`) 33 | * Fixed factor 1: category (level = ingroup, outgroup) 34 | * within subject: subjects see both ingroup and outgroup faces 35 | * between face: faces are either ingroup or outgroup 36 | 37 | ### Required software 38 | 39 | ```{r, message=FALSE} 40 | # load required packages 41 | library("lme4") # model specification / estimation 42 | library("afex") # anova and deriving p-values from lmer 43 | library("broom.mixed") # extracting data from model fits 44 | library("faux") # data simulation 45 | library("tidyverse") # data wrangling and visualisation 46 | 47 | # ensure this script returns the same results on each run 48 | set.seed(8675309) 49 | faux_options(verbose = FALSE) 50 | ``` 51 | 52 | This example presents a simulation for a binomial logistic mixed regression. Part of the process involves conversion between probability and the logit function of probability. The code below converts between these. 53 | 54 | ```{r fig.width = 8, fig.height = 3} 55 | 56 | logit <- function(x) { log(x / (1 - x)) } 57 | inv_logit <- function(x) { 1 / (1 + exp(-x)) } 58 | 59 | data.frame( 60 | prob = seq(0,1,.01) 61 | ) %>% 62 | mutate(logit = logit(prob)) %>% 63 | ggplot(aes(prob, logit)) + 64 | geom_point() 65 | 66 | ``` 67 | 68 | ### Data simulation function 69 | 70 | The data generating process is slighly different for binomial logistic regression. The random effects and their correlations are set the same way as for a gaussian model (you'll need some pilot data to estimate reasonable parameters), but we don't need an error term. 71 | 72 | 73 | ```{r} 74 | 75 | # set up the custom data simulation function 76 | my_bin_data <- function( 77 | n_subj = 100, # number of subjects 78 | n_ingroup = 25, # number of faces in ingroup 79 | n_outgroup = 25, # number of faces in outgroup 80 | beta_0 = 0, # intercept 81 | beta_1 = 0, # effect of category 82 | omega_0 = 1, # by-item random intercept sd 83 | tau_0 = 1, # by-subject random intercept sd 84 | tau_1 = 1, # by-subject random slope sd 85 | rho = 0 # correlation between intercept and slope 86 | ) { 87 | # simulate a sample of items 88 | items <- data.frame( 89 | item_id = 1:(n_ingroup + n_outgroup), 90 | category = rep(c("ingroup", "outgroup"), 91 | c(n_ingroup, n_outgroup)), 92 | O_0i = rnorm(n_ingroup + n_outgroup, 0, omega_0) 93 | ) 94 | 95 | # effect code category 96 | items$X_i <- recode(items$category, 97 | "ingroup" = -0.5, 98 | "outgroup" = 0.5) 99 | 100 | # simulate a sample of subjects 101 | subjects <- faux::rnorm_multi( 102 | n = n_subj, 103 | mu = 0, 104 | sd = c(tau_0, tau_1), 105 | r = rho, 106 | varnames = c("T_0s", "T_1s") 107 | ) 108 | subjects$subj_id <- 1:n_subj 109 | 110 | # cross subject and item IDs 111 | crossing(subjects, items) %>% 112 | mutate( 113 | # calculate gaussian DV 114 | Y = beta_0 + T_0s + O_0i + (beta_1 + T_1s) * X_i, 115 | pr = inv_logit(Y), # transform to probability of getting 1 116 | Y_bin = rbinom(nrow(.), 1, pr) # sample from bernoulli distribution 117 | ) %>% 118 | select(subj_id, item_id, category, X_i, Y, Y_bin) 119 | } 120 | ``` 121 | 122 | 123 | ```{r} 124 | dat_sim <- my_bin_data() 125 | head(dat_sim) 126 | ``` 127 | 128 | ### Power function 129 | 130 | ```{r} 131 | single_run <- function(filename = NULL, ...) { 132 | # ... is a shortcut that forwards any arguments to my_sim_data() 133 | dat_sim <- my_bin_data(...) 134 | mod_sim <- glmer(Y_bin ~ 1 + X_i + (1 | item_id) + (1 + X_i | subj_id), 135 | data = dat_sim, family = "binomial") 136 | 137 | sim_results <- broom.mixed::tidy(mod_sim) 138 | 139 | # append the results to a file if filename is set 140 | if (!is.null(filename)) { 141 | append <- file.exists(filename) # append if the file exists 142 | write_csv(sim_results, filename, append = append) 143 | } 144 | 145 | # return the tidy table 146 | sim_results 147 | } 148 | 149 | ``` 150 | 151 | ```{r} 152 | # run one model with default parameters 153 | single_run() 154 | ``` 155 | 156 | The following function converts probabilities of getting a 1 in the first and second category levels into beta values. You will need to figure out a custom function for each design to do this, or estimate fixed effect parameters from analysis of pilot data. 157 | 158 | ```{r} 159 | prob2param <- function(a = 0, b = 0) { 160 | list( 161 | beta_0 = (logit(a) + logit(b))/2, 162 | beta_1 = logit(a) - logit(b) 163 | ) 164 | } 165 | ``` 166 | 167 | To get an accurate estimation of power, you need to run the simulation many times. We use 20 here as an example because the analysis is very slow, but your results are more accurate the more replications you run. This will depend on the specifics of your analysis, but we recommend at least 1000 replications. 168 | 169 | ```{r} 170 | # run simulations and save to a file on each rep 171 | filename <- "sims/binomial.csv" 172 | reps <- 20 173 | b <- prob2param(.4, .6) 174 | tau_0 <- 1 175 | tau_1 <- 1 176 | omega_0 <- 1 177 | rho <- 0.5 178 | 179 | if (!file.exists(filename)) { 180 | # run simulations and save to a file 181 | sims <- purrr::map_df(1:reps, ~single_run( 182 | filename = filename, 183 | beta_0 = b$beta_0, 184 | beta_1 = b$beta_1, 185 | tau_0 = tau_0, 186 | tau_1 = tau_1, 187 | omega_0 = omega_0, 188 | rho = 0.5) 189 | ) 190 | } 191 | 192 | # read saved simulation data 193 | ct <- cols(# makes sure plots display in this order 194 | group = col_factor(ordered = TRUE), 195 | term = col_factor(ordered = TRUE)) 196 | sims <- read_csv(filename, col_types = ct) 197 | ``` 198 | 199 | 200 | ### Calculate mean estimates and cell probabilities 201 | 202 | ```{r} 203 | est <- sims %>% 204 | group_by(group, term) %>% 205 | summarise( 206 | mean_estimate = mean(estimate), 207 | .groups = "drop" 208 | ) 209 | 210 | int_est <- filter(est, is.na(group), term == "(Intercept)") %>% 211 | pull(mean_estimate) 212 | cat_est <- filter(est, is.na(group), term == "X_i") %>% 213 | pull(mean_estimate) 214 | 215 | pr0 <- inv_logit(int_est) %>% round(2) 216 | pr1_plus <- inv_logit(int_est + .5*cat_est) %>% round(2) 217 | pr1_minus <- inv_logit(int_est - .5*cat_est) %>% round(2) 218 | 219 | est %>% 220 | arrange(!is.na(group), group, term) %>% 221 | mutate( 222 | sim = c(b$beta_0, b$beta_1, omega_0, rho, tau_0, tau_1), 223 | prob = c(pr0, paste0(pr1_minus, ":", pr1_plus), rep(NA, 4)) 224 | ) %>% 225 | mutate_if(is.numeric, round, 2) 226 | ``` 227 | 228 | -------------------------------------------------------------------------------- /inst/appendices/appendix3a_binomial.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: 'Appendix 3a: Binomial Example' 3 | subtitle: "Understanding mixed effects models through data simulation" 4 | author: "Lisa M. DeBruine & Dale J. Barr" 5 | output: rmarkdown::html_vignette 6 | vignette: > 7 | %\VignetteIndexEntry{Appendix 3a: Binomial Example} 8 | %\VignetteEngine{knitr::rmarkdown} 9 | %\VignetteEncoding{UTF-8} 10 | --- 11 | 12 | ```{r setup, include = FALSE} 13 | knitr::opts_chunk$set( 14 | echo = TRUE, 15 | warning = FALSE, 16 | message = FALSE, 17 | fig.width = 8, 18 | fig.height = 5, 19 | out.width = "100%" 20 | ) 21 | ``` 22 | 23 | [Download the .Rmd for this example](https://github.com/debruine/lmem_sim/blob/master/vignettes/appendix3a_binomial.Rmd) 24 | 25 | ## Simulating binomial data with crossed random factors 26 | 27 | To give an overview of the simulation task, we will simulate data from a design with crossed random factors of subjects and stimuli, fit a model to the simulated data, and then try to recover the parameter values we put in from the output. In this hypothetical study, subjects classify the emotional expressions of faces as quickly as possible, and we use accuracy (correct/incorrect) as the primary dependent variable. The faces are of two types: either from the subject's ingroup or from an outgroup. For simplicity, we further assume that each face appears only once in the stimulus set. The key question is whether there is any difference in classification accuracy across the type of face. 28 | 29 | The important parts of the design are: 30 | 31 | * Random factor 1: subjects (associated variables will be prefixed by T, $\tau$, or `tau`) 32 | * Random factor 2: faces (associated variables will be prefixed by O, $\omega$, or `omega`) 33 | * Fixed factor 1: category (level = ingroup, outgroup) 34 | * within subject: subjects see both ingroup and outgroup faces 35 | * between face: faces are either ingroup or outgroup 36 | 37 | ### Required software 38 | 39 | ```{r, message=FALSE} 40 | # load required packages 41 | library("lme4") # model specification / estimation 42 | library("afex") # anova and deriving p-values from lmer 43 | library("broom.mixed") # extracting data from model fits 44 | library("faux") # data simulation 45 | library("tidyverse") # data wrangling and visualisation 46 | 47 | # ensure this script returns the same results on each run 48 | set.seed(8675309) 49 | faux_options(verbose = FALSE) 50 | ``` 51 | 52 | This example presents a simulation for a binomial logistic mixed regression. Part of the process involves conversion between probability and the logit function of probability. The code below converts between these. 53 | 54 | ```{r fig.width = 8, fig.height = 3} 55 | 56 | logit <- function(x) { log(x / (1 - x)) } 57 | inv_logit <- function(x) { 1 / (1 + exp(-x)) } 58 | 59 | data.frame( 60 | prob = seq(0,1,.01) 61 | ) %>% 62 | mutate(logit = logit(prob)) %>% 63 | ggplot(aes(prob, logit)) + 64 | geom_point() 65 | 66 | ``` 67 | 68 | ### Data simulation function 69 | 70 | The data generating process is slighly different for binomial logistic regression. The random effects and their correlations are set the same way as for a gaussian model (you'll need some pilot data to estimate reasonable parameters), but we don't need an error term. 71 | 72 | 73 | ```{r} 74 | 75 | # set up the custom data simulation function 76 | my_bin_data <- function( 77 | n_subj = 100, # number of subjects 78 | n_ingroup = 25, # number of faces in ingroup 79 | n_outgroup = 25, # number of faces in outgroup 80 | beta_0 = 0, # intercept 81 | beta_1 = 0, # effect of category 82 | omega_0 = 1, # by-item random intercept sd 83 | tau_0 = 1, # by-subject random intercept sd 84 | tau_1 = 1, # by-subject random slope sd 85 | rho = 0 # correlation between intercept and slope 86 | ) { 87 | # simulate a sample of items 88 | items <- data.frame( 89 | item_id = 1:(n_ingroup + n_outgroup), 90 | category = rep(c("ingroup", "outgroup"), 91 | c(n_ingroup, n_outgroup)), 92 | O_0i = rnorm(n_ingroup + n_outgroup, 0, omega_0) 93 | ) 94 | 95 | # effect code category 96 | items$X_i <- recode(items$category, 97 | "ingroup" = -0.5, 98 | "outgroup" = 0.5) 99 | 100 | # simulate a sample of subjects 101 | subjects <- faux::rnorm_multi( 102 | n = n_subj, 103 | mu = 0, 104 | sd = c(tau_0, tau_1), 105 | r = rho, 106 | varnames = c("T_0s", "T_1s") 107 | ) 108 | subjects$subj_id <- 1:n_subj 109 | 110 | # cross subject and item IDs 111 | crossing(subjects, items) %>% 112 | mutate( 113 | # calculate gaussian DV 114 | Y = beta_0 + T_0s + O_0i + (beta_1 + T_1s) * X_i, 115 | pr = inv_logit(Y), # transform to probability of getting 1 116 | Y_bin = rbinom(nrow(.), 1, pr) # sample from bernoulli distribution 117 | ) %>% 118 | select(subj_id, item_id, category, X_i, Y, Y_bin) 119 | } 120 | ``` 121 | 122 | 123 | ```{r} 124 | dat_sim <- my_bin_data() 125 | head(dat_sim) 126 | ``` 127 | 128 | ### Power function 129 | 130 | ```{r} 131 | single_run <- function(filename = NULL, ...) { 132 | # ... is a shortcut that forwards any arguments to my_sim_data() 133 | dat_sim <- my_bin_data(...) 134 | mod_sim <- glmer(Y_bin ~ 1 + X_i + (1 | item_id) + (1 + X_i | subj_id), 135 | data = dat_sim, family = "binomial") 136 | 137 | sim_results <- broom.mixed::tidy(mod_sim) 138 | 139 | # append the results to a file if filename is set 140 | if (!is.null(filename)) { 141 | append <- file.exists(filename) # append if the file exists 142 | write_csv(sim_results, filename, append = append) 143 | } 144 | 145 | # return the tidy table 146 | sim_results 147 | } 148 | 149 | ``` 150 | 151 | ```{r} 152 | # run one model with default parameters 153 | single_run() 154 | ``` 155 | 156 | The following function converts probabilities of getting a 1 in the first and second category levels into beta values. You will need to figure out a custom function for each design to do this, or estimate fixed effect parameters from analysis of pilot data. 157 | 158 | ```{r} 159 | prob2param <- function(a = 0, b = 0) { 160 | list( 161 | beta_0 = (logit(a) + logit(b))/2, 162 | beta_1 = logit(a) - logit(b) 163 | ) 164 | } 165 | ``` 166 | 167 | To get an accurate estimation of power, you need to run the simulation many times. We use 20 here as an example because the analysis is very slow, but your results are more accurate the more replications you run. This will depend on the specifics of your analysis, but we recommend at least 1000 replications. 168 | 169 | ```{r} 170 | # run simulations and save to a file on each rep 171 | filename <- "sims/binomial.csv" 172 | reps <- 20 173 | b <- prob2param(.4, .6) 174 | tau_0 <- 1 175 | tau_1 <- 1 176 | omega_0 <- 1 177 | rho <- 0.5 178 | 179 | if (!file.exists(filename)) { 180 | # run simulations and save to a file 181 | sims <- purrr::map_df(1:reps, ~single_run( 182 | filename = filename, 183 | beta_0 = b$beta_0, 184 | beta_1 = b$beta_1, 185 | tau_0 = tau_0, 186 | tau_1 = tau_1, 187 | omega_0 = omega_0, 188 | rho = 0.5) 189 | ) 190 | } 191 | 192 | # read saved simulation data 193 | ct <- cols(# makes sure plots display in this order 194 | group = col_factor(ordered = TRUE), 195 | term = col_factor(ordered = TRUE)) 196 | sims <- read_csv(filename, col_types = ct) 197 | ``` 198 | 199 | 200 | ### Calculate mean estimates and cell probabilities 201 | 202 | ```{r} 203 | est <- sims %>% 204 | group_by(group, term) %>% 205 | summarise( 206 | mean_estimate = mean(estimate), 207 | .groups = "drop" 208 | ) 209 | 210 | int_est <- filter(est, is.na(group), term == "(Intercept)") %>% 211 | pull(mean_estimate) 212 | cat_est <- filter(est, is.na(group), term == "X_i") %>% 213 | pull(mean_estimate) 214 | 215 | pr0 <- inv_logit(int_est) %>% round(2) 216 | pr1_plus <- inv_logit(int_est + .5*cat_est) %>% round(2) 217 | pr1_minus <- inv_logit(int_est - .5*cat_est) %>% round(2) 218 | 219 | est %>% 220 | arrange(!is.na(group), group, term) %>% 221 | mutate( 222 | sim = c(b$beta_0, b$beta_1, omega_0, rho, tau_0, tau_1), 223 | prob = c(pr0, paste0(pr1_minus, ":", pr1_plus), rep(NA, 4)) 224 | ) %>% 225 | mutate_if(is.numeric, round, 2) 226 | ``` 227 | 228 | -------------------------------------------------------------------------------- /inst/app/intro_tab.R: -------------------------------------------------------------------------------- 1 | ### intro_tab ---- 2 | intro_tab <- tabItem( 3 | tabName = "intro_tab", 4 | h3("Introduction"), 5 | p("This app is a companion to Understanding mixed effects models through data simulation by Lisa M. DeBruine and Dale J. Barr."), 6 | tags$a(href="https://psyarxiv.com/xp5cy", "Preprint on PsyArXiv"), 7 | span(" | "), 8 | tags$a(href="https://debruine.github.io/lmem_sim/articles/appendix1_example_code.html", "Example R code"), 9 | span(" | "), 10 | tags$a(href="https://github.com/debruine/lmem_sim/tree/master/inst/app", "Code for this app"), 11 | 12 | 13 | p("Set the parameters in the sidebar menu for a crossed design where raters (subjects) classify the emotional expression of faces (items) as fast as possible. Faces are either from an ingroup or an outgroup category (X_i). The hypothesis is that people will classify the emotions of ingroup faces more quickly than outgroup faces. Learn more about what these parameters mean below."), 14 | HTML("

    Click on Simulating LMER in the sidebar menu to view the output of the lmer summary and see how the parameters you specified affect the output. Click on Compare ANOVA & LMER to compare the results of the mixed effect model with by-subject and by-item aggregated ANOVA. Click on Power & False Positives to run a power analysis using your parameters and compare power and false positive rate between lmer and ANOVA.

    "), 15 | 16 | HTML("

    17 | RTsi = 18 | β0 + 19 | T0s + 20 | O0i + 21 | (β1 + 22 | T1s) * 23 | Xi + 24 | esi 25 |

    "), 26 | 27 | tabBox(width = 12, 28 | tabPanel("Data Generating Process", 29 | HTML("

    The response time for subject s on item i (RTsi) is decomposed into:

    "), 30 | HTML(""), 40 | HTML("

    Our data-generating process is fully determined by seven parameters: two fixed effects (intercept beta_0 and slope beta_1), four variance parameters governing the random effects (tau_0, tau_1, rho, and omega_0), and one parameter governing the trial level variance (sigma).

    ") 41 | ), 42 | tabPanel("Fixed Effects", 43 | HTML("

    The parameters β0 and β1 are fixed effects: they characterize properties of the population of encounters between subjects and stimuli. The grand mean, or intercept (beta_0) is the mean RT for a typical subject encountering a typical stimulus. The main effect of category, or slope (beta_1) is how much faster RT is for ingroup than outgroup faces, on average.

    "), 44 | 45 | sliderInput("beta_0_", "intercept (beta_0)", 46 | min = 600, max = 1000, value = 800, step = 100), 47 | sliderInput("beta_1_", "effect of category (beta_1)", 48 | min = -200, max = 200, value = 50, step = 10), 49 | 50 | HTML("

    Our predictor is categorical, so we need to assign a numeric value to the levels ingroup and ourgroup. In this app, we will use deviation coding where ingroup = -0.5 and outgroup = +0.5. See coding categorical predictor variables in factorial designs for further discussion.

    ") 51 | ), 52 | 53 | tabPanel("Random Intercepts", 54 | 55 | HTML("

    Subjects are not identical in their response characteristics: some will be faster than average, and some slower. We can characterize the difference from the grand mean (beta_0) for each subject s in terms of a random effect T0s. In other words, we assign each subject a unique random intercept.

    "), 56 | 57 | HTML("

    The actual values for T0s in our sampled dataset will depend on which subjects we happened to have sampled from their respective populations. Although the individual values will differ for each sample, we can set a fixed standard deviation (tau_0) for the population to use when we sample subjects.

    "), 58 | sliderInput("tau_0_", "subject intercept SD (tau_0)", 59 | min = 0, max = 200, value = 100, step = 10), 60 | HTML("

    Likewise, it is unrealistic to assume that it is equally easy to categorize emotional expressions across all faces in the dataset; some will be easier than others. We incorporate this assumption by including by-item random intercepts O0i. Again, although the individual values will differ for each sample, we can set a fixed standard deviation (omega_0) for the population to use when we sample items

    "), 61 | sliderInput("omega_0_", "item intercept SD (omega_0)", 62 | min = 0, max = 200, value = 80, step = 10) 63 | ), 64 | 65 | tabPanel("Random Slopes", 66 | HTML("

    The random slope T1s is an estimate of how much faster or slower subject s is in categorizing ingroup/outgroup faces than the population mean effect beta_1. Again, we can set a fixed standard deviation (tau_1) for the population to use when we sample subjects.

    "), 67 | 68 | sliderInput("tau_1_", "subject slope SD (tau_1)", 69 | min = 0, max = 200, value = 40, step = 10) 70 | ), 71 | 72 | tabPanel("Random Correlations", 73 | HTML("

    Note that we are sampling two random effects for each subject s, a random intercept T0s and a random slope T1s. It is possible for these values to be correlated, in which case we should not sample them independently. For instance, perhaps people who are faster than average overall (negative random intercept) also show a smaller than average of the ingroup/outgroup manipulation (negative random slope) due to allocating less attention to the task. We can capture this by allowing for a small correlation between the two factors, rho.

    "), 74 | sliderInput("rho_", "subject intercept*slope correlation (rho)", 75 | min = -0.9, max = 0.9, value = 0.2, step = 0.1) 76 | ), 77 | 78 | tabPanel("Residual Error", 79 | HTML("

    Finally, we need to characterize the trial-level noise in the study (esi) in terms of its standard deviation, sigma.

    "), 80 | sliderInput("sigma_", "residual SD (sigma)", 81 | min = 0, max = 400, value = 200, step = 10) 82 | ), 83 | 84 | tabPanel("Sample Size", 85 | p("Set the number of subjects and faces per group."), 86 | sliderInput("n_subj_", "number of subjects (n_subj)", 87 | min = 10, max = 200, value = 100, step = 10), 88 | sliderInput("n_ingroup_", "faces in the ingroup (n_ingroup)", 89 | min = 5, max = 50, value = 25, step = 5), 90 | sliderInput("n_outgroup_", "faces in the outgroup (n_outgroup)", 91 | min = 5, max = 50, value = 25, step = 5) 92 | ) 93 | ) 94 | ) 95 | -------------------------------------------------------------------------------- /docs/pkgdown.css: -------------------------------------------------------------------------------- 1 | /* Sticky footer */ 2 | 3 | /** 4 | * Basic idea: https://philipwalton.github.io/solved-by-flexbox/demos/sticky-footer/ 5 | * Details: https://github.com/philipwalton/solved-by-flexbox/blob/master/assets/css/components/site.css 6 | * 7 | * 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fixed,NA,(Intercept),-0.282125989112989,0.15943355307907797,-1.7695521655536108,0.07680177341450482 117 | fixed,NA,X_i,-0.6907969122636091,0.26919949586658126,-2.566115178038732,0.010284467188435644 118 | ran_pars,subj_id,sd__(Intercept),1.0142032424974767,NA,NA,NA 119 | ran_pars,subj_id,cor__(Intercept).X_i,0.43606603844721653,NA,NA,NA 120 | ran_pars,subj_id,sd__X_i,1.093598706643477,NA,NA,NA 121 | ran_pars,item_id,sd__(Intercept),0.8339034710654499,NA,NA,NA 122 | -------------------------------------------------------------------------------- /docs/index.html: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Simulating for LMEM • lmem.sim 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 20 | 21 | 22 |
    23 |
    93 | 94 | 95 | 96 | 97 |
    98 |
    99 |
    100 |

    101 | Understanding mixed effects models through data simulation

    102 |

    Lisa M. DeBruine & Dale J. Barr

    103 |

    This repository contains all materials needed to reproduce the manuscript, as well as supplemental scripts and shiny apps.

    104 |

    Abstract Experimental designs that sample both subjects and stimuli from a larger population need to account for random effects of both subjects and stimuli using mixed effects models. However, much of this research is analyzed using ANOVA on aggregated responses because researchers are not confident specifying and interpreting mixed effects models. The tutorial will explain how to simulate data with random effects structure and analyse the data using linear mixed effects regression (with the lme4 R package), with a focus on interpreting the output in light of the simulated parameters. Data simulation can not only enhance understanding of how these models work, but also enables researchers to perform power calculations for complex designs.

    105 | 114 |
    115 |

    116 | Installation

    117 |

    You can install the development version of a package that include all the packages you’ll need for the examples, plus a local version of the shiny app, from GitHub with:

    118 | 
    119 | devtools::install_github("debruine/lmem_sim")
    120 |

    Here are some functions included in the app:

    121 | 
    122 | lmem.sim::paper()        # open the pdf version of the paper
123 | lmem.sim::paper("html")  # open the html version of the paper
124 | lmem.sim::appendix("1a") # open appendix 1a
125 | lmem.sim::app()          # start the app
126 | citation("lmem.sim")     # get the citation
    127 |
    128 |
    129 |
    130 | 131 | 163 |
    164 | 165 | 166 | 175 |
    176 | 177 | 178 | 179 | 180 | 181 | 182 | -------------------------------------------------------------------------------- /inst/appendices/appendix1c_sensitivity.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: 'Appendix 1c: Sensitivity Analysis' 3 | author: "Lisa M. DeBruine & Dale J. Barr" 4 | subtitle: Understanding mixed effects models through data simulation 5 | output: html_document 6 | --- 7 | 8 | ```{r setup, include = FALSE} 9 | knitr::opts_chunk$set( 10 | echo = TRUE, 11 | warning = FALSE, 12 | message = FALSE, 13 | fig.width = 8, 14 | fig.height = 5, 15 | out.width = "100%" 16 | ) 17 | ``` 18 | 19 | [Download the .Rmd for this example](https://github.com/debruine/lmem_sim/blob/master/vignettes/appendix1c_sensitivity.Rmd) 20 | 21 | ### Required software 22 | 23 | ```{r, message=FALSE} 24 | # load required packages 25 | library("lme4") # model specification / estimation 26 | library("lmerTest") # deriving p-values from lmer 27 | library("broom.mixed") # extracting data from model fits 28 | library("faux") # generate correlated values 29 | library("tidyverse") # data wrangling and visualisation 30 | 31 | # ensure this script returns the same results on each run 32 | set.seed(8675309) 33 | faux_options(verbose = FALSE) 34 | ``` 35 | 36 | ### Data simulation function 37 | 38 | The custom simulation function for the example in Appendix 1A is copied below. 39 | 40 | ```{r} 41 | # set up the custom data simulation function 42 | my_sim_data <- function( 43 | n_subj = 100, # number of subjects 44 | n_ingroup = 25, # number of ingroup stimuli 45 | n_outgroup = 25, # number of outgroup stimuli 46 | beta_0 = 800, # grand mean 47 | beta_1 = 50, # effect of category 48 | omega_0 = 80, # by-item random intercept sd 49 | tau_0 = 100, # by-subject random intercept sd 50 | tau_1 = 40, # by-subject random slope sd 51 | rho = 0.2, # correlation between intercept and slope 52 | sigma = 200) { # residual (standard deviation) 53 | 54 | # simulate a sample of items 55 | items <- data.frame( 56 | item_id = seq_len(n_ingroup + n_outgroup), 57 | category = rep(c("ingroup", "outgroup"), c(n_ingroup, n_outgroup)), 58 | X_i = rep(c(-0.5, 0.5), c(n_ingroup, n_outgroup)), 59 | O_0i = rnorm(n = n_ingroup + n_outgroup, mean = 0, sd = omega_0) 60 | ) 61 | 62 | # simulate a sample of subjects 63 | subjects <- faux::rnorm_multi( 64 | n = n_subj, mu = 0, sd = c(tau_0, tau_1), r = rho, 65 | varnames = c("T_0s", "T_1s") 66 | ) 67 | subjects$subj_id <- 1:n_subj 68 | 69 | # cross subject and item IDs 70 | crossing(subjects, items) %>% 71 | mutate( 72 | e_si = rnorm(nrow(.), mean = 0, sd = sigma), 73 | RT = beta_0 + T_0s + O_0i + (beta_1 + T_1s) * X_i + e_si 74 | ) %>% 75 | select(subj_id, item_id, category, X_i, RT) 76 | } 77 | ``` 78 | 79 | 80 | ## Power calculation function 81 | 82 | The power calculation function is slightly more complicated than the one for the basic example. Since sensitivity analyses usually push analyses into parameter spaces where the models produce warnings, we're capturing the warnings and adding them to the results table. We're also adding the parameters to the results table so you can group by the different parameter options when visualising the results. 83 | 84 | ```{r} 85 | # set up the power function 86 | single_run <- function(filename = NULL, ...) { 87 | # ... is a shortcut that forwards any arguments to my_sim_data() 88 | dat_sim <- my_sim_data(...) 89 | 90 | # run lmer and capture any warnings 91 | ww <- "" 92 | suppressMessages(suppressWarnings( 93 | mod_sim <- withCallingHandlers({ 94 | lmer(RT ~ X_i + (1 | item_id) + (1 + X_i | subj_id), 95 | dat_sim, REML = FALSE)}, 96 | warning = function(w) { ww <<- w$message } 97 | ) 98 | )) 99 | 100 | # get results table and add rep number and any warnings 101 | sim_results <- broom.mixed::tidy(mod_sim) %>% 102 | mutate(warnings = ww) 103 | 104 | # add columns for the specified parameters 105 | params <- list(...) 106 | for (name in names(params)) { 107 | sim_results[name] <- params[name] 108 | } 109 | 110 | # append the results to a file if filename is set 111 | if (!is.null(filename)) { 112 | append <- file.exists(filename) # append if the file exists 113 | write_csv(sim_results, filename, append = append) 114 | } 115 | 116 | sim_results 117 | } 118 | 119 | ``` 120 | 121 | ### Example 1: Effect size 122 | 123 | Set up a data table with all of the parameter combinations you want to test. For example, the code below sets up 100 replications for effects of category ranging from 0 to 100 ms in steps of 10. All of the other parameters are default, but we're specifying them anyways so they are saved in the results table. 124 | 125 | ```{r} 126 | filename1 <- "sims/sens1.csv" 127 | nreps <- 100 # number of replications per parameter combo 128 | 129 | params <- crossing( 130 | rep = 1:nreps, # repeats each combo nreps times 131 | n_subj = 100, # number of subjects 132 | n_ingroup = 25, # number of ingroup stimuli 133 | n_outgroup = 25, # number of outgroup stimuli 134 | beta_0 = 800, # grand mean 135 | beta_1 = seq(0, 100, by = 10), # effect of category 136 | omega_0 = 100, # by-item random intercept sd 137 | tau_0 = 80, # by-subject random intercept sd 138 | tau_1 = 40, # by-subject random slope sd 139 | rho = 0.2, # correlation between intercept and slope 140 | sigma = 200 # residual (standard deviation) 141 | ) %>% 142 | select(-rep) # remove rep column 143 | ``` 144 | 145 | This table has 1100 rows, so will run 1100 simulations below. The code below saves the results to a named file or appends them to the file if one exists already. Run a small number of replicates to start and add to it after you're sure your code works and you have an idea how long it takes. 146 | 147 | ```{r, message = FALSE} 148 | if (!file.exists(filename1)) { 149 | # run a simulation for each row of params 150 | # and save to a file on each rep 151 | sims1 <- purrr::pmap_df(params, single_run, filename = filename1) 152 | } 153 | 154 | # read saved simulation data 155 | # NB: col_types is set for warnings in case 156 | # the first 1000 rows don't have any 157 | ct <- cols(warnings = col_character(), 158 | # makes sure plots display in this order 159 | group = col_factor(ordered = TRUE), 160 | term = col_factor(ordered = TRUE)) 161 | sims1 <- read_csv(filename1, col_types = ct) 162 | ``` 163 | 164 | The chunk above will just read the saved data from the named file, if it exists. The code below calculates the mean estimates and power for each group. Make sure to set the `group_by` to the parameters you altered above. 165 | 166 | 167 | ```{r, message=FALSE} 168 | # calculate mean estimates and power for specified alpha 169 | alpha <- 0.05 170 | 171 | power1 <- sims1 %>% 172 | filter(effect == "fixed", term == "X_i") %>% 173 | group_by(term, beta_1) %>% 174 | summarise( 175 | mean_estimate = mean(estimate), 176 | mean_se = mean(std.error), 177 | power = mean(p.value < alpha), 178 | .groups = "drop" 179 | ) 180 | 181 | power1 %>% 182 | ggplot(aes(beta_1, power)) + 183 | geom_point() + 184 | geom_smooth(se = FALSE) + 185 | ylim(0, 1) + 186 | scale_x_continuous(name = "Effect of category in ms (beta_1)", 187 | breaks = seq(0, 100, 10)) + 188 | ggtitle("Power for designs varying in effect size") 189 | ``` 190 | 191 | ### Example 2: Number of subjects and items 192 | 193 | The code below sets up 50 replications for each of 20 combinations of 10 to 50 subjects (by steps of 10) and 10 to 25 stimuli (by steps of 5). 194 | 195 | ```{r} 196 | filename2 <- "sims/sens2.csv" 197 | nreps <- 50 # number of replications per parameter combo 198 | 199 | params <- crossing( 200 | rep = 1:nreps, 201 | n_subj = seq(10, 50, by = 10), 202 | n_ingroup = seq(10, 25, by = 5), 203 | beta_0 = 800, # grand mean 204 | beta_1 = 100, # effect of category 205 | omega_0 = 100, # by-item random intercept sd 206 | tau_0 = 80, # by-subject random intercept sd 207 | tau_1 = 40, # by-subject random slope sd 208 | rho = 0.2, # correlation between intercept and slope 209 | sigma = 200 # residual (standard deviation) 210 | ) %>% 211 | mutate(n_outgroup = n_ingroup) %>% 212 | select(-rep) # remove rep column 213 | ``` 214 | 215 | 216 | ```{r, message = FALSE} 217 | if (!file.exists(filename2)) { 218 | # run a simulation for each row of params 219 | # and save to a file on each rep 220 | sims2 <- purrr::pmap_df(params, single_run, filename = filename2) 221 | } 222 | 223 | # read saved simulation data 224 | sims2 <- read_csv(filename2, col_types = ct) 225 | ``` 226 | 227 | ```{r} 228 | # calculate mean estimates and power for specified alpha 229 | alpha <- 0.05 230 | 231 | power2 <- sims2 %>% 232 | filter(effect == "fixed", term == "X_i") %>% 233 | group_by(term, n_subj, n_ingroup) %>% 234 | summarise( 235 | mean_estimate = mean(estimate), 236 | mean_se = mean(std.error), 237 | power = mean(p.value < alpha), 238 | .groups = "drop" 239 | ) 240 | 241 | power2 %>% 242 | ggplot(aes(n_subj, n_ingroup, fill = power)) + 243 | geom_tile(show.legend = FALSE) + 244 | geom_text(aes(label = round(power, 2)), 245 | color = "black", size = 6) + 246 | scale_x_continuous(name = "Number of subjects", 247 | breaks = seq(10, 50, 10)) + 248 | scale_y_continuous(name = "Number of items/group", 249 | breaks = seq(5, 25, 5)) + 250 | scale_fill_viridis_c(limits = c(0, 1)) + 251 | ggtitle("Power for designs varying in number of subjects and items") 252 | ``` 253 | 254 | 255 | ### Example 3: Random intercept SDs 256 | 257 | The code below sets up 50 replications for designs with 50 subjects, 10 items, and by-item and by-subject random intercept SDs ranging from 20 to 100 in steps of 20. 258 | 259 | ```{r} 260 | 261 | filename3 <- "sims/sens3.csv" 262 | nreps <- 50 # number of replications per parameter combo 263 | 264 | params <- crossing( 265 | rep = 1:nreps, 266 | n_subj = 50, # number of subjects 267 | n_ingroup = 10, # number of ingroup items 268 | n_outgroup = 10, # number of outgroup items 269 | beta_0 = 800, # grand mean 270 | beta_1 = 50, # effect of category 271 | omega_0 = seq(20, 100, by = 20), # by-item random intercept sd 272 | tau_0 = seq(20, 100, by = 20), # by-subject random intercept sd 273 | tau_1 = 40, # by-subject random slope sd 274 | rho = 0.2, # correlation between intercept and slope 275 | sigma = 200 # residual (standard deviation) 276 | ) %>% 277 | select(-rep) # remove rep column 278 | ``` 279 | 280 | ```{r, message = FALSE} 281 | if (!file.exists(filename3)) { 282 | # run a simulation for each row of params 283 | # and save to a file on each rep 284 | sims3 <- purrr::pmap_df(params, single_run, filename = filename3) 285 | } 286 | 287 | # read saved simulation data 288 | sims3 <- read_csv(filename3, col_types = ct) 289 | ``` 290 | 291 | ```{r, message=FALSE} 292 | # calculate mean estimates and power for specified alpha 293 | alpha <- 0.05 294 | 295 | power3 <- sims3 %>% 296 | filter(effect == "fixed", term == "X_i") %>% 297 | group_by(term, omega_0, tau_0) %>% 298 | summarise( 299 | mean_estimate = mean(estimate), 300 | mean_se = mean(std.error), 301 | power = mean(p.value < alpha), 302 | .groups = "drop" 303 | ) 304 | 305 | power3 %>% 306 | ggplot(aes(omega_0, tau_0, fill = power)) + 307 | geom_tile(show.legend = FALSE) + 308 | geom_text(aes(label = round(power, 2)), 309 | color = "white", size = 6) + 310 | scale_x_continuous(name = "By-item random intercept SD (omega_0)", 311 | breaks = seq(20, 100, 20)) + 312 | scale_y_continuous(name = "By-subject random intercept SD (tau_0)", 313 | breaks = seq(20, 100, 20)) + 314 | scale_fill_viridis_c(limits = c(0, 1)) + 315 | ggtitle("Power for designs varying in random intercept SDs") 316 | ``` 317 | 318 | -------------------------------------------------------------------------------- /vignettes/appendix1c_sensitivity.Rmd: -------------------------------------------------------------------------------- 1 | --- 2 | title: 'Appendix 1c: Sensitivity Analysis' 3 | author: "Lisa M. DeBruine & Dale J. Barr" 4 | subtitle: Understanding mixed effects models through data simulation 5 | output: rmarkdown::html_vignette 6 | vignette: > 7 | %\VignetteIndexEntry{Appendix 1c: Sensitivity Analysis} 8 | %\VignetteEngine{knitr::rmarkdown} 9 | %\VignetteEncoding{UTF-8} 10 | --- 11 | 12 | ```{r setup, include = FALSE} 13 | knitr::opts_chunk$set( 14 | echo = TRUE, 15 | warning = FALSE, 16 | message = FALSE, 17 | fig.width = 8, 18 | fig.height = 5, 19 | out.width = "100%" 20 | ) 21 | ``` 22 | 23 | [Download the .Rmd for this example](https://github.com/debruine/lmem_sim/blob/master/vignettes/appendix1c_sensitivity.Rmd) 24 | 25 | ### Required software 26 | 27 | ```{r, message=FALSE} 28 | # load required packages 29 | library("lme4") # model specification / estimation 30 | library("lmerTest") # deriving p-values from lmer 31 | library("broom.mixed") # extracting data from model fits 32 | library("faux") # generate correlated values 33 | library("tidyverse") # data wrangling and visualisation 34 | 35 | # ensure this script returns the same results on each run 36 | set.seed(8675309) 37 | faux_options(verbose = FALSE) 38 | ``` 39 | 40 | ### Data simulation function 41 | 42 | The custom simulation function for the example in Appendix 1A is copied below. 43 | 44 | ```{r} 45 | # set up the custom data simulation function 46 | my_sim_data <- function( 47 | n_subj = 100, # number of subjects 48 | n_ingroup = 25, # number of ingroup stimuli 49 | n_outgroup = 25, # number of outgroup stimuli 50 | beta_0 = 800, # grand mean 51 | beta_1 = 50, # effect of category 52 | omega_0 = 80, # by-item random intercept sd 53 | tau_0 = 100, # by-subject random intercept sd 54 | tau_1 = 40, # by-subject random slope sd 55 | rho = 0.2, # correlation between intercept and slope 56 | sigma = 200) { # residual (standard deviation) 57 | 58 | # simulate a sample of items 59 | items <- data.frame( 60 | item_id = seq_len(n_ingroup + n_outgroup), 61 | category = rep(c("ingroup", "outgroup"), c(n_ingroup, n_outgroup)), 62 | X_i = rep(c(-0.5, 0.5), c(n_ingroup, n_outgroup)), 63 | O_0i = rnorm(n = n_ingroup + n_outgroup, mean = 0, sd = omega_0) 64 | ) 65 | 66 | # simulate a sample of subjects 67 | subjects <- faux::rnorm_multi( 68 | n = n_subj, mu = 0, sd = c(tau_0, tau_1), r = rho, 69 | varnames = c("T_0s", "T_1s") 70 | ) 71 | subjects$subj_id <- 1:n_subj 72 | 73 | # cross subject and item IDs 74 | crossing(subjects, items) %>% 75 | mutate( 76 | e_si = rnorm(nrow(.), mean = 0, sd = sigma), 77 | RT = beta_0 + T_0s + O_0i + (beta_1 + T_1s) * X_i + e_si 78 | ) %>% 79 | select(subj_id, item_id, category, X_i, RT) 80 | } 81 | ``` 82 | 83 | 84 | ## Power calculation function 85 | 86 | The power calculation function is slightly more complicated than the one for the basic example. Since sensitivity analyses usually push analyses into parameter spaces where the models produce warnings, we're capturing the warnings and adding them to the results table. We're also adding the parameters to the results table so you can group by the different parameter options when visualising the results. 87 | 88 | ```{r} 89 | # set up the power function 90 | single_run <- function(filename = NULL, ...) { 91 | # ... is a shortcut that forwards any arguments to my_sim_data() 92 | dat_sim <- my_sim_data(...) 93 | 94 | # run lmer and capture any warnings 95 | ww <- "" 96 | suppressMessages(suppressWarnings( 97 | mod_sim <- withCallingHandlers({ 98 | lmer(RT ~ X_i + (1 | item_id) + (1 + X_i | subj_id), 99 | dat_sim, REML = FALSE)}, 100 | warning = function(w) { ww <<- w$message } 101 | ) 102 | )) 103 | 104 | # get results table and add rep number and any warnings 105 | sim_results <- broom.mixed::tidy(mod_sim) %>% 106 | mutate(warnings = ww) 107 | 108 | # add columns for the specified parameters 109 | params <- list(...) 110 | for (name in names(params)) { 111 | sim_results[name] <- params[name] 112 | } 113 | 114 | # append the results to a file if filename is set 115 | if (!is.null(filename)) { 116 | append <- file.exists(filename) # append if the file exists 117 | write_csv(sim_results, filename, append = append) 118 | } 119 | 120 | sim_results 121 | } 122 | 123 | ``` 124 | 125 | ### Example 1: Effect size 126 | 127 | Set up a data table with all of the parameter combinations you want to test. For example, the code below sets up 100 replications for effects of category ranging from 0 to 100 ms in steps of 10. All of the other parameters are default, but we're specifying them anyways so they are saved in the results table. 128 | 129 | ```{r} 130 | filename1 <- "sims/sens1.csv" 131 | nreps <- 100 # number of replications per parameter combo 132 | 133 | params <- crossing( 134 | rep = 1:nreps, # repeats each combo nreps times 135 | n_subj = 100, # number of subjects 136 | n_ingroup = 25, # number of ingroup stimuli 137 | n_outgroup = 25, # number of outgroup stimuli 138 | beta_0 = 800, # grand mean 139 | beta_1 = seq(0, 100, by = 10), # effect of category 140 | omega_0 = 100, # by-item random intercept sd 141 | tau_0 = 80, # by-subject random intercept sd 142 | tau_1 = 40, # by-subject random slope sd 143 | rho = 0.2, # correlation between intercept and slope 144 | sigma = 200 # residual (standard deviation) 145 | ) %>% 146 | select(-rep) # remove rep column 147 | ``` 148 | 149 | This table has 1100 rows, so will run 1100 simulations below. The code below saves the results to a named file or appends them to the file if one exists already. Run a small number of replicates to start and add to it after you're sure your code works and you have an idea how long it takes. 150 | 151 | ```{r, message = FALSE} 152 | if (!file.exists(filename1)) { 153 | # run a simulation for each row of params 154 | # and save to a file on each rep 155 | sims1 <- purrr::pmap_df(params, single_run, filename = filename1) 156 | } 157 | 158 | # read saved simulation data 159 | # NB: col_types is set for warnings in case 160 | # the first 1000 rows don't have any 161 | ct <- cols(warnings = col_character(), 162 | # makes sure plots display in this order 163 | group = col_factor(ordered = TRUE), 164 | term = col_factor(ordered = TRUE)) 165 | sims1 <- read_csv(filename1, col_types = ct) 166 | ``` 167 | 168 | The chunk above will just read the saved data from the named file, if it exists. The code below calculates the mean estimates and power for each group. Make sure to set the `group_by` to the parameters you altered above. 169 | 170 | 171 | ```{r, message=FALSE} 172 | # calculate mean estimates and power for specified alpha 173 | alpha <- 0.05 174 | 175 | power1 <- sims1 %>% 176 | filter(effect == "fixed", term == "X_i") %>% 177 | group_by(term, beta_1) %>% 178 | summarise( 179 | mean_estimate = mean(estimate), 180 | mean_se = mean(std.error), 181 | power = mean(p.value < alpha), 182 | .groups = "drop" 183 | ) 184 | 185 | power1 %>% 186 | ggplot(aes(beta_1, power)) + 187 | geom_point() + 188 | geom_smooth(se = FALSE) + 189 | ylim(0, 1) + 190 | scale_x_continuous(name = "Effect of category in ms (beta_1)", 191 | breaks = seq(0, 100, 10)) + 192 | ggtitle("Power for designs varying in effect size") 193 | ``` 194 | 195 | ### Example 2: Number of subjects and items 196 | 197 | The code below sets up 50 replications for each of 20 combinations of 10 to 50 subjects (by steps of 10) and 10 to 25 stimuli (by steps of 5). 198 | 199 | ```{r} 200 | filename2 <- "sims/sens2.csv" 201 | nreps <- 50 # number of replications per parameter combo 202 | 203 | params <- crossing( 204 | rep = 1:nreps, 205 | n_subj = seq(10, 50, by = 10), 206 | n_ingroup = seq(10, 25, by = 5), 207 | beta_0 = 800, # grand mean 208 | beta_1 = 100, # effect of category 209 | omega_0 = 100, # by-item random intercept sd 210 | tau_0 = 80, # by-subject random intercept sd 211 | tau_1 = 40, # by-subject random slope sd 212 | rho = 0.2, # correlation between intercept and slope 213 | sigma = 200 # residual (standard deviation) 214 | ) %>% 215 | mutate(n_outgroup = n_ingroup) %>% 216 | select(-rep) # remove rep column 217 | ``` 218 | 219 | 220 | ```{r, message = FALSE} 221 | if (!file.exists(filename2)) { 222 | # run a simulation for each row of params 223 | # and save to a file on each rep 224 | sims2 <- purrr::pmap_df(params, single_run, filename = filename2) 225 | } 226 | 227 | # read saved simulation data 228 | sims2 <- read_csv(filename2, col_types = ct) 229 | ``` 230 | 231 | ```{r} 232 | # calculate mean estimates and power for specified alpha 233 | alpha <- 0.05 234 | 235 | power2 <- sims2 %>% 236 | filter(effect == "fixed", term == "X_i") %>% 237 | group_by(term, n_subj, n_ingroup) %>% 238 | summarise( 239 | mean_estimate = mean(estimate), 240 | mean_se = mean(std.error), 241 | power = mean(p.value < alpha), 242 | .groups = "drop" 243 | ) 244 | 245 | power2 %>% 246 | ggplot(aes(n_subj, n_ingroup, fill = power)) + 247 | geom_tile(show.legend = FALSE) + 248 | geom_text(aes(label = round(power, 2)), 249 | color = "black", size = 6) + 250 | scale_x_continuous(name = "Number of subjects", 251 | breaks = seq(10, 50, 10)) + 252 | scale_y_continuous(name = "Number of items/group", 253 | breaks = seq(5, 25, 5)) + 254 | scale_fill_viridis_c(limits = c(0, 1)) + 255 | ggtitle("Power for designs varying in number of subjects and items") 256 | ``` 257 | 258 | 259 | ### Example 3: Random intercept SDs 260 | 261 | The code below sets up 50 replications for designs with 50 subjects, 10 items, and by-item and by-subject random intercept SDs ranging from 20 to 100 in steps of 20. 262 | 263 | ```{r} 264 | 265 | filename3 <- "sims/sens3.csv" 266 | nreps <- 50 # number of replications per parameter combo 267 | 268 | params <- crossing( 269 | rep = 1:nreps, 270 | n_subj = 50, # number of subjects 271 | n_ingroup = 10, # number of ingroup items 272 | n_outgroup = 10, # number of outgroup items 273 | beta_0 = 800, # grand mean 274 | beta_1 = 50, # effect of category 275 | omega_0 = seq(20, 100, by = 20), # by-item random intercept sd 276 | tau_0 = seq(20, 100, by = 20), # by-subject random intercept sd 277 | tau_1 = 40, # by-subject random slope sd 278 | rho = 0.2, # correlation between intercept and slope 279 | sigma = 200 # residual (standard deviation) 280 | ) %>% 281 | select(-rep) # remove rep column 282 | ``` 283 | 284 | ```{r, message = FALSE} 285 | if (!file.exists(filename3)) { 286 | # run a simulation for each row of params 287 | # and save to a file on each rep 288 | sims3 <- purrr::pmap_df(params, single_run, filename = filename3) 289 | } 290 | 291 | # read saved simulation data 292 | sims3 <- read_csv(filename3, col_types = ct) 293 | ``` 294 | 295 | ```{r, message=FALSE} 296 | # calculate mean estimates and power for specified alpha 297 | alpha <- 0.05 298 | 299 | power3 <- sims3 %>% 300 | filter(effect == "fixed", term == "X_i") %>% 301 | group_by(term, omega_0, tau_0) %>% 302 | summarise( 303 | mean_estimate = mean(estimate), 304 | mean_se = mean(std.error), 305 | power = mean(p.value < alpha), 306 | .groups = "drop" 307 | ) 308 | 309 | power3 %>% 310 | ggplot(aes(omega_0, tau_0, fill = power)) + 311 | geom_tile(show.legend = FALSE) + 312 | geom_text(aes(label = round(power, 2)), 313 | color = "white", size = 6) + 314 | scale_x_continuous(name = "By-item random intercept SD (omega_0)", 315 | breaks = seq(20, 100, 20)) + 316 | scale_y_continuous(name = "By-subject random intercept SD (tau_0)", 317 | breaks = seq(20, 100, 20)) + 318 | scale_fill_viridis_c(limits = c(0, 1)) + 319 | ggtitle("Power for designs varying in random intercept SDs") 320 | ``` 321 | 322 | --------------------------------------------------------------------------------