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<!DOCTYPE html>
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<head>
<title>Bayesian Factor Analysis in R with blavaan</title>
<meta charset="utf-8">
<meta name="Description" content="Fit a Bayesian confirmatory factor analysis in R with blavaan: set priors, read posterior factor loadings and credible intervals, and check Rhat convergence.">
<meta name="Keywords" content="Bayesian factor analysis in R, blavaan, bcfa, Bayesian CFA, confirmatory factor analysis, posterior distribution, credible interval, factor loadings, Rhat, prior distribution">
<meta name="Distribution" content="Global">
<meta name="Author" content="Selva Prabhakaran">
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.sidebar-section-header{padding:7px 12px;font-size:15px;font-weight:700;color:#212529;cursor:pointer;border-radius:4px}
.sidebar-chevron{display:inline-block;font-size:10px;margin-right:4px;color:#757575}
.sidebar-section-items{display:none;padding-left:0;margin:2px 0 6px}
.sidebar-section.expanded .sidebar-section-items{display:block}
.sidebar-section-items li{line-height:1.5}
.sidebar-section-items li a{display:block;padding:4px 10px 4px 32px;font-size:14px;color:#495057;text-decoration:none;border-left:2px solid transparent;border-radius:0 4px 4px 0}
.sidebar-divider{margin:12px 0 2px;padding:0 12px 4px 24px;font-size:11px;font-weight:700;letter-spacing:0.06em;text-transform:uppercase;color:#9ca3af;border-bottom:1px solid #f0f2f5;list-style:none}
.sidebar-divider:first-child{margin-top:4px}
.progress-dot{display:inline-block;width:10px;height:10px;border-radius:50%;border:1.5px solid #d1d5db;margin-right:7px;vertical-align:middle;flex-shrink:0;position:relative}
/* Empty progress-dot (no status class) reads as an unchecked todo /
disabled radio next to every sidebar item — visual noise that doesn't
belong in a nav. Reserve the layout slot but hide the circle until
the item actually has progress. visibility:hidden (not display:none)
keeps the width stable when state flips. */
.progress-dot:not(.started):not(.visited):not(.completed){visibility:hidden}
/* CLS prevention: TOC sidebar matches main.css final state */
#toc-wrapper{position:sticky;top:20px;max-height:calc(100vh - 40px);overflow-y:auto;padding-left:14px;border-left:1px solid #e9ecef}
.toc-title{font-size:11px;font-weight:600;text-transform:uppercase;letter-spacing:0.8px;color:#6c757d;margin-bottom:10px;padding-bottom:0}
#toc{margin:0;padding:0}
#toc li{line-height:1.45;margin-bottom:1px}
#toc li a{font-size:13.5px;color:#6c757d;text-decoration:none;display:block;padding:3px 0;border-left:2px solid transparent;padding-left:8px;margin-left:-15px}
#toc li a.toc-active{color:#1d3158;font-weight:600;border-left-color:#1d3158}
/* CLS prevention: engagement strip layout (matches engagement.css) */
.engagement-header{display:flex;flex-wrap:wrap;align-items:center;gap:6px 10px;font-family:'Inter',-apple-system,BlinkMacSystemFont,'Segoe UI',sans-serif;font-size:12px;color:#64748b;letter-spacing:0.01em;margin:0.4em 0 1em;min-height:22px}
.engagement-header:empty{display:none}
/* CLS prevention: progress bar space (matches engagement.css) */
.engagement-progress{min-height:32px;margin:1.2em 0 1.6em}
/* CLS prevention: WebR editor min-height so the static→textarea swap doesn't shift layout */
.webr-editor{min-height:60px}
/* CLS prevention: images in content always reserve aspect ratio */
#content img{max-width:100%;height:auto}
/* =====================================================
LAYOUT V2 (opt-in via body.layout-v2). Retry 2026-05-29.
Differences from the first attempt:
1. Sidebar columns use clamp(180px, 16vw, 260px) so they
SHRINK on narrow viewports (first attempt used minmax
which pinned both sides at 260px, squeezing content on
typical laptops to ~460px).
2. Sidebar links get overflow-wrap so long tutorial titles
don't escape the narrower column.
3. min-width:0 on every grid child so they can shrink.
4. Right TOC breakpoint raised from 1100px -> 1280px so it
only shows when the viewport can actually afford it.
5. The inline-code background restyle is dropped - kept
current syntax-highlighter behavior.
All rules scoped under body.layout-v2 so pages without it
render identically.
===================================================== */
body.layout-v2{
--lv2-bg:#f8f9fb;--lv2-card:#fff;--lv2-ink:#0d1117;
--lv2-mut:#4b5260;--lv2-faint:#5b6573;
--lv2-navy:#1c2c4f;--lv2-navy-h:#2d4173;--lv2-navy-soft:#eef1f7;
--lv2-accent:#2056d2;--lv2-accent-soft:#e9efff;
--lv2-line:#e4e7ee;--lv2-border:#d4d9e3;
--lv2-green:#15803d;
background:var(--lv2-bg);color:var(--lv2-ink);
}
html.dark body.layout-v2{
--lv2-bg:#0a0f1c;--lv2-card:#0f1525;--lv2-ink:#eef2fa;
--lv2-mut:#a5afc4;--lv2-faint:#9aa6c0;
--lv2-navy:#5170b3;--lv2-navy-h:#6587c4;--lv2-navy-soft:#192240;
--lv2-accent:#7faaff;--lv2-accent-soft:#1a2748;
--lv2-line:#1f2a48;--lv2-border:#2c3a62;
}
/* Wider container; clamp-based grid that scales with viewport.
width:auto is REQUIRED because the base critical CSS has
@media(min-width:1200px){.container{width:1170px}} which would
otherwise pin width to 1170 and ignore max-width:1340. */
body.layout-v2 .container{max-width:1340px;width:auto;padding:0 22px}
body.layout-v2 .row{
display:grid;
grid-template-columns:
clamp(180px, 16vw, 260px)
minmax(0, 1fr)
clamp(180px, 16vw, 260px);
gap:0;margin-left:0;margin-right:0;
}
/* Bootstrap inserts .row::before AND .row::after pseudo-elements
(content:" "; display:table) as a clearfix. Under display:grid
these pseudos count as grid items. ::before grabs col 1, pushing
every real child one column to the right and wrapping the last
child to a new row. The 2026-05-29 first attempt only disabled
::after, resulting in nav in col 2, content in col 3, and toc
wrapping to a new row at col 1 (the bug the user reported as
"sidebar wide, content narrow"). BOTH pseudos must be killed. */
body.layout-v2 .row::before,
body.layout-v2 .row::after{display:none;content:none}
/* min-width:0 lets grid children shrink below their content's
intrinsic min-width; without this, long unbreakable text in any
child forces the column wider than the grid template intended. */
/* Drop Bootstrap's float and width on the legacy .col-sm-* hooks
so the parent .row's CSS grid owns sizing. DO NOT zero horizontal
padding here — per-column padding lives in the dedicated rules
below (sidebar, #content, #toc-sidebar) and gives the article
the 44px breathing room the mock has. */
body.layout-v2 #nav.col-sm-3,
body.layout-v2 #content.col-sm-7,
body.layout-v2 #toc-sidebar.col-sm-2{
width:auto!important;float:none!important;
min-width:0;min-height:0;
}
body.layout-v2 #nav.col-sm-3{
padding:14px 10px 40px;border-right:1px solid var(--lv2-line);
position:sticky;top:60px;height:calc(100vh - 60px);overflow-y:auto;
}
/* Inner #sidebar-nav had its own sticky + overflow from the legacy critical
CSS; under layout-v2 the outer #nav owns scrolling, so flatten the inner
one to avoid a double scrollbar. */
body.layout-v2 #sidebar-nav{
position:static;max-height:none;overflow:visible;padding:0;
}
/* Wrap long tutorial titles in the sidebar so they never overflow */
body.layout-v2 #nav a,
body.layout-v2 #nav span,
body.layout-v2 #sidebar-nav a,
body.layout-v2 #sidebar-nav li{
overflow-wrap:break-word;word-break:break-word;
}
body.layout-v2 #content{padding:24px 44px 60px}
/* S3 — Code-block bottom spacing.
Default .webr-container margin is 22/22; the dark block visually
carries a lot of weight, so the next paragraph reads as cramped.
Lift bottom to 30px under layout-v2. */
body.layout-v2 #content .webr-container{margin-bottom:30px}
/* S7 — Further Reading: convert auto-injected <ul> to a 2-column
card grid that matches the .rt-grid pattern used elsewhere.
No HTML/auto_link.py changes needed — pure CSS. */
body.layout-v2 #content #auto-further-reading .further-reading-list{
list-style:none;padding:0;margin:14px 0 0;
display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:12px;
}
body.layout-v2 #content #auto-further-reading .further-reading-list li{margin:0}
body.layout-v2 #content #auto-further-reading .further-reading-list li a{
display:block;padding:14px 16px;
background:var(--lv2-card);border:1px solid var(--lv2-border);
border-radius:8px;color:var(--lv2-ink);
font-weight:500;font-size:15px;line-height:1.4;
text-decoration:none;
transition:border-color .15s,background .15s,transform .15s;
}
body.layout-v2 #content #auto-further-reading .further-reading-list li a:hover{
border-color:var(--lv2-accent);background:var(--lv2-accent-soft);
text-decoration:none;transform:translateY(-1px);
}
@media(max-width:820px){
body.layout-v2 #content #auto-further-reading .further-reading-list{
grid-template-columns:1fr;
}
}
body.layout-v2 #toc-sidebar{padding:24px 18px;position:sticky;top:74px;align-self:start}
@media(max-width:1280px){
body.layout-v2 .row{grid-template-columns:clamp(180px, 18vw, 260px) minmax(0,1fr)}
body.layout-v2 #toc-sidebar{display:none}
}
@media(max-width:820px){
body.layout-v2 .row{grid-template-columns:1fr}
body.layout-v2 #nav{display:none}
body.layout-v2 #content{padding:20px}
}
/* Typography refresh - sized to mock spec */
body.layout-v2 #content{
font-size:16.5px;line-height:1.7;color:var(--lv2-ink);
font-feature-settings:"tnum","ss01","cv11";text-rendering:optimizeLegibility;
}
body.layout-v2 #content p{line-height:1.7;margin:13px 0;color:var(--lv2-ink);text-wrap:pretty}
body.layout-v2 #content h1{
font-size:38px;font-weight:700;line-height:1.2;letter-spacing:-0.018em;
margin:10px 0 13px;text-wrap:balance;color:var(--lv2-ink);
}
/* H2: hairline divider + breathing room above. Mock breaks each
section with a top rule and ~48px space; staging used 34px and no
divider, leaving sections to blur together. :first-of-type keeps
the very first H2 flush with the actionbar (no double divider). */
body.layout-v2 #content h2{
font-size:25px;font-weight:600;line-height:1.25;letter-spacing:-0.018em;
margin:48px 0 12px;padding-top:32px;border-top:1px solid var(--lv2-line);
text-wrap:balance;color:var(--lv2-ink);
}
body.layout-v2 #content h2:first-of-type{
margin-top:24px;padding-top:0;border-top:none;
}
body.layout-v2 #content h3,body.layout-v2 #content h4{
font-size:18px;font-weight:600;line-height:1.3;margin:24px 0 8px;text-wrap:balance;color:var(--lv2-ink);
}
/* Specificity bump: `body.layout-v2 #content p` (1 id + 1 class
+ 2 elements) was beating `body.layout-v2 p.lead` (2 classes +
2 elements) and forcing the dek to var(--lv2-ink) instead of
var(--lv2-mut). Adding #content here matches that specificity. */
body.layout-v2 #content p.lead{
font-size:18.5px;line-height:1.6;color:var(--lv2-mut);
border-left:3px solid var(--lv2-navy);padding-left:17px;margin:-2px 0 20px;font-weight:400;
}
/* Body link color: legacy a{color:#1d3158} and Bootstrap .text-muted
leave inline links almost indistinguishable from body text. Use
the mock accent so links are obviously clickable. Excludes
buttons, cards, prev/next nav, and TOC items which have their
own palette. */
body.layout-v2 #content a:not(.btn):not(.rt-card):not(.pn-link):not(.lv2-anchor):not([class*="toc"]){
color:var(--lv2-accent);
}
body.layout-v2 #content a:not(.btn):not(.rt-card):not(.pn-link):not(.lv2-anchor):not([class*="toc"]):hover{
text-decoration:underline;
}
/* Inline <code> palette: match the mock's navy-soft tint instead
of the legacy purple-blue (#eef vs #eef1f7). */
body.layout-v2 #content :not(pre) > code{
background:var(--lv2-navy-soft);color:var(--lv2-ink);
border-radius:4px;padding:2px 5px;font-size:0.92em;
}
/* TOC right rail */
body.layout-v2 #toc-sidebar .toc-title{font-size:10.5px;font-weight:700;text-transform:uppercase;letter-spacing:.08em;color:var(--lv2-faint);margin-bottom:9px}
body.layout-v2 #toc{font-size:13px}
body.layout-v2 #toc li{margin:0;line-height:1.45}
body.layout-v2 #toc li a{
display:block;padding:5px 0 5px 11px;
border-left:2px solid var(--lv2-line);
color:var(--lv2-faint);font-size:13px;
transition:color .15s,border-color .15s;
}
body.layout-v2 #toc li a:hover{color:var(--lv2-ink)}
body.layout-v2 #toc li a.toc-active{
border-left-color:var(--lv2-navy);color:var(--lv2-ink);font-weight:600;
}
/* Reading progress bar - uses transform:scaleX so we don't fight any
containing-block / overflow quirks that can pin a width-% bar to 0. */
.lv2-progress{
position:fixed;top:0;left:0;width:100vw;height:3px;
background:var(--lv2-accent,#2056d2);z-index:90;
transform:scaleX(0);transform-origin:left center;
transition:transform .1s ease-out;pointer-events:none;
}
/* Heading anchor links (hover-reveal) */
body.layout-v2 #content h2,
body.layout-v2 #content h3,
body.layout-v2 #content h4{position:relative}
body.layout-v2 .lv2-anchor{
position:absolute;left:-26px;top:50%;transform:translateY(-50%);
font-size:.55em;color:var(--lv2-faint);text-decoration:none;
opacity:0;transition:opacity .15s,color .15s;
cursor:pointer;padding:4px 6px;line-height:1;font-weight:400;
}
body.layout-v2 #content h2:hover .lv2-anchor,
body.layout-v2 #content h3:hover .lv2-anchor,
body.layout-v2 #content h4:hover .lv2-anchor,
body.layout-v2 .lv2-anchor:focus-visible{opacity:1}
body.layout-v2 .lv2-anchor:hover{color:var(--lv2-accent)}
@media(max-width:820px){body.layout-v2 .lv2-anchor{left:0;top:-22px;transform:none}}
/* Focus ring refresh */
body.layout-v2 a:focus-visible,
body.layout-v2 button:focus-visible,
body.layout-v2 input:focus-visible,
body.layout-v2 textarea:focus-visible{
outline:none;
box-shadow:0 0 0 3px rgba(32,86,210,.22);
border-radius:4px;
}
html.dark body.layout-v2 a:focus-visible,
html.dark body.layout-v2 button:focus-visible,
html.dark body.layout-v2 input:focus-visible{box-shadow:0 0 0 3px rgba(127,170,255,.22)}
/* Reduced motion: shut everything down for users who request it */
@media (prefers-reduced-motion: reduce){
body.layout-v2 *,body.layout-v2 *::before,body.layout-v2 *::after{
animation-duration:0.01ms!important;
animation-iteration-count:1!important;
transition-duration:0.01ms!important;
scroll-behavior:auto!important;
}
}
</style>
<!-- Full Bootstrap deferred (non-render-blocking) -->
<link href="www/bootstrap.min.css?h=dae0a568" rel="stylesheet" media="print" onload="this.media='all'">
<noscript><link href="www/bootstrap.min.css?h=dae0a568" rel="stylesheet"></noscript>
<!-- Roadmap-jel: load code-highlight CSS normally (not deferred) so code blocks paint COLORED on first load, not after interaction. Small file; negligible render cost. -->
<link href="www/highlight.min.css?h=f103014a" rel="stylesheet">
<link href="css/main.min.css?h=78c68235" rel="stylesheet" media="print" onload="this.media='all'">
<noscript><link href="css/main.min.css?h=78c68235" rel="stylesheet"></noscript>
<!-- Sitewide navbar (canonical roadmap .nav design). Loaded sync: the nav
is above the fold and must never flash unstyled. -->
<link href="/www/site-nav.css?v=19" rel="stylesheet">
<style>
a{color:#1d3158}a:hover{text-decoration:underline}
li{line-height:1.65}
.MathJax_Display{margin:0}
blockquote p{line-height:1.75;color:#717171}
/* engagement.js renders a meta strip into .engagement-header that
duplicates the byline (difficulty + time). Hide it; saved-posts-
button.js reads the data-* attrs directly for the byline. */
.engagement-header{display:none!important}
/* Byline (saved-posts widget rebuilds this after H1+lead, mock-style) */
.byline{display:flex;flex-wrap:wrap;align-items:center;gap:8px;
font-size:13.5px;color:#4b5260;margin:6px 0 16px;line-height:1.5}
/* P1 — bump avatar 26→30 to match mock visual weight. */
.byline .av-sm{width:30px;height:30px;border-radius:50%;
background:linear-gradient(135deg,#1c2c4f,#2d4173);color:#fff;
display:inline-flex;align-items:center;justify-content:center;
font-weight:700;font-size:12px;flex:none;letter-spacing:.02em}
.byline .who{color:#0d1117;font-weight:600}
.byline .dot{color:#c0c5cf}
.byline .rev{color:#137a3e;font-weight:600;display:inline-flex;align-items:center;gap:4px}
.byline .time{display:inline-flex;align-items:center;gap:4px;color:#6b7280}
.byline .diff{font-size:10.5px;font-weight:700;text-transform:uppercase;
letter-spacing:.05em;background:#eef1f7;color:#4b5260;
padding:3px 8px;border-radius:999px;margin-left:2px}
/* Action bar (saved-posts widget injects this after byline) */
.actionbar{display:flex;align-items:center;gap:9px;margin:10px 0 26px;padding:12px 0;
border-top:1px solid #e4e7ee;border-bottom:1px solid #e4e7ee;flex-wrap:wrap}
.actionbar .act{display:inline-flex;align-items:center;gap:6px;border:1px solid #d4d9e3;
background:#fff;border-radius:9px;padding:7px 12px;font-size:13px;font-weight:600;
color:#4b5260;cursor:pointer;font-family:inherit;
transition:border-color .15s,color .15s,background .15s}
.actionbar .act:hover{border-color:#0a0d14;color:#0a0d14}
.actionbar .act.bookmark-btn[data-saved="1"]{background:#fef3c7;border-color:#f59e0b;color:#92400e}
.actionbar .act.bookmark-btn[data-saved="1"] svg{fill:#f59e0b}
.actionbar .act:disabled{opacity:.55;cursor:wait}
.actionbar-sync{margin-left:auto;font-size:12px;color:#6b7280}
.actionbar-sync a{color:#2056d2;font-weight:600;text-decoration:none}
.actionbar-sync a:hover{text-decoration:underline}
/* Dark-mode overrides for byline + actionbar. The hard-coded #0d1117
on .who renders invisible on the dark background; the action-bar
borders and surfaces also need to flip. Tokens (--lv2-ink, --lv2-mut,
--lv2-line, --lv2-card) already swap under html.dark body.layout-v2;
we just need to point the hard-coded rules at them under dark. */
html.dark body.layout-v2 .byline{color:var(--lv2-mut)}
html.dark body.layout-v2 .byline .who{color:var(--lv2-ink)}
html.dark body.layout-v2 .byline .dot{color:var(--lv2-faint)}
html.dark body.layout-v2 .byline .time{color:var(--lv2-mut)}
html.dark body.layout-v2 .byline .diff{background:var(--lv2-navy-soft);color:var(--lv2-mut)}
html.dark body.layout-v2 .actionbar{border-top-color:var(--lv2-line);border-bottom-color:var(--lv2-line)}
html.dark body.layout-v2 .actionbar .act{background:var(--lv2-card);border-color:var(--lv2-border);color:var(--lv2-mut)}
html.dark body.layout-v2 .actionbar .act:hover{border-color:var(--lv2-ink);color:var(--lv2-ink)}
html.dark body.layout-v2 .actionbar-sync{color:var(--lv2-mut)}
/* Toast (Share button "Link copied" feedback) */
.rs-toast{position:fixed;bottom:24px;left:50%;transform:translateX(-50%) translateY(8px);
background:#0a0d14;color:#fff;padding:9px 18px;border-radius:8px;font-size:13px;
font-family:'IBM Plex Sans',sans-serif;z-index:1000;opacity:0;pointer-events:none;
transition:opacity .2s,transform .2s;box-shadow:0 8px 24px rgba(10,13,20,.25)}
.rs-toast.show{opacity:1;transform:translateX(-50%) translateY(0)}
/* Auth-state visibility helpers (used by masthead variants) */
.auth-anon,.auth-user{display:none}
body.state-anon .auth-anon{display:inline-flex;align-items:center}
body.state-pro .auth-user{display:inline-flex;align-items:center;gap:8px}
.auth-signout.masthead-icon-btn{background:none;border:1px solid #d8dce2;border-radius:6px;padding:4px 9px;font-size:14px;line-height:1;color:#4a5160;cursor:pointer;transition:border-color .15s,color .15s}
.auth-signout.masthead-icon-btn:hover{border-color:#9a1f1f;color:#9a1f1f}
html.dark .auth-signout.masthead-icon-btn{border-color:#262a31;color:#c3cad9}
html.dark .auth-signout.masthead-icon-btn:hover{border-color:#f08989;color:#f08989}
@media(min-width:1200px){.container{width:1170px}}
#nav,#content,#toc-sidebar{box-sizing:border-box}
#content{padding-left:15px;padding-right:15px;overflow-wrap:break-word;word-wrap:break-word;overflow-x:clip}
@media(max-width:767px){#nav{display:none}}
.mobile-sidebar-overlay{display:none;position:fixed;top:0;left:0;right:0;bottom:0;z-index:9999;background:rgba(0,0,0,0.4)}
.mobile-sidebar-overlay.open{display:block}
.mobile-sidebar-panel{position:fixed;top:0;left:0;bottom:0;width:280px;background:#fff;z-index:10000;overflow-y:auto;padding:16px;box-shadow:2px 0 16px rgba(0,0,0,0.15);transform:translateX(-100%);transition:transform 0.25s ease}
.mobile-sidebar-overlay.open .mobile-sidebar-panel{transform:translateX(0)}
.mobile-sidebar-close{position:absolute;top:10px;right:12px;background:none;border:none;font-size:22px;cursor:pointer;color:#666}
/* Mobile top-nav drawer section */
.mnav-section{margin-bottom:18px;padding-bottom:14px;border-bottom:1px solid #e5e7eb}
.mnav-section:last-child{border-bottom:none}
.mnav-title{font-family:'IBM Plex Sans',sans-serif;font-size:11px;font-weight:600;color:#8a8f99;text-transform:uppercase;letter-spacing:0.06em;margin:0 0 8px}
.mnav-link{display:block;padding:9px 10px;color:#3a3f4a;text-decoration:none;font-size:15px;border-radius:6px;font-family:'IBM Plex Sans',sans-serif}
.mnav-link:hover,.mnav-link:active{background:#f1f3f6;color:#0d1117;text-decoration:none}
.mnav-accordion{padding:0}
.mnav-accordion>summary{padding:9px 10px;cursor:pointer;font-size:15px;font-weight:500;color:#3a3f4a;list-style:none;border-radius:6px;font-family:'IBM Plex Sans',sans-serif;display:flex;align-items:center;justify-content:space-between}
.mnav-accordion>summary::-webkit-details-marker{display:none}
.mnav-accordion>summary::after{content:'\25BE';font-size:11px;color:#8a8f99;transition:transform 0.15s}
.mnav-accordion[open]>summary::after{transform:rotate(180deg)}
.mnav-accordion>summary:hover{background:#f1f3f6}
.mnav-accordion-body{padding:4px 6px 8px 10px}
.mnav-accordion-body .mnav-link{padding:7px 8px;font-size:14px;color:#4a5160}
.mnav-accordion-body h6{margin:10px 0 4px 8px;font-family:'IBM Plex Sans',sans-serif;font-size:10px;font-weight:600;color:#8a8f99;text-transform:uppercase;letter-spacing:0.06em}
html.dark .mobile-sidebar-panel{background:#1e293b}
html.dark .mobile-sidebar-overlay{background:rgba(0,0,0,0.6)}
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title="R Control Flow"><span class="progress-dot"></span>R Control Flow</a></li><li data-subkey="sec0sub2"><a href="/R-Special-Values.html" title="R Special Values"><span class="progress-dot"></span>R Special Values</a></li><li data-subkey="sec0sub2"><a href="/R-Type-Coercion.html" title="R Type Coercion"><span class="progress-dot"></span>R Type Coercion</a></li><li data-subkey="sec0sub2"><a href="/R-Functions.html" title="Writing R Functions"><span class="progress-dot"></span>Writing R Functions</a></li><li data-subkey="sec0sub2" class="is-quiz"><a href="/R-Beginner-Exercises-quiz.html" title="R Fundamentals Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec0sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Working Effectively</li><li data-subkey="sec0sub3"><a href="/R-Subsetting.html" title="R Subsetting"><span class="progress-dot"></span>R Subsetting</a></li><li data-subkey="sec0sub3"><a href="/Getting-Help-in-R.html" title="Getting Help in R"><span class="progress-dot"></span>Getting Help in R</a></li><li data-subkey="sec0sub3"><a href="/R-Project-Structure.html" title="R Project Structure"><span class="progress-dot"></span>R Project Structure</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec0sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> R Career & Resources</li><li data-subkey="sec0sub4"><a href="/R-vs-Python.html" title="R vs Python"><span class="progress-dot"></span>R vs Python</a></li><li data-subkey="sec0sub4"><a href="/How-to-Learn-R.html" title="How to Learn R"><span class="progress-dot"></span>How to Learn R</a></li><li data-subkey="sec0sub4"><a href="/R-for-Excel-Users.html" title="R for Excel Users"><span class="progress-dot"></span>R for Excel Users</a></li><li data-subkey="sec0sub4"><a href="/R-Interview-Questions.html" title="R Interview Questions"><span class="progress-dot"></span>R Interview Questions</a></li><li data-subkey="sec0sub4" class="is-quiz"><a href="/R-Interview-Questions-quiz.html" title="R Interview Readiness Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec0sub4"><a href="/R-Cheat-Sheet.html" title="R Cheat Sheet"><span class="progress-dot"></span>R Cheat Sheet</a></li><li data-subkey="sec0sub4"><a href="/Bias-in-Data-and-Models.html" title="Bias in Data and Models"><span class="progress-dot"></span>Bias in Data and Models</a></li><li data-subkey="sec0sub4"><a href="/Communicating-Uncertainty.html" title="Communicating Uncertainty"><span class="progress-dot"></span>Communicating Uncertainty</a></li><li data-subkey="sec0sub4"><a href="/Data-Ethics-in-R.html" title="Data Ethics"><span class="progress-dot"></span>Data Ethics</a></li><li data-subkey="sec0sub4"><a href="/Data-Privacy-in-R.html" title="Data Privacy in R"><span class="progress-dot"></span>Data Privacy in R</a></li><li data-subkey="sec0sub4"><a href="/R-Foundations-Basics-Course.html" title="R Foundations: The Basics (Course)"><span class="progress-dot"></span>R Foundations: The Basics (Course)</a></li><li data-subkey="sec0sub4"><a href="/R-Foundations-Debugging-Course.html" title="R Foundations: Debugging (Course)"><span class="progress-dot"></span>R Foundations: Debugging (Course)</a></li><li data-subkey="sec0sub4"><a href="/R-Foundations-Iteration-Course.html" title="R Foundations: Iteration (Course)"><span class="progress-dot"></span>R Foundations: Iteration (Course)</a></li><li data-subkey="sec0sub4"><a href="/R-Foundations-Structures-Course.html" title="R Foundations: Data Structures (Course)"><span class="progress-dot"></span>R Foundations: Data Structures (Course)</a></li><li data-subkey="sec0sub4"><a href="/R-Foundations-Workflow-Course.html" title="R Foundations: Reproducible Workflow (Course)"><span class="progress-dot"></span>R Foundations: Reproducible Workflow (Course)</a></li><li data-subkey="sec0sub4"><a href="/Reproducibility-Crisis.html" title="Reproducibility Crisis"><span class="progress-dot"></span>Reproducibility Crisis</a></li></ul></li><li class="sidebar-section expanded"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span><span class="sec-num">2.</span> <span class="sec-title-t">Data Wrangling</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Import & Setup</li><li data-subkey="sec1sub1"><a href="/Importing-Data-in-R.html" title="Importing Data"><span class="progress-dot"></span>Importing Data</a></li><li data-subkey="sec1sub1"><a href="/R-Pipe-Operator.html" title="Pipe Operator"><span class="progress-dot"></span>Pipe Operator</a></li><li data-subkey="sec1sub1"><a href="/Tidy-Data-in-R.html" title="Tidy Data"><span class="progress-dot"></span>Tidy Data</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> dplyr Essentials</li><li data-subkey="sec1sub2"><a href="/dplyr-filter-select.html" title="dplyr filter & select"><span class="progress-dot"></span>dplyr filter & select</a></li><li data-subkey="sec1sub2"><a href="/dplyr-mutate-rename.html" title="dplyr mutate & rename"><span class="progress-dot"></span>dplyr mutate & rename</a></li><li data-subkey="sec1sub2"><a href="/dplyr-group-by-summarise.html" title="dplyr group_by & summarise"><span class="progress-dot"></span>dplyr group_by & summarise</a></li><li data-subkey="sec1sub2"><a href="/dplyr-arrange-slice.html" title="dplyr arrange & slice"><span class="progress-dot"></span>dplyr arrange & slice</a></li><li data-subkey="sec1sub2"><a href="/dplyr-across.html" title="dplyr across()"><span class="progress-dot"></span>dplyr across()</a></li><li data-subkey="sec1sub2"><a href="/dplyr-case-when.html" title="dplyr case_when()"><span class="progress-dot"></span>dplyr case_when()</a></li><li data-subkey="sec1sub2" class="is-quiz"><a href="/dplyr-Exercises-in-R-quiz.html" title="dplyr Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Join & Reshape</li><li data-subkey="sec1sub3"><a href="/R-Joins.html" title="R Joins"><span class="progress-dot"></span>R Joins</a></li><li data-subkey="sec1sub3"><a href="/pivot_longer-pivot_wider-Reshape-Data-in-R.html" title="pivot_longer & pivot_wider"><span class="progress-dot"></span>pivot_longer & pivot_wider</a></li><li data-subkey="sec1sub3"><a href="/tidyr-separate-unite-Split-Combine-Columns-in-R.html" title="separate() & unite()"><span class="progress-dot"></span>separate() & unite()</a></li><li data-subkey="sec1sub3" class="is-quiz"><a href="/tidyr-Exercises-in-R-quiz.html" title="tidyr Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Clean & Quality</li><li data-subkey="sec1sub4"><a href="/Missing-Values-in-R-Detect-Count-Remove-Impute-NA.html" title="Missing Values (NA)"><span class="progress-dot"></span>Missing Values (NA)</a></li><li data-subkey="sec1sub4"><a href="/Data-Quality-Checking-in-R.html" title="Data Quality Checking"><span class="progress-dot"></span>Data Quality Checking</a></li><li data-subkey="sec1sub4"><a href="/janitor-Package-in-R.html" title="janitor Package"><span class="progress-dot"></span>janitor Package</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub5" data-collapsed="false"><span class="subsec-chevron">▼</span> Strings & Dates</li><li data-subkey="sec1sub5"><a href="/stringr-in-R.html" title="stringr"><span class="progress-dot"></span>stringr</a></li><li data-subkey="sec1sub5"><a href="/R-Regex-stringr-Pattern-Matching.html" title="Regex Patterns"><span class="progress-dot"></span>Regex Patterns</a></li><li data-subkey="sec1sub5"><a href="/lubridate-in-R.html" title="lubridate"><span class="progress-dot"></span>lubridate</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub6" data-collapsed="false"><span class="subsec-chevron">▼</span> Scale & Connect</li><li data-subkey="sec1sub6"><a href="/DBI-in-R.html" title="DBI & Databases"><span class="progress-dot"></span>DBI & Databases</a></li><li data-subkey="sec1sub6"><a href="/DuckDB-in-R.html" title="DuckDB & duckplyr"><span class="progress-dot"></span>DuckDB & duckplyr</a></li><li data-subkey="sec1sub6"><a href="/Web-Scraping-in-R-with-rvest.html" title="Web Scraping (rvest)"><span class="progress-dot"></span>Web Scraping (rvest)</a></li><li data-subkey="sec1sub6"><a href="/REST-APIs-in-R-with-httr2.html" title="REST APIs (httr2)"><span class="progress-dot"></span>REST APIs (httr2)</a></li><li data-subkey="sec1sub6"><a href="/Data-Wrangling-dplyr-Course.html" title="Data Wrangling with dplyr (Course)"><span class="progress-dot"></span>Data Wrangling with dplyr (Course)</a></li><li data-subkey="sec1sub6"><a href="/Join-Reshape-Course.html" title="Join & Reshape (Course)"><span class="progress-dot"></span>Join & Reshape (Course)</a></li><li data-subkey="sec1sub6"><a href="/data-table-Course.html" title="data.table (Course)"><span class="progress-dot"></span>data.table (Course)</a></li><li data-subkey="sec1sub6"><a href="/Report-Tables-Course.html" title="Report-Ready Tables (Course)"><span class="progress-dot"></span>Report-Ready Tables (Course)</a></li><li data-subkey="sec1sub6"><a href="/Communicate-Automate-Course.html" title="Communicate & Automate (Course)"><span class="progress-dot"></span>Communicate & Automate (Course)</a></li></ul></li><li class="sidebar-section expanded"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span><span class="sec-num">3.</span> <span class="sec-title-t">Statistics</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> EDA & Data Quality</li><li data-subkey="sec2sub1"><a href="/Automated-EDA-in-R.html" title="Automated EDA"><span class="progress-dot"></span>Automated EDA</a></li><li data-subkey="sec2sub1"><a href="/Missing-Data-Visualization-in-R-naniar.html" title="Missing Data Viz (naniar)"><span class="progress-dot"></span>Missing Data Viz (naniar)</a></li><li data-subkey="sec2sub1"><a href="/Outlier-Detection-in-R.html" title="Outlier Detection"><span class="progress-dot"></span>Outlier Detection</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> Probability</li><li data-subkey="sec2sub2"><a href="/Sample-Spaces-Events-and-Probability-Axioms-in-R-With-Monte-Carlo-Proof.html" title="Probability Axioms"><span class="progress-dot"></span>Probability Axioms</a></li><li data-subkey="sec2sub2"><a href="/Conditional-Probability-in-R.html" title="Conditional Probability"><span class="progress-dot"></span>Conditional Probability</a></li><li data-subkey="sec2sub2"><a href="/Random-Variables-in-R.html" title="Random Variables"><span class="progress-dot"></span>Random Variables</a></li><li data-subkey="sec2sub2"><a href="/Binomial-and-Poisson-Distributions-in-R.html" title="Binomial vs Poisson"><span class="progress-dot"></span>Binomial vs Poisson</a></li><li data-subkey="sec2sub2"><a href="/Normal-t-F-and-Chi-Squared-Distributions-in-R.html" title="Normal, t, F, Chi-Squared"><span class="progress-dot"></span>Normal, t, F, Chi-Squared</a></li><li data-subkey="sec2sub2"><a href="/Central-Limit-Theorem-in-R.html" title="Central Limit Theorem"><span class="progress-dot"></span>Central Limit Theorem</a></li><li data-subkey="sec2sub2"><a href="/Sampling-Distributions-in-R.html" title="Sampling Distributions"><span class="progress-dot"></span>Sampling Distributions</a></li><li data-subkey="sec2sub2"><a href="/Law-of-Large-Numbers-vs-CLT-in-R.html" title="LLN vs CLT"><span class="progress-dot"></span>LLN vs CLT</a></li><li data-subkey="sec2sub2"><a href="/What-Is-Probability-Simulation-First-Intuition-in-R-Before-the-Formulas.html" title="Probability (Simulation-First)"><span class="progress-dot"></span>Probability (Simulation-First)</a></li><li data-subkey="sec2sub2"><a href="/Expected-Value-and-Variance-in-R.html" title="Expected Value and Variance"><span class="progress-dot"></span>Expected Value and Variance</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Inference & Estimation</li><li data-subkey="sec2sub3"><a href="/Maximum-Likelihood-Estimation-in-R.html" title="Maximum Likelihood Estimation"><span class="progress-dot"></span>Maximum Likelihood Estimation</a></li><li data-subkey="sec2sub3"><a href="/Hypothesis-Testing-in-R.html" title="Hypothesis Testing"><span class="progress-dot"></span>Hypothesis Testing</a></li><li data-subkey="sec2sub3"><a href="/Sample-Size-Planning-in-R.html" title="Sample Size Planning"><span class="progress-dot"></span>Sample Size Planning</a></li><li data-subkey="sec2sub3"><a href="/Which-Statistical-Test-in-R.html" title="Choosing the Right Test"><span class="progress-dot"></span>Choosing the Right Test</a></li><li data-subkey="sec2sub3"><a href="/Statistical-Tests-in-R.html" title="Statistical Tests"><span class="progress-dot"></span>Statistical Tests</a></li><li data-subkey="sec2sub3"><a href="/Measures-of-Association-in-R.html" title="Measures of Association"><span class="progress-dot"></span>Measures of Association</a></li><li data-subkey="sec2sub3"><a href="/Point-Estimation-in-R.html" title="Point Estimation"><span class="progress-dot"></span>Point Estimation</a></li><li data-subkey="sec2sub3"><a href="/Confidence-Intervals-in-R.html" title="Confidence Intervals"><span class="progress-dot"></span>Confidence Intervals</a></li><li data-subkey="sec2sub3"><a href="/Type-I-and-Type-II-Errors-in-R.html" title="Type I and II Errors"><span class="progress-dot"></span>Type I and II Errors</a></li><li data-subkey="sec2sub3"><a href="/Statistical-Power-Analysis-in-R.html" title="Power Analysis"><span class="progress-dot"></span>Power Analysis</a></li><li data-subkey="sec2sub3"><a href="/Effect-Size-in-R.html" title="Effect Size"><span class="progress-dot"></span>Effect Size</a></li><li data-subkey="sec2sub3"><a href="/t-Tests-in-R.html" title="t-Tests"><span class="progress-dot"></span>t-Tests</a></li><li data-subkey="sec2sub3"><a href="/Proportion-Tests-in-R.html" title="Proportion Tests"><span class="progress-dot"></span>Proportion Tests</a></li><li data-subkey="sec2sub3"><a href="/Normality-and-Variance-Tests-in-R.html" title="Normality & Variance Tests"><span class="progress-dot"></span>Normality & Variance Tests</a></li><li data-subkey="sec2sub3"><a href="/Chi-Square-Tests-in-R.html" title="Chi-Square Tests"><span class="progress-dot"></span>Chi-Square Tests</a></li><li data-subkey="sec2sub3"><a href="/Wilcoxon-Mann-Whitney-and-Kruskal-Wallis-in-R.html" title="Wilcoxon, Mann-Whitney & Kruskal-Wallis"><span class="progress-dot"></span>Wilcoxon, Mann-Whitney & Kruskal-Wallis</a></li><li data-subkey="sec2sub3"><a href="/Multiple-Comparisons-in-R.html" title="Multiple Testing Correction"><span class="progress-dot"></span>Multiple Testing Correction</a></li><li data-subkey="sec2sub3" class="is-quiz"><a href="/Hypothesis-Testing-Exercises-in-R-quiz.html" title="Hypothesis Testing Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Regression</li><li data-subkey="sec2sub4"><a href="/Linear-Regression.html" title="Linear Regression"><span class="progress-dot"></span>Linear Regression</a></li><li data-subkey="sec2sub4"><a href="/Logistic-Regression-With-R.html" title="Logistic Regression"><span class="progress-dot"></span>Logistic Regression</a></li><li data-subkey="sec2sub4"><a href="/Variable-Selection-and-Importance-With-R.html" title="Feature Selection"><span class="progress-dot"></span>Feature Selection</a></li><li data-subkey="sec2sub4"><a href="/Model-Selection-in-R.html" title="Model Selection"><span class="progress-dot"></span>Model Selection</a></li><li data-subkey="sec2sub4"><a href="/Missing-Value-Treatment-With-R.html" title="Missing Value Treatment"><span class="progress-dot"></span>Missing Value Treatment</a></li><li data-subkey="sec2sub4"><a href="/Outlier-Treatment-With-R.html" title="Outlier Analysis"><span class="progress-dot"></span>Outlier Analysis</a></li><li data-subkey="sec2sub4"><a href="/adv-regression-models.html" title="Advanced Regression Models"><span class="progress-dot"></span>Advanced Regression Models</a></li><li data-subkey="sec2sub4" class="is-quiz"><a href="/Linear-Regression-Exercises-in-R-quiz.html" title="Linear Regression Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub5" data-collapsed="false"><span class="subsec-chevron">▼</span> Reporting & Communication</li><li data-subkey="sec2sub5"><a href="/Statistical-Consulting-in-R.html" title="Statistical Consulting"><span class="progress-dot"></span>Statistical Consulting</a></li><li data-subkey="sec2sub5"><a href="/Statistical-Report-Writing-in-R.html" title="Statistical Report Writing"><span class="progress-dot"></span>Statistical Report Writing</a></li><li data-subkey="sec2sub5"><a href="/Bootstrap-Confidence-Intervals-in-R.html" title="Bootstrap Confidence Intervals"><span class="progress-dot"></span>Bootstrap Confidence Intervals</a></li><li data-subkey="sec2sub5"><a href="/Reporting-Statistics-in-R.html" title="Reporting Statistics"><span class="progress-dot"></span>Reporting Statistics</a></li><li data-subkey="sec2sub5"><a href="/Regression-Tables-in-R.html" title="Regression Tables (3 packages)"><span class="progress-dot"></span>Regression Tables (3 packages)</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub6" data-collapsed="false"><span class="subsec-chevron">▼</span> Regression in Practice</li><li data-subkey="sec2sub6"><a href="/Simple-Linear-Regression-in-R.html" title="Simple Linear Regression"><span class="progress-dot"></span>Simple Linear Regression</a></li><li data-subkey="sec2sub6"><a href="/Multiple-Regression-in-R.html" title="Multiple Regression"><span class="progress-dot"></span>Multiple Regression</a></li><li data-subkey="sec2sub6"><a href="/Correlation-in-R.html" title="Correlation (Pearson, Spearman, Kendall)"><span class="progress-dot"></span>Correlation (Pearson, Spearman, Kendall)</a></li><li data-subkey="sec2sub6"><a href="/Linear-Regression-Assumptions-in-R.html" title="Linear Regression Assumptions"><span class="progress-dot"></span>Linear Regression Assumptions</a></li><li data-subkey="sec2sub6"><a href="/Dummy-Variables-in-R.html" title="Dummy Variables in R"><span class="progress-dot"></span>Dummy Variables in R</a></li><li data-subkey="sec2sub6"><a href="/Interaction-Effects-in-R.html" title="Interaction Effects"><span class="progress-dot"></span>Interaction Effects</a></li><li data-subkey="sec2sub6"><a href="/Regression-Diagnostics-in-R.html" title="Regression Diagnostics"><span class="progress-dot"></span>Regression Diagnostics</a></li><li data-subkey="sec2sub6"><a href="/Variable-Selection-in-R.html" title="Variable Selection"><span class="progress-dot"></span>Variable Selection</a></li><li data-subkey="sec2sub6"><a href="/Polynomial-and-Spline-Regression-in-R.html" title="Polynomial & Splines"><span class="progress-dot"></span>Polynomial & Splines</a></li><li data-subkey="sec2sub6"><a href="/Ridge-and-Lasso-Regression-in-R.html" title="Ridge & Lasso Regression"><span class="progress-dot"></span>Ridge & Lasso Regression</a></li><li data-subkey="sec2sub6"><a href="/Robust-Regression-in-R.html" title="Robust Regression (rlm)"><span class="progress-dot"></span>Robust Regression (rlm)</a></li><li data-subkey="sec2sub6"><a href="/Quantile-Regression-in-R-2.html" title="Quantile Regression"><span class="progress-dot"></span>Quantile Regression</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub7" data-collapsed="false"><span class="subsec-chevron">▼</span> ANOVA & Experiments</li><li data-subkey="sec2sub7"><a href="/One-Way-ANOVA-in-R.html" title="One-Way ANOVA"><span class="progress-dot"></span>One-Way ANOVA</a></li><li data-subkey="sec2sub7"><a href="/Post-Hoc-Tests-After-ANOVA.html" title="Post-Hoc Tests After ANOVA"><span class="progress-dot"></span>Post-Hoc Tests After ANOVA</a></li><li data-subkey="sec2sub7"><a href="/Two-Way-ANOVA-in-R.html" title="Two-Way ANOVA"><span class="progress-dot"></span>Two-Way ANOVA</a></li><li data-subkey="sec2sub7"><a href="/Repeated-Measures-ANOVA-in-R.html" title="Repeated Measures ANOVA"><span class="progress-dot"></span>Repeated Measures ANOVA</a></li><li data-subkey="sec2sub7"><a href="/ANCOVA-in-R.html" title="ANCOVA"><span class="progress-dot"></span>ANCOVA</a></li><li data-subkey="sec2sub7"><a href="/Experimental-Design-Principles-in-R.html" title="Experimental Design in R"><span class="progress-dot"></span>Experimental Design in R</a></li><li data-subkey="sec2sub7"><a href="/Factorial-Experiments-in-R.html" title="Factorial Designs (2^k)"><span class="progress-dot"></span>Factorial Designs (2^k)</a></li><li data-subkey="sec2sub7"><a href="/AB-Testing-in-R.html" title="A/B Testing"><span class="progress-dot"></span>A/B Testing</a></li><li data-subkey="sec2sub7"><a href="/MANOVA-in-R.html" title="MANOVA"><span class="progress-dot"></span>MANOVA</a></li><li data-subkey="sec2sub7"><a href="/Mixed-ANOVA-in-R.html" title="Mixed ANOVA"><span class="progress-dot"></span>Mixed ANOVA</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub8" data-collapsed="false"><span class="subsec-chevron">▼</span> GLMs & Categorical Data</li><li data-subkey="sec2sub8"><a href="/Categorical-Data-in-R.html" title="Categorical Data (Tables & Mosaic)"><span class="progress-dot"></span>Categorical Data (Tables & Mosaic)</a></li><li data-subkey="sec2sub8"><a href="/Chi-Square-Test-of-Independence-in-R.html" title="Chi-Square Test of Independence"><span class="progress-dot"></span>Chi-Square Test of Independence</a></li><li data-subkey="sec2sub8"><a href="/Chi-Square-Goodness-of-Fit-Test-in-R.html" title="Chi-Square Goodness-of-Fit"><span class="progress-dot"></span>Chi-Square Goodness-of-Fit</a></li><li data-subkey="sec2sub8"><a href="/Fishers-Exact-Test-in-R.html" title="Fisher's Exact Test"><span class="progress-dot"></span>Fisher's Exact Test</a></li><li data-subkey="sec2sub8"><a href="/Odds-Ratios-and-Relative-Risk-in-R.html" title="Odds Ratios & Relative Risk"><span class="progress-dot"></span>Odds Ratios & Relative Risk</a></li><li data-subkey="sec2sub8"><a href="/Logistic-Regression-in-R.html" title="Logistic Regression (glm + ROC)"><span class="progress-dot"></span>Logistic Regression (glm + ROC)</a></li><li data-subkey="sec2sub8"><a href="/Logistic-Regression-in-R-2.html" title="Logistic Regression (Diagnostics)"><span class="progress-dot"></span>Logistic Regression (Diagnostics)</a></li><li data-subkey="sec2sub8"><a href="/Poisson-Regression-in-R.html" title="Poisson Regression"><span class="progress-dot"></span>Poisson Regression</a></li><li data-subkey="sec2sub8"><a href="/Poisson-and-Negative-Binomial-Regression.html" title="Poisson & Negative Binomial Regression"><span class="progress-dot"></span>Poisson & Negative Binomial Regression</a></li><li data-subkey="sec2sub8"><a href="/Multinomial-and-Ordinal-Logistic-Regression-in-R.html" title="Multinomial & Ordinal Logistic Regression"><span class="progress-dot"></span>Multinomial & Ordinal Logistic Regression</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub9" data-collapsed="false"><span class="subsec-chevron">▼</span> Multivariate Methods</li><li data-subkey="sec2sub9"><a href="/Multivariate-Statistics-in-R.html" title="Multivariate Distances & Hotelling's T²"><span class="progress-dot"></span>Multivariate Distances & Hotelling's T²</a></li><li data-subkey="sec2sub9"><a href="/PCA-in-R.html" title="PCA with prcomp()"><span class="progress-dot"></span>PCA with prcomp()</a></li><li data-subkey="sec2sub9"><a href="/Interpreting-PCA-Results-in-R.html" title="Interpreting PCA Output"><span class="progress-dot"></span>Interpreting PCA Output</a></li><li data-subkey="sec2sub9"><a href="/factoextra-and-FactoMineR.html" title="factoextra (PCA + Clusters)"><span class="progress-dot"></span>factoextra (PCA + Clusters)</a></li><li data-subkey="sec2sub9"><a href="/Exploratory-Factor-Analysis-in-R.html" title="Exploratory Factor Analysis"><span class="progress-dot"></span>Exploratory Factor Analysis</a></li><li data-subkey="sec2sub9"><a href="/CFA-and-Structural-Equation-Modeling-in-R.html" title="SEM and CFA (lavaan)"><span class="progress-dot"></span>SEM and CFA (lavaan)</a></li><li data-subkey="sec2sub9"><a href="/Linear-Discriminant-Analysis-in-R.html" title="LDA (Linear Discriminant Analysis)"><span class="progress-dot"></span>LDA (Linear Discriminant Analysis)</a></li><li data-subkey="sec2sub9"><a href="/Cluster-Analysis-in-R.html" title="Clustering (k-Means / HC / DBSCAN)"><span class="progress-dot"></span>Clustering (k-Means / HC / DBSCAN)</a></li><li data-subkey="sec2sub9"><a href="/Correspondence-Analysis-in-R.html" title="Correspondence Analysis"><span class="progress-dot"></span>Correspondence Analysis</a></li><li data-subkey="sec2sub9"><a href="/t-SNE-and-UMAP-in-R.html" title="t-SNE and UMAP"><span class="progress-dot"></span>t-SNE and UMAP</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub10" data-collapsed="false"><span class="subsec-chevron">▼</span> Nonparametric & Resampling</li><li data-subkey="sec2sub10"><a href="/When-to-Use-Nonparametric-Tests-in-R.html" title="When to Use Nonparametric Tests"><span class="progress-dot"></span>When to Use Nonparametric Tests</a></li><li data-subkey="sec2sub10"><a href="/Wilcoxon-Signed-Rank-Test-in-R.html" title="Wilcoxon Signed-Rank Test"><span class="progress-dot"></span>Wilcoxon Signed-Rank Test</a></li><li data-subkey="sec2sub10"><a href="/Mann-Whitney-U-Test-in-R.html" title="Mann-Whitney U Test"><span class="progress-dot"></span>Mann-Whitney U Test</a></li><li data-subkey="sec2sub10"><a href="/Kruskal-Wallis-Test-in-R-2.html" title="Kruskal-Wallis Test"><span class="progress-dot"></span>Kruskal-Wallis Test</a></li><li data-subkey="sec2sub10"><a href="/Friedman-Test-in-R.html" title="Friedman Test"><span class="progress-dot"></span>Friedman Test</a></li><li data-subkey="sec2sub10"><a href="/Spearman-and-Kendall-Correlation-in-R.html" title="Spearman & Kendall Correlation"><span class="progress-dot"></span>Spearman & Kendall Correlation</a></li><li data-subkey="sec2sub10"><a href="/Bootstrap-in-R.html" title="Bootstrap (boot package)"><span class="progress-dot"></span>Bootstrap (boot package)</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub11" data-collapsed="false"><span class="subsec-chevron">▼</span> Linear Algebra for Statistics</li><li data-subkey="sec2sub11"><a href="/Matrix-Operations-in-R.html" title="Matrix Operations in R"><span class="progress-dot"></span>Matrix Operations in R</a></li><li data-subkey="sec2sub11"><a href="/Solving-Linear-Systems-in-R.html" title="Solving Linear Systems in R"><span class="progress-dot"></span>Solving Linear Systems in R</a></li><li data-subkey="sec2sub11"><a href="/Eigenvalues-and-Eigenvectors-in-R.html" title="Eigenvalues & Eigenvectors in R"><span class="progress-dot"></span>Eigenvalues & Eigenvectors in R</a></li><li data-subkey="sec2sub11"><a href="/Singular-Value-Decomposition-in-R.html" title="Singular Value Decomposition in R"><span class="progress-dot"></span>Singular Value Decomposition in R</a></li><li data-subkey="sec2sub11"><a href="/Projections-and-the-Hat-Matrix-in-R.html" title="Projections & the Hat Matrix"><span class="progress-dot"></span>Projections & the Hat Matrix</a></li><li data-subkey="sec2sub11"><a href="/QR-Decomposition-in-R.html" title="QR Decomposition in R"><span class="progress-dot"></span>QR Decomposition in R</a></li><li data-subkey="sec2sub11"><a href="/Quadratic-Forms-in-R.html" title="Quadratic Forms"><span class="progress-dot"></span>Quadratic Forms</a></li><li data-subkey="sec2sub11"><a href="/Matrix-Derivatives-and-the-Hessian-in-R.html" title="Matrix Derivatives & Hessian"><span class="progress-dot"></span>Matrix Derivatives & Hessian</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub12" data-collapsed="false"><span class="subsec-chevron">▼</span> Statistical Theory</li><li data-subkey="sec2sub12"><a href="/Exponential-Family-Distributions-in-R.html" title="Exponential Family Distributions"><span class="progress-dot"></span>Exponential Family Distributions</a></li><li data-subkey="sec2sub12"><a href="/Sufficient-Statistics-in-R.html" title="Sufficient Statistics"><span class="progress-dot"></span>Sufficient Statistics</a></li><li data-subkey="sec2sub12"><a href="/Complete-and-Ancillary-Statistics-in-R.html" title="Complete & Ancillary Statistics"><span class="progress-dot"></span>Complete & Ancillary Statistics</a></li><li data-subkey="sec2sub12"><a href="/UMVUE-in-R-2.html" title="UMVUE (Rao-Blackwell & Lehmann-Scheffé)"><span class="progress-dot"></span>UMVUE (Rao-Blackwell & Lehmann-Scheffé)</a></li><li data-subkey="sec2sub12"><a href="/Cramer-Rao-Lower-Bound-in-R-2.html" title="Cramér-Rao Lower Bound"><span class="progress-dot"></span>Cramér-Rao Lower Bound</a></li><li data-subkey="sec2sub12"><a href="/Asymptotic-Theory-in-R-2.html" title="Asymptotic Theory"><span class="progress-dot"></span>Asymptotic Theory</a></li><li data-subkey="sec2sub12"><a href="/Neyman-Pearson-Lemma-in-R-2.html" title="Neyman-Pearson Lemma"><span class="progress-dot"></span>Neyman-Pearson Lemma</a></li><li data-subkey="sec2sub12"><a href="/Likelihood-Ratio-Tests-and-Pivotal-Methods.html" title="Likelihood Ratio & Pivotal Methods"><span class="progress-dot"></span>Likelihood Ratio & Pivotal Methods</a></li><li data-subkey="sec2sub12"><a href="/Decision-Theory-in-R.html" title="Decision Theory"><span class="progress-dot"></span>Decision Theory</a></li><li data-subkey="sec2sub12"><a href="/Asymptotic-Relative-Efficiency-in-R.html" title="Asymptotic Relative Efficiency"><span class="progress-dot"></span>Asymptotic Relative Efficiency</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub13" data-collapsed="false"><span class="subsec-chevron">▼</span> Bayesian Foundations</li><li data-subkey="sec2sub13"><a href="/Bayes-Theorem-in-R.html" title="Bayes' Theorem"><span class="progress-dot"></span>Bayes' Theorem</a></li><li data-subkey="sec2sub13"><a href="/Bayesian-Statistics-in-R.html" title="Bayesian Statistics"><span class="progress-dot"></span>Bayesian Statistics</a></li><li data-subkey="sec2sub13"><a href="/Conjugate-Priors-in-R.html" title="Conjugate Priors"><span class="progress-dot"></span>Conjugate Priors</a></li><li data-subkey="sec2sub13"><a href="/Grid-Approximation-in-R.html" title="Grid Approximation"><span class="progress-dot"></span>Grid Approximation</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub14" data-collapsed="false"><span class="subsec-chevron">▼</span> MCMC & Stan</li><li data-subkey="sec2sub14"><a href="/MCMC-in-R.html" title="MCMC in R"><span class="progress-dot"></span>MCMC in R</a></li><li data-subkey="sec2sub14"><a href="/Gibbs-Sampling-in-R.html" title="Gibbs Sampling"><span class="progress-dot"></span>Gibbs Sampling</a></li><li data-subkey="sec2sub14"><a href="/Hamiltonian-Monte-Carlo-in-R.html" title="Hamiltonian Monte Carlo"><span class="progress-dot"></span>Hamiltonian Monte Carlo</a></li><li data-subkey="sec2sub14"><a href="/Stan-in-R.html" title="Stan"><span class="progress-dot"></span>Stan</a></li><li data-subkey="sec2sub14"><a href="/brms-in-R.html" title="brms"><span class="progress-dot"></span>brms</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub15" data-collapsed="false"><span class="subsec-chevron">▼</span> Bayesian Modeling</li><li data-subkey="sec2sub15"><a href="/Choosing-Priors-in-R.html" title="Choosing Priors"><span class="progress-dot"></span>Choosing Priors</a></li><li data-subkey="sec2sub15"><a href="/Prior-Predictive-Checks-in-R.html" title="Prior Predictive Checks"><span class="progress-dot"></span>Prior Predictive Checks</a></li><li data-subkey="sec2sub15"><a href="/Compare-Bayesian-Models-in-R.html" title="Compare Bayesian Models"><span class="progress-dot"></span>Compare Bayesian Models</a></li><li data-subkey="sec2sub15"><a href="/Posterior-Predictive-Checks-in-R.html" title="Posterior Predictive Checks"><span class="progress-dot"></span>Posterior Predictive Checks</a></li><li data-subkey="sec2sub15"><a href="/Bayesian-Linear-Regression-in-R.html" title="Bayesian Linear Regression"><span class="progress-dot"></span>Bayesian Linear Regression</a></li><li data-subkey="sec2sub15"><a href="/Bayesian-Logistic-Regression-in-R.html" title="Bayesian Logistic Regression"><span class="progress-dot"></span>Bayesian Logistic Regression</a></li><li data-subkey="sec2sub15"><a href="/Bayesian-Hierarchical-Models-in-R.html" title="Bayesian Hierarchical Models"><span class="progress-dot"></span>Bayesian Hierarchical Models</a></li><li data-subkey="sec2sub15"><a href="/Multilevel-Models-in-R.html" title="Multilevel Models"><span class="progress-dot"></span>Multilevel Models</a></li><li data-subkey="sec2sub15"><a href="/Bayesian-ANOVA-in-R.html" title="Bayesian ANOVA"><span class="progress-dot"></span>Bayesian ANOVA</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub16" data-collapsed="false"><span class="subsec-chevron">▼</span> Machine Learning</li><li data-subkey="sec2sub16"><a href="/Random-Forest-Course.html" title="Random Forests (Course)"><span class="progress-dot"></span>Random Forests (Course)</a></li><li data-subkey="sec2sub16"><a href="/R-Gradient-Boosting-Course.html" title="Gradient Boosting (Course)"><span class="progress-dot"></span>Gradient Boosting (Course)</a></li><li data-subkey="sec2sub16"><a href="/R-tidymodels-Course.html" title="tidymodels (Course)"><span class="progress-dot"></span>tidymodels (Course)</a></li><li data-subkey="sec2sub16" class="is-quiz"><a href="/Machine-Learning-Exercises-in-R-quiz.html" title="Machine Learning Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec2sub16"><a href="/T-Test-Course.html" title="The t-test (Lesson)"><span class="progress-dot"></span>The t-test (Lesson)</a></li><li data-subkey="sec2sub16"><a href="/Populations-Samples-and-Bias-in-R.html" title="Populations & Sampling Bias"><span class="progress-dot"></span>Populations & Sampling Bias</a></li><li data-subkey="sec2sub16"><a href="/Types-of-Data-in-Statistics.html" title="Types of Data"><span class="progress-dot"></span>Types of Data</a></li><li data-subkey="sec2sub16"><a href="/What-Statistics-Is-For.html" title="What Statistics Is For"><span class="progress-dot"></span>What Statistics Is For</a></li><li data-subkey="sec2sub16"><a href="/Mean-vs-Median-SD-vs-IQR.html" title="Mean, Median, SD & IQR"><span class="progress-dot"></span>Mean, Median, SD & IQR</a></li><li data-subkey="sec2sub16"><a href="/Sampling-Methods-in-R.html" title="Sampling Methods"><span class="progress-dot"></span>Sampling Methods</a></li><li data-subkey="sec2sub16"><a href="/Z-Scores-and-Percentiles-in-R.html" title="Z-Scores & Percentiles"><span class="progress-dot"></span>Z-Scores & Percentiles</a></li><li data-subkey="sec2sub16"><a href="/Covariance-and-Correlation-in-R.html" title="Covariance & Correlation"><span class="progress-dot"></span>Covariance & Correlation</a></li><li data-subkey="sec2sub16"><a href="/The-Normal-Distribution-Explained-in-R.html" title="Normal Distribution"><span class="progress-dot"></span>Normal Distribution</a></li><li data-subkey="sec2sub16"><a href="/Which-Distribution-When-in-R.html" title="Which Distribution When"><span class="progress-dot"></span>Which Distribution When</a></li><li data-subkey="sec2sub16"><a href="/First-Hypothesis-Test-Three-Ways-in-R.html" title="First Hypothesis Test"><span class="progress-dot"></span>First Hypothesis Test</a></li><li data-subkey="sec2sub16"><a href="/How-Statistical-Inference-Works.html" title="How Inference Works"><span class="progress-dot"></span>How Inference Works</a></li><li data-subkey="sec2sub16"><a href="/Margin-of-Error-in-R.html" title="Margin of Error & Sample Size"><span class="progress-dot"></span>Margin of Error & Sample Size</a></li><li data-subkey="sec2sub16"><a href="/Paired-Designs-in-R.html" title="Paired Designs"><span class="progress-dot"></span>Paired Designs</a></li><li data-subkey="sec2sub16"><a href="/Statistical-vs-Practical-Significance.html" title="Statistical vs Practical"><span class="progress-dot"></span>Statistical vs Practical</a></li><li data-subkey="sec2sub16"><a href="/What-p-Values-Mean.html" title="What p-Values Mean"><span class="progress-dot"></span>What p-Values Mean</a></li><li data-subkey="sec2sub16"><a href="/Power-by-Simulation-in-R.html" title="Power by Simulation"><span class="progress-dot"></span>Power by Simulation</a></li><li data-subkey="sec2sub16"><a href="/Read-Logistic-Output-in-R.html" title="Reading glm() Output"><span class="progress-dot"></span>Reading glm() Output</a></li><li data-subkey="sec2sub16"><a href="/Read-lm-Output-in-R.html" title="Reading lm() Output"><span class="progress-dot"></span>Reading lm() Output</a></li><li data-subkey="sec2sub16"><a href="/Offsets-and-Exposure-in-R.html" title="Offsets & Exposure"><span class="progress-dot"></span>Offsets & Exposure</a></li><li data-subkey="sec2sub16"><a href="/Zero-Inflated-Hurdle-Models-in-R.html" title="Zero-Inflated & Hurdle Models"><span class="progress-dot"></span>Zero-Inflated & Hurdle Models</a></li><li data-subkey="sec2sub16"><a href="/GLM-Diagnostics-in-R.html" title="GLM Diagnostics"><span class="progress-dot"></span>GLM Diagnostics</a></li><li data-subkey="sec2sub16"><a href="/Random-Intercepts-and-Slopes-in-R.html" title="Random Intercepts & Slopes"><span class="progress-dot"></span>Random Intercepts & Slopes</a></li><li data-subkey="sec2sub16"><a href="/Checking-Assumptions-in-R.html" title="Checking Model Assumptions"><span class="progress-dot"></span>Checking Model Assumptions</a></li><li data-subkey="sec2sub16"><a href="/Crossed-vs-Nested-Effects-in-R.html" title="Crossed vs Nested Effects"><span class="progress-dot"></span>Crossed vs Nested Effects</a></li><li data-subkey="sec2sub16"><a href="/GEE-vs-Mixed-Models-in-R.html" title="GEE vs Mixed Models"><span class="progress-dot"></span>GEE vs Mixed Models</a></li><li data-subkey="sec2sub16"><a href="/Mixed-Model-Inference-in-R.html" title="Mixed Model Inference"><span class="progress-dot"></span>Mixed Model Inference</a></li><li data-subkey="sec2sub16"><a href="/Measurement-Reliability-in-R.html" title="Measurement Reliability"><span class="progress-dot"></span>Measurement Reliability</a></li><li data-subkey="sec2sub16"><a href="/Multiple-Imputation-mice-in-R.html" title="Multiple Imputation with mice"><span class="progress-dot"></span>Multiple Imputation with mice</a></li><li data-subkey="sec2sub16"><a href="/p-Hacking-and-Preregistration.html" title="p-Hacking and Preregistration"><span class="progress-dot"></span>p-Hacking and Preregistration</a></li><li data-subkey="sec2sub16"><a href="/Business-Experiment-Capstone-in-R.html" title="Business Experiment Capstone"><span class="progress-dot"></span>Business Experiment Capstone</a></li><li data-subkey="sec2sub16"><a href="/Clinical-Comparison-Capstone-in-R.html" title="Clinical Comparison Capstone"><span class="progress-dot"></span>Clinical Comparison Capstone</a></li><li data-subkey="sec2sub16"><a href="/Survey-Analysis-Capstone-in-R.html" title="Survey Analysis Capstone"><span class="progress-dot"></span>Survey Analysis Capstone</a></li><li data-subkey="sec2sub16"><a href="/Bayesian-Workflow-in-R.html" title="Bayesian Workflow"><span class="progress-dot"></span>Bayesian Workflow</a></li><li data-subkey="sec2sub16"><a href="/MCMC-Diagnostics-in-R.html" title="MCMC Diagnostics"><span class="progress-dot"></span>MCMC Diagnostics</a></li><li data-subkey="sec2sub16"><a href="/Answering-Statistical-Reviewer-Comments.html" title="Answering Reviewer Comments"><span class="progress-dot"></span>Answering Reviewer Comments</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span><span class="sec-num">4.</span> <span class="sec-title-t">Visualization</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> ggplot2 Foundations</li><li data-subkey="sec3sub1"><a href="/ggplot2-Grammar-of-Graphics.html" title="Grammar of Graphics"><span class="progress-dot"></span>Grammar of Graphics</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Getting-Started.html" title="ggplot2 Getting Started"><span class="progress-dot"></span>ggplot2 Getting Started</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Aesthetics-aes-Map-Data.html" title="ggplot2 Aesthetics (aes)"><span class="progress-dot"></span>ggplot2 Aesthetics (aes)</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Colours.html" title="ggplot2 Colours"><span class="progress-dot"></span>ggplot2 Colours</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Scales.html" title="ggplot2 Scales"><span class="progress-dot"></span>ggplot2 Scales</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Themes-in-R.html" title="ggplot2 Themes"><span class="progress-dot"></span>ggplot2 Themes</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Labels-and-Annotations.html" title="Labels & Annotations"><span class="progress-dot"></span>Labels & Annotations</a></li><li data-subkey="sec3sub1"><a href="/ggplot2-Facets.html" title="ggplot2 Facets"><span class="progress-dot"></span>ggplot2 Facets</a></li><li data-subkey="sec3sub1" class="is-quiz"><a href="/ggplot2-Exercises-in-R-quiz.html" title="ggplot2 Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> Core Charts</li><li data-subkey="sec3sub2"><a href="/ggplot2-Scatter-Plots.html" title="Scatter Plots"><span class="progress-dot"></span>Scatter Plots</a></li><li data-subkey="sec3sub2"><a href="/ggplot2-Line-Charts.html" title="Line Charts"><span class="progress-dot"></span>Line Charts</a></li><li data-subkey="sec3sub2"><a href="/ggplot2-Bar-Charts.html" title="Bar Charts"><span class="progress-dot"></span>Bar Charts</a></li><li data-subkey="sec3sub2"><a href="/ggplot2-Distribution-Charts.html" title="Distribution Charts"><span class="progress-dot"></span>Distribution Charts</a></li><li data-subkey="sec3sub2"><a href="/Error-Bars-in-R.html" title="Error Bars"><span class="progress-dot"></span>Error Bars</a></li><li data-subkey="sec3sub2"><a href="/geom_smooth-in-R.html" title="geom_smooth()"><span class="progress-dot"></span>geom_smooth()</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Distributions & Groups</li><li data-subkey="sec3sub3"><a href="/Violin-Plot-in-R.html" title="Violin Plot"><span class="progress-dot"></span>Violin Plot</a></li><li data-subkey="sec3sub3"><a href="/Ridgeline-Plot-in-R.html" title="Ridgeline Plot"><span class="progress-dot"></span>Ridgeline Plot</a></li><li data-subkey="sec3sub3"><a href="/Lollipop-Chart-in-R.html" title="Lollipop Chart"><span class="progress-dot"></span>Lollipop Chart</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Relationships</li><li data-subkey="sec3sub4"><a href="/Bubble-Chart-in-R.html" title="Bubble Chart"><span class="progress-dot"></span>Bubble Chart</a></li><li data-subkey="sec3sub4"><a href="/Heatmap-in-R.html" title="Heatmap in R"><span class="progress-dot"></span>Heatmap in R</a></li><li data-subkey="sec3sub4"><a href="/Correlation-Matrix-Plot-in-R.html" title="Correlation Matrix"><span class="progress-dot"></span>Correlation Matrix</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub5" data-collapsed="false"><span class="subsec-chevron">▼</span> Advanced Charts</li><li data-subkey="sec3sub5"><a href="/Pie-Donut-Chart-in-R.html" title="Pie & Donut Chart"><span class="progress-dot"></span>Pie & Donut Chart</a></li><li data-subkey="sec3sub5"><a href="/Treemap-in-R.html" title="Treemap"><span class="progress-dot"></span>Treemap</a></li><li data-subkey="sec3sub5"><a href="/Waffle-Chart-in-R.html" title="Waffle Chart"><span class="progress-dot"></span>Waffle Chart</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub6" data-collapsed="false"><span class="subsec-chevron">▼</span> Exploratory Analysis</li><li data-subkey="sec3sub6"><a href="/Exploratory-Data-Analysis-in-R.html" title="EDA (7-Step Framework)"><span class="progress-dot"></span>EDA (7-Step Framework)</a></li><li data-subkey="sec3sub6"><a href="/Univariate-EDA-in-R.html" title="Univariate EDA"><span class="progress-dot"></span>Univariate EDA</a></li><li data-subkey="sec3sub6"><a href="/Bivariate-EDA-in-R.html" title="Bivariate EDA"><span class="progress-dot"></span>Bivariate EDA</a></li><li data-subkey="sec3sub6"><a href="/Descriptive-Statistics-in-R.html" title="Descriptive Statistics"><span class="progress-dot"></span>Descriptive Statistics</a></li><li data-subkey="sec3sub6"><a href="/Correlation-Analysis-in-R.html" title="Correlation Analysis"><span class="progress-dot"></span>Correlation Analysis</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub7" data-collapsed="false"><span class="subsec-chevron">▼</span> Interactive & Maps</li><li data-subkey="sec3sub7"><a href="/Combining-ggplot2-with-plotly.html" title="ggplot2 + plotly Interactive"><span class="progress-dot"></span>ggplot2 + plotly Interactive</a></li><li data-subkey="sec3sub7"><a href="/Interactive-Maps-in-R-with-leaflet.html" title="Leaflet Interactive Maps"><span class="progress-dot"></span>Leaflet Interactive Maps</a></li><li data-subkey="sec3sub7"><a href="/Spatial-Data-in-R-with-sf.html" title="Spatial Data (sf)"><span class="progress-dot"></span>Spatial Data (sf)</a></li><li data-subkey="sec3sub7"><a href="/Choropleth-Maps-in-R.html" title="Choropleth Maps (sf)"><span class="progress-dot"></span>Choropleth Maps (sf)</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub8" data-collapsed="false"><span class="subsec-chevron">▼</span> Customization & Reference</li><li data-subkey="sec3sub8"><a href="/ggplot2-Legends-in-R.html" title="ggplot2 Legends"><span class="progress-dot"></span>ggplot2 Legends</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Secondary-Axis.html" title="Secondary Axis"><span class="progress-dot"></span>Secondary Axis</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Log-Scale.html" title="Log Scale"><span class="progress-dot"></span>Log Scale</a></li><li data-subkey="sec3sub8"><a href="/patchwork-Package.html" title="patchwork (Combine Plots)"><span class="progress-dot"></span>patchwork (Combine Plots)</a></li><li data-subkey="sec3sub8"><a href="/Publication-Quality-Figures-in-R.html" title="Publication-Ready Figures"><span class="progress-dot"></span>Publication-Ready Figures</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-cheatsheet.html" title="ggplot2 Quickref"><span class="progress-dot"></span>ggplot2 Quickref</a></li><li data-subkey="sec3sub8"><a href="/Advanced-ggplot2-Course.html" title="Advanced ggplot2 (Course)"><span class="progress-dot"></span>Advanced ggplot2 (Course)</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Course.html" title="ggplot2 (Course)"><span class="progress-dot"></span>ggplot2 (Course)</a></li><li data-subkey="sec3sub8"><a href="/Dashboards-Course.html" title="Interactive Dashboards (Course)"><span class="progress-dot"></span>Interactive Dashboards (Course)</a></li><li data-subkey="sec3sub8"><a href="/Reading-ggplot2-Code-in-R.html" title="Reading ggplot2 Code"><span class="progress-dot"></span>Reading ggplot2 Code</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Area-Charts-and-Ribbons-in-R.html" title="Area Charts & Ribbons"><span class="progress-dot"></span>Area Charts & Ribbons</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Text-Labels-in-R.html" title="Text Labels in ggplot2"><span class="progress-dot"></span>Text Labels in ggplot2</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-2D-Density-and-Hexbin-in-R.html" title="2D Density & Hexbin"><span class="progress-dot"></span>2D Density & Hexbin</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Error-Bars-in-R.html" title="Error Bars"><span class="progress-dot"></span>Error Bars</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Stat-System-in-R.html" title="The stat System"><span class="progress-dot"></span>The stat System</a></li><li data-subkey="sec3sub8"><a href="/Summary-Statistics-on-Plots-in-R.html" title="Summary Stats on Plots"><span class="progress-dot"></span>Summary Stats on Plots</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Date-Axis-in-R.html" title="Date & Time Axes"><span class="progress-dot"></span>Date & Time Axes</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Position-Adjustments-in-R.html" title="Position Adjustments"><span class="progress-dot"></span>Position Adjustments</a></li><li data-subkey="sec3sub8"><a href="/Statistical-Significance-on-Plots-in-R.html" title="Significance Brackets"><span class="progress-dot"></span>Significance Brackets</a></li><li data-subkey="sec3sub8"><a href="/Visualizing-Uncertainty-in-R.html" title="Visualizing Uncertainty"><span class="progress-dot"></span>Visualizing Uncertainty</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Scale-Transformations-in-R.html" title="Scale Transformations"><span class="progress-dot"></span>Scale Transformations</a></li><li data-subkey="sec3sub8"><a href="/Coefficient-Plots-and-Marginal-Effects-in-R.html" title="Coefficient Plots"><span class="progress-dot"></span>Coefficient Plots</a></li><li data-subkey="sec3sub8"><a href="/Custom-Fonts-in-R-Plots.html" title="Custom Fonts in Plots"><span class="progress-dot"></span>Custom Fonts in Plots</a></li><li data-subkey="sec3sub8"><a href="/Raincloud-Plots-in-R.html" title="Raincloud Plots"><span class="progress-dot"></span>Raincloud Plots</a></li><li data-subkey="sec3sub8"><a href="/Build-a-ggplot2-Theme-in-R.html" title="Build a ggplot2 Theme"><span class="progress-dot"></span>Build a ggplot2 Theme</a></li><li data-subkey="sec3sub8"><a href="/Chart-Annotation-Techniques-in-R.html" title="Chart Annotation"><span class="progress-dot"></span>Chart Annotation</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Extensions-in-R.html" title="ggplot2 Extensions"><span class="progress-dot"></span>ggplot2 Extensions</a></li><li data-subkey="sec3sub8"><a href="/Plot-Templates-and-Functions-in-R.html" title="Plot Template Functions"><span class="progress-dot"></span>Plot Template Functions</a></li><li data-subkey="sec3sub8"><a href="/Plotting-Big-Data-in-R.html" title="Plotting Big Data"><span class="progress-dot"></span>Plotting Big Data</a></li><li data-subkey="sec3sub8"><a href="/Write-a-ggplot2-Extension-in-R.html" title="Write a Geom & Stat"><span class="progress-dot"></span>Write a Geom & Stat</a></li><li data-subkey="sec3sub8"><a href="/Bump-Charts-in-R.html" title="Bump Charts"><span class="progress-dot"></span>Bump Charts</a></li><li data-subkey="sec3sub8"><a href="/Dumbbell-and-Slope-Charts-in-R.html" title="Dumbbell & Slope Charts"><span class="progress-dot"></span>Dumbbell & Slope Charts</a></li><li data-subkey="sec3sub8"><a href="/Population-Pyramids-and-Diverging-Bars-in-R.html" title="Population Pyramids"><span class="progress-dot"></span>Population Pyramids</a></li><li data-subkey="sec3sub8"><a href="/Bubble-Maps-in-R.html" title="Bubble & Point Maps"><span class="progress-dot"></span>Bubble & Point Maps</a></li><li data-subkey="sec3sub8"><a href="/Pie-Charts-and-Polar-Coordinates-in-R.html" title="Pie Charts and Polar Coords"><span class="progress-dot"></span>Pie Charts and Polar Coords</a></li><li data-subkey="sec3sub8"><a href="/Multi-Panel-Figures-in-R.html" title="Multi-Panel Figures"><span class="progress-dot"></span>Multi-Panel Figures</a></li><li data-subkey="sec3sub8"><a href="/Small-Multiples-in-R.html" title="Small Multiples"><span class="progress-dot"></span>Small Multiples</a></li><li data-subkey="sec3sub8"><a href="/ggplot2-Inset-Plots-in-R.html" title="Inset & Magnifier Plots"><span class="progress-dot"></span>Inset & Magnifier Plots</a></li><li data-subkey="sec3sub8"><a href="/Export-Plots-in-R.html" title="Export & Save Plots"><span class="progress-dot"></span>Export & Save Plots</a></li><li data-subkey="sec3sub8"><a href="/gganimate-in-R.html" title="gganimate"><span class="progress-dot"></span>gganimate</a></li><li data-subkey="sec3sub8"><a href="/ggiraph-Interactive-Charts-in-R.html" title="ggiraph: Interactive Charts"><span class="progress-dot"></span>ggiraph: Interactive Charts</a></li><li data-subkey="sec3sub8"><a href="/Accessible-Data-Visualization-in-R.html" title="Accessible Charts"><span class="progress-dot"></span>Accessible Charts</a></li><li data-subkey="sec3sub8"><a href="/Publication-Figure-System-in-R.html" title="Publication Figure System"><span class="progress-dot"></span>Publication Figure System</a></li><li data-subkey="sec3sub8"><a href="/Recreating-Professional-Charts-in-R.html" title="Recreating Pro Charts"><span class="progress-dot"></span>Recreating Pro Charts</a></li><li data-subkey="sec3sub8"><a href="/Advanced-Faceting-in-R.html" title="Advanced Faceting"><span class="progress-dot"></span>Advanced Faceting</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span><span class="sec-num">5.</span> <span class="sec-title-t">Time Series</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li data-subkey="sec4sub0"><a href="/Time-Series-Analysis-With-R.html" title="Time Series Analysis"><span class="progress-dot"></span>Time Series Analysis</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Forecasting-With-R.html" title="Time Series Forecasting"><span class="progress-dot"></span>Time Series Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Forecasting-With-R-part2.html" title="More Time Series Forecasting"><span class="progress-dot"></span>More Time Series Forecasting</a></li><li data-subkey="sec4sub0" class="is-quiz"><a href="/Time-Series-Exercises-in-R-quiz.html" title="Time Series Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec4sub0"><a href="/Test-Stationarity-in-R.html" title="Test Stationarity"><span class="progress-dot"></span>Test Stationarity</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Objects-in-R.html" title="Time Series Objects"><span class="progress-dot"></span>Time Series Objects</a></li><li data-subkey="sec4sub0"><a href="/Visualize-Time-Series-in-R.html" title="Visualize Time Series"><span class="progress-dot"></span>Visualize Time Series</a></li><li data-subkey="sec4sub0"><a href="/ACF-and-PACF-in-R.html" title="ACF and PACF"><span class="progress-dot"></span>ACF and PACF</a></li><li data-subkey="sec4sub0"><a href="/Moving-Averages-in-R.html" title="Moving Averages"><span class="progress-dot"></span>Moving Averages</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Decomposition-in-R.html" title="Time Series Decomposition"><span class="progress-dot"></span>Time Series Decomposition</a></li><li data-subkey="sec4sub0"><a href="/ETS-Models-in-R.html" title="ETS Models"><span class="progress-dot"></span>ETS Models</a></li><li data-subkey="sec4sub0"><a href="/Exponential-Smoothing-in-R.html" title="Exponential Smoothing"><span class="progress-dot"></span>Exponential Smoothing</a></li><li data-subkey="sec4sub0"><a href="/Holt-Winters-in-R.html" title="Holt-Winters"><span class="progress-dot"></span>Holt-Winters</a></li><li data-subkey="sec4sub0"><a href="/ARIMA-Diagnostics-in-R.html" title="ARIMA Diagnostics"><span class="progress-dot"></span>ARIMA Diagnostics</a></li><li data-subkey="sec4sub0"><a href="/ARIMA-in-R.html" title="ARIMA Models"><span class="progress-dot"></span>ARIMA Models</a></li><li data-subkey="sec4sub0"><a href="/How-to-Choose-ARIMA-Order-in-R.html" title="Choose ARIMA Order"><span class="progress-dot"></span>Choose ARIMA Order</a></li><li data-subkey="sec4sub0"><a href="/SARIMA-in-R.html" title="SARIMA Models"><span class="progress-dot"></span>SARIMA Models</a></li><li data-subkey="sec4sub0"><a href="/auto-arima-in-R.html" title="auto.arima()"><span class="progress-dot"></span>auto.arima()</a></li><li data-subkey="sec4sub0"><a href="/Forecast-Accuracy-in-R.html" title="Forecast Accuracy"><span class="progress-dot"></span>Forecast Accuracy</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Cross-Validation-in-R.html" title="Time Series Cross-Validation"><span class="progress-dot"></span>Time Series Cross-Validation</a></li><li data-subkey="sec4sub0"><a href="/NNETAR-Model-in-R.html" title="NNETAR Models"><span class="progress-dot"></span>NNETAR Models</a></li><li data-subkey="sec4sub0"><a href="/Prophet-in-R.html" title="Prophet"><span class="progress-dot"></span>Prophet</a></li><li data-subkey="sec4sub0"><a href="/TBATS-Model-in-R.html" title="TBATS Model"><span class="progress-dot"></span>TBATS Model</a></li><li data-subkey="sec4sub0"><a href="/fable-in-R.html" title="fable and tsibble"><span class="progress-dot"></span>fable and tsibble</a></li><li data-subkey="sec4sub0"><a href="/GARCH-Models-in-R.html" title="GARCH Models"><span class="progress-dot"></span>GARCH Models</a></li><li data-subkey="sec4sub0"><a href="/Prediction-Intervals-in-R.html" title="Prediction Intervals"><span class="progress-dot"></span>Prediction Intervals</a></li><li data-subkey="sec4sub0"><a href="/VAR-Models-in-R.html" title="VAR Models"><span class="progress-dot"></span>VAR Models</a></li><li data-subkey="sec4sub0"><a href="/Anomaly-Detection-in-Time-Series-in-R.html" title="Anomaly Detection"><span class="progress-dot"></span>Anomaly Detection</a></li><li data-subkey="sec4sub0"><a href="/Changepoint-Detection-in-R.html" title="Changepoint Detection"><span class="progress-dot"></span>Changepoint Detection</a></li><li data-subkey="sec4sub0"><a href="/Combining-Forecasts-in-R.html" title="Combining Forecasts"><span class="progress-dot"></span>Combining Forecasts</a></li><li data-subkey="sec4sub0"><a href="/Cointegration-in-R.html" title="Cointegration"><span class="progress-dot"></span>Cointegration</a></li><li data-subkey="sec4sub0"><a href="/Kalman-Filter-in-R.html" title="Kalman Filter"><span class="progress-dot"></span>Kalman Filter</a></li><li data-subkey="sec4sub0"><a href="/Threshold-ARMA-TARSTAR-in-R.html" title="TAR and STAR Models"><span class="progress-dot"></span>TAR and STAR Models</a></li><li data-subkey="sec4sub0"><a href="/Forecast-Reconciliation-in-R.html" title="Forecast Reconciliation"><span class="progress-dot"></span>Forecast Reconciliation</a></li><li data-subkey="sec4sub0"><a href="/Hierarchical-Time-Series-in-R.html" title="Hierarchical Time Series"><span class="progress-dot"></span>Hierarchical Time Series</a></li><li data-subkey="sec4sub0"><a href="/MinT-Reconciliation-in-R.html" title="MinT Reconciliation"><span class="progress-dot"></span>MinT Reconciliation</a></li><li data-subkey="sec4sub0"><a href="/Benchmark-Forecasts-in-R.html" title="Benchmark Forecasts"><span class="progress-dot"></span>Benchmark Forecasts</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Features-in-R.html" title="Time Series Features"><span class="progress-dot"></span>Time Series Features</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Transformations-in-R.html" title="Box-Cox Transformations"><span class="progress-dot"></span>Box-Cox Transformations</a></li><li data-subkey="sec4sub0"><a href="/Feature-Engineering-for-Forecasting-in-R.html" title="Feature Engineering for Forecasting"><span class="progress-dot"></span>Feature Engineering for Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Regression-in-R.html" title="Time Series Regression"><span class="progress-dot"></span>Time Series Regression</a></li><li data-subkey="sec4sub0"><a href="/tsibble-in-R.html" title="tsibble Objects"><span class="progress-dot"></span>tsibble Objects</a></li><li data-subkey="sec4sub0"><a href="/Conformal-Prediction-in-R.html" title="Conformal Prediction"><span class="progress-dot"></span>Conformal Prediction</a></li><li data-subkey="sec4sub0"><a href="/Global-Forecasting-Models-in-R.html" title="Global Forecasting Models"><span class="progress-dot"></span>Global Forecasting Models</a></li><li data-subkey="sec4sub0"><a href="/XGBoost-Forecasting-in-R.html" title="Gradient Boosting for Forecasting"><span class="progress-dot"></span>Gradient Boosting for Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Backtesting-Forecasts-in-R.html" title="Backtesting Forecasts"><span class="progress-dot"></span>Backtesting Forecasts</a></li><li data-subkey="sec4sub0"><a href="/Distributional-Forecasts-in-R.html" title="Distributional Forecasts"><span class="progress-dot"></span>Distributional Forecasts</a></li><li data-subkey="sec4sub0"><a href="/Forecast-Scoring-Rules-in-R.html" title="Forecast Scoring Rules"><span class="progress-dot"></span>Forecast Scoring Rules</a></li><li data-subkey="sec4sub0"><a href="/Calendar-Effects-in-R.html" title="Calendar Effects"><span class="progress-dot"></span>Calendar Effects</a></li><li data-subkey="sec4sub0"><a href="/CausalImpact-in-R.html" title="CausalImpact"><span class="progress-dot"></span>CausalImpact</a></li><li data-subkey="sec4sub0"><a href="/Missing-Values-in-Time-Series-in-R.html" title="Missing Values in Time Series"><span class="progress-dot"></span>Missing Values in Time Series</a></li><li data-subkey="sec4sub0"><a href="/Bootstrap-Forecasting-in-R.html" title="Bootstrapping and Bagging"><span class="progress-dot"></span>Bootstrapping and Bagging</a></li><li data-subkey="sec4sub0"><a href="/MSTL-in-R.html" title="MSTL: Multiple Seasonalities"><span class="progress-dot"></span>MSTL: Multiple Seasonalities</a></li><li data-subkey="sec4sub0"><a href="/Multiple-Seasonality-Forecasting-in-R.html" title="Multiple Seasonality"><span class="progress-dot"></span>Multiple Seasonality</a></li><li data-subkey="sec4sub0"><a href="/Deep-Learning-Forecasting-in-R.html" title="Deep Learning for Forecasting"><span class="progress-dot"></span>Deep Learning for Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Granger-Causality-in-R.html" title="Granger Causality and IRFs"><span class="progress-dot"></span>Granger Causality and IRFs</a></li><li data-subkey="sec4sub0"><a href="/Structural-Time-Series-in-R.html" title="Structural Time Series"><span class="progress-dot"></span>Structural Time Series</a></li><li data-subkey="sec4sub0"><a href="/Count-Time-Series-in-R.html" title="Count Time Series (INGARCH)"><span class="progress-dot"></span>Count Time Series (INGARCH)</a></li><li data-subkey="sec4sub0"><a href="/Croston-Method-in-R.html" title="Intermittent Demand (Croston)"><span class="progress-dot"></span>Intermittent Demand (Croston)</a></li><li data-subkey="sec4sub0"><a href="/M-Competition-Lessons-in-R.html" title="M-Competition Lessons"><span class="progress-dot"></span>M-Competition Lessons</a></li><li data-subkey="sec4sub0"><a href="/Batch-Forecasting-in-R.html" title="Batch Forecasting"><span class="progress-dot"></span>Batch Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Forecasting-Short-Time-Series-in-R.html" title="Short and Long Series"><span class="progress-dot"></span>Short and Long Series</a></li><li data-subkey="sec4sub0"><a href="/Forecasting-Structural-Breaks-in-R.html" title="Structural Breaks"><span class="progress-dot"></span>Structural Breaks</a></li><li data-subkey="sec4sub0"><a href="/Forecast-Monitoring-in-R.html" title="Forecast Monitoring"><span class="progress-dot"></span>Forecast Monitoring</a></li><li data-subkey="sec4sub0"><a href="/Forecast-Value-Added-in-R.html" title="Forecast Value Added"><span class="progress-dot"></span>Forecast Value Added</a></li><li data-subkey="sec4sub0"><a href="/Retail-Demand-Forecasting-in-R.html" title="Retail Demand Forecasting"><span class="progress-dot"></span>Retail Demand Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Energy-Load-Forecasting-in-R.html" title="Energy Load Forecasting"><span class="progress-dot"></span>Energy Load Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Foundations-Course.html" title="Time Series Foundations (Course)"><span class="progress-dot"></span>Time Series Foundations (Course)</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Decomposition-Course.html" title="Time Series Decomposition (Course)"><span class="progress-dot"></span>Time Series Decomposition (Course)</a></li><li data-subkey="sec4sub0"><a href="/Forecasting-Toolbox-Course.html" title="Forecasting Toolbox (Course)"><span class="progress-dot"></span>Forecasting Toolbox (Course)</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Regression-Course.html" title="Time Series Regression (Course)"><span class="progress-dot"></span>Time Series Regression (Course)</a></li><li data-subkey="sec4sub0"><a href="/Exponential-Smoothing-ETS-Course.html" title="Exponential Smoothing ETS (Course)"><span class="progress-dot"></span>Exponential Smoothing ETS (Course)</a></li><li data-subkey="sec4sub0"><a href="/ARIMA-and-Seasonal-ARIMA-Course.html" title="ARIMA and Seasonal ARIMA (Course)"><span class="progress-dot"></span>ARIMA and Seasonal ARIMA (Course)</a></li><li data-subkey="sec4sub0"><a href="/Dynamic-Regression-and-Complex-Seasonality-Course.html" title="Dynamic Regression and Complex Seasonality (Course)"><span class="progress-dot"></span>Dynamic Regression and Complex Seasonality (Course)</a></li><li data-subkey="sec4sub0"><a href="/State-Space-Models-and-the-Kalman-Filter-Course.html" title="State Space Models and the Kalman Filter (Course)"><span class="progress-dot"></span>State Space Models and the Kalman Filter (Course)</a></li><li data-subkey="sec4sub0"><a href="/Spectral-and-Frequency-Domain-Analysis-Course.html" title="Spectral and Frequency Domain Analysis (Course)"><span class="progress-dot"></span>Spectral and Frequency Domain Analysis (Course)</a></li><li data-subkey="sec4sub0"><a href="/Volatility-Modeling-ARCH-and-GARCH-Course.html" title="Volatility Modeling with ARCH and GARCH (Course)"><span class="progress-dot"></span>Volatility Modeling with ARCH and GARCH (Course)</a></li><li data-subkey="sec4sub0"><a href="/Multivariate-Time-Series-Course.html" title="Multivariate Time Series (Course)"><span class="progress-dot"></span>Multivariate Time Series (Course)</a></li><li data-subkey="sec4sub0"><a href="/Hierarchical-and-Grouped-Forecasting-Course.html" title="Hierarchical and Grouped Forecasting (Course)"><span class="progress-dot"></span>Hierarchical and Grouped Forecasting (Course)</a></li><li data-subkey="sec4sub0"><a href="/Machine-Learning-and-Deep-Forecasting-Course.html" title="Machine Learning and Deep Forecasting (Course)"><span class="progress-dot"></span>Machine Learning and Deep Forecasting (Course)</a></li><li data-subkey="sec4sub0"><a href="/Intervention-Causal-Impact-and-Anomaly-Detection-Course.html" title="Intervention, Causal Impact and Anomaly Detection (Course)"><span class="progress-dot"></span>Intervention, Causal Impact and Anomaly Detection (Course)</a></li><li data-subkey="sec4sub0"><a href="/The-Expert-Edge-Forecasting-Like-a-Pro-Course.html" title="The Expert Edge in Forecasting Like a Pro (Course)"><span class="progress-dot"></span>The Expert Edge in Forecasting Like a Pro (Course)</a></li><li data-subkey="sec4sub0"><a href="/Production-Forecasting-Course.html" title="Production Forecasting (Course)"><span class="progress-dot"></span>Production Forecasting (Course)</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span><span class="sec-num">6.</span> <span class="sec-title-t">Advanced R</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Functional Programming</li><li data-subkey="sec5sub1"><a href="/Functional-Programming-in-R.html" title="Functional Programming"><span class="progress-dot"></span>Functional Programming</a></li><li data-subkey="sec5sub1" class="is-quiz"><a href="/R-Functional-Programming-Exercises-quiz.html" title="Functional Programming Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec5sub1"><a href="/purrr-map-Variants.html" title="purrr map() Variants"><span class="progress-dot"></span>purrr map() Variants</a></li><li data-subkey="sec5sub1"><a href="/R-Anonymous-Functions.html" title="R Anonymous Functions"><span class="progress-dot"></span>R Anonymous Functions</a></li><li data-subkey="sec5sub1"><a href="/R-Function-Factories.html" title="R Function Factories"><span class="progress-dot"></span>R Function Factories</a></li><li data-subkey="sec5sub1"><a href="/R-Function-Operators.html" title="R Function Operators"><span class="progress-dot"></span>R Function Operators</a></li><li data-subkey="sec5sub1"><a href="/Reduce-Filter-Map-in-R.html" title="Reduce, Filter, Map"><span class="progress-dot"></span>Reduce, Filter, Map</a></li><li data-subkey="sec5sub1"><a href="/Memoization-in-R.html" title="Memoization in R"><span class="progress-dot"></span>Memoization in R</a></li><li data-subkey="sec5sub1"><a href="/Writing-Composable-R-Code.html" title="Composable R Code"><span class="progress-dot"></span>Composable R Code</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> OOP in R</li><li data-subkey="sec5sub2"><a href="/OOP-in-R.html" title="OOP in R: S3/S4/R6"><span class="progress-dot"></span>OOP in R: S3/S4/R6</a></li><li data-subkey="sec5sub2"><a href="/S3-Classes-in-R.html" title="S3 Classes"><span class="progress-dot"></span>S3 Classes</a></li><li data-subkey="sec5sub2"><a href="/S3-Method-Dispatch-in-R.html" title="S3 Method Dispatch"><span class="progress-dot"></span>S3 Method Dispatch</a></li><li data-subkey="sec5sub2"><a href="/S4-Classes-in-R.html" title="S4 Classes"><span class="progress-dot"></span>S4 Classes</a></li><li data-subkey="sec5sub2"><a href="/S4-Methods-in-R.html" title="S4 Methods & Dispatch"><span class="progress-dot"></span>S4 Methods & Dispatch</a></li><li data-subkey="sec5sub2"><a href="/R6-Classes-in-R.html" title="R6 Classes"><span class="progress-dot"></span>R6 Classes</a></li><li data-subkey="sec5sub2"><a href="/R6-Advanced.html" title="R6 Advanced"><span class="progress-dot"></span>R6 Advanced</a></li><li data-subkey="sec5sub2"><a href="/Operator-Overloading-in-R.html" title="Operator Overloading"><span class="progress-dot"></span>Operator Overloading</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> How R Works</li><li data-subkey="sec5sub3"><a href="/R-Names-and-Values.html" title="R Names & Values"><span class="progress-dot"></span>R Names & Values</a></li><li data-subkey="sec5sub3"><a href="/R-Assignment-Deep-Dive.html" title="R Assignment Deep Dive"><span class="progress-dot"></span>R Assignment Deep Dive</a></li><li data-subkey="sec5sub3"><a href="/R-Memory-lobstr.html" title="R Memory & lobstr"><span class="progress-dot"></span>R Memory & lobstr</a></li><li data-subkey="sec5sub3"><a href="/R-Environments.html" title="R Environments"><span class="progress-dot"></span>R Environments</a></li><li data-subkey="sec5sub3"><a href="/R-Lexical-Scoping.html" title="Lexical Scoping"><span class="progress-dot"></span>Lexical Scoping</a></li><li data-subkey="sec5sub3"><a href="/R-Closures.html" title="R Closures"><span class="progress-dot"></span>R Closures</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Debugging & Performance</li><li data-subkey="sec5sub4"><a href="/R-Conditions-System.html" title="Conditions System"><span class="progress-dot"></span>Conditions System</a></li><li data-subkey="sec5sub4"><a href="/R-Debugging.html" title="Debugging R Code"><span class="progress-dot"></span>Debugging R Code</a></li><li data-subkey="sec5sub4"><a href="/R-Common-Errors.html" title="50 Common R Errors"><span class="progress-dot"></span>50 Common R Errors</a></li><li data-subkey="sec5sub4"><a href="/Parallel-Computing-With-R.html" title="Parallel Computing"><span class="progress-dot"></span>Parallel Computing</a></li><li data-subkey="sec5sub4"><a href="/Strategies-To-Improve-And-Speedup-R-Code.html" title="Speedup R Code"><span class="progress-dot"></span>Speedup R Code</a></li><li data-subkey="sec5sub4" class="is-quiz"><a href="/Shiny-Exercises-in-R-quiz.html" title="Shiny Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span><span class="sec-num">7.</span> <span class="sec-title-t">Classic Tutorials</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li data-subkey="sec6sub0"><a href="/R-Tutorial.html" title="R Tutorial (Classic)"><span class="progress-dot"></span>R Tutorial (Classic)</a></li><li data-subkey="sec6sub0"><a href="/ggplot2-Tutorial-With-R.html" title="ggplot2 Short Tutorial"><span class="progress-dot"></span>ggplot2 Short Tutorial</a></li><li data-subkey="sec6sub0"><a href="/Complete-Ggplot2-Tutorial-Part1-With-R-Code.html" title="ggplot2 Tutorial 1 - Intro"><span class="progress-dot"></span>ggplot2 Tutorial 1 - Intro</a></li><li data-subkey="sec6sub0"><a href="/Complete-Ggplot2-Tutorial-Part2-Customizing-Theme-With-R-Code.html" title="ggplot2 Tutorial 2 - Theme"><span class="progress-dot"></span>ggplot2 Tutorial 2 - Theme</a></li><li data-subkey="sec6sub0"><a href="/Top50-Ggplot2-Visualizations-MasterList-R-Code.html" title="ggplot2 Tutorial 3 - Masterlist"><span class="progress-dot"></span>ggplot2 Tutorial 3 - Masterlist</a></li><li data-subkey="sec6sub0"><a href="/Association-Mining-With-R.html" title="Association Mining"><span class="progress-dot"></span>Association Mining</a></li><li data-subkey="sec6sub0"><a href="/Multi-Dimensional-Scaling-With-R.html" title="Multi Dimensional Scaling"><span class="progress-dot"></span>Multi Dimensional Scaling</a></li><li data-subkey="sec6sub0"><a href="/Optimization-With-R.html" title="Optimization"><span class="progress-dot"></span>Optimization</a></li><li data-subkey="sec6sub0"><a href="/Information-Value-With-R.html" title="InformationValue Package"><span class="progress-dot"></span>InformationValue Package</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span><span class="sec-num">8.</span> <span class="sec-title-t">Practice Exercises</span><span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Featured Problem Sets</li><li data-subkey="sec7sub1"><a href="/R-Interview-Questions.html" title="R Interview Questions (Top 50)"><span class="progress-dot"></span>R Interview Questions (Top 50)</a></li><li data-subkey="sec7sub1"><a href="/Statistics-Interview-Questions.html" title="Statistics Interview Questions (25)"><span class="progress-dot"></span>Statistics Interview Questions (25)</a></li><li data-subkey="sec7sub1"><a href="/ML-Interview-Questions-in-R.html" title="ML Interview Questions (25)"><span class="progress-dot"></span>ML Interview Questions (25)</a></li><li data-subkey="sec7sub1"><a href="/Top-20-Bayesian-Problems-in-R.html" title="Top 20 Bayesian Problems"><span class="progress-dot"></span>Top 20 Bayesian Problems</a></li><li data-subkey="sec7sub1"><a href="/Probability-Puzzles-for-Interviews.html" title="Probability Puzzles (Top 20)"><span class="progress-dot"></span>Probability Puzzles (Top 20)</a></li><li data-subkey="sec7sub1"><a href="/AB-Testing-Interview-Cases.html" title="A/B Testing Interview Cases (20)"><span class="progress-dot"></span>A/B Testing Interview Cases (20)</a></li><li data-subkey="sec7sub1"><a href="/SQL-to-dplyr-Translations.html" title="SQL to dplyr (30 Translations)"><span class="progress-dot"></span>SQL to dplyr (30 Translations)</a></li><li data-subkey="sec7sub1"><a href="/Top-25-Regression-Problems-in-R.html" title="Top 25 Regression Problems"><span class="progress-dot"></span>Top 25 Regression Problems</a></li><li data-subkey="sec7sub1"><a href="/Top-20-Time-Series-Problems-in-R.html" title="Top 20 Time Series Problems"><span class="progress-dot"></span>Top 20 Time Series Problems</a></li><li data-subkey="sec7sub1"><a href="/Resampling-Problems-in-R.html" title="The Resampling 15"><span class="progress-dot"></span>The Resampling 15</a></li><li data-subkey="sec7sub1"><a href="/Data-Cleaning-Gauntlet.html" title="Data Cleaning Gauntlet (25)"><span class="progress-dot"></span>Data Cleaning Gauntlet (25)</a></li><li data-subkey="sec7sub1"><a href="/Error-Triage-Drills-in-R.html" title="Error Triage Drills (20)"><span class="progress-dot"></span>Error Triage Drills (20)</a></li><li data-subkey="sec7sub1"><a href="/Regex-Drills-in-R.html" title="The Regex 20"><span class="progress-dot"></span>The Regex 20</a></li><li data-subkey="sec7sub1"><a href="/Dates-and-Times-Drills-in-R.html" title="Dates and Times Drills"><span class="progress-dot"></span>Dates and Times Drills</a></li><li data-subkey="sec7sub1"><a href="/Base-R-Speed-Round.html" title="Base R Speed Round"><span class="progress-dot"></span>Base R Speed Round</a></li><li data-subkey="sec7sub1"><a href="/ggplot2-Recreation-Challenge.html" title="ggplot2 Recreation Challenge"><span class="progress-dot"></span>ggplot2 Recreation Challenge</a></li><li data-subkey="sec7sub1"><a href="/Take-Home-Assignment-Simulator.html" title="Take-Home Simulator"><span class="progress-dot"></span>Take-Home Simulator</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> Mastery Quizzes (Certificate)</li><li data-subkey="sec7sub2" class="is-quiz"><a href="/R-Beginner-Exercises-quiz.html" title="R Fundamentals Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/dplyr-Exercises-in-R-quiz.html" title="dplyr Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/ggplot2-Exercises-in-R-quiz.html" title="ggplot2 Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/Hypothesis-Testing-Exercises-in-R-quiz.html" title="Hypothesis Testing Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/Linear-Regression-Exercises-in-R-quiz.html" title="Linear Regression Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/Machine-Learning-Exercises-in-R-quiz.html" title="Machine Learning Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/tidyr-Exercises-in-R-quiz.html" title="tidyr Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/Time-Series-Exercises-in-R-quiz.html" title="Time Series Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/Shiny-Exercises-in-R-quiz.html" title="Shiny Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/R-Interview-Questions-quiz.html" title="R Interview Readiness Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li data-subkey="sec7sub2" class="is-quiz"><a href="/R-Functional-Programming-Exercises-quiz.html" title="Functional Programming Quiz"><span class="quiz-marker" aria-hidden="true"><svg viewBox="0 0 24 24" fill="currentColor" aria-hidden="true"><path d="M12 2 4 5.1v5.7c0 4.9 3.4 8.4 8 9.9 4.6-1.5 8-5 8-9.9V5.1L12 2z"/></svg></span>Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> R Fundamentals</li><li data-subkey="sec7sub3"><a href="/R-Basics-Exercises.html" title="R Basics (15 problems)"><span class="progress-dot"></span>R Basics (15 problems)</a></li><li data-subkey="sec7sub3"><a href="/R-Vectors-Exercises.html" title="R Vectors (12 problems)"><span class="progress-dot"></span>R Vectors (12 problems)</a></li><li data-subkey="sec7sub3"><a href="/R-Data-Frames-Exercises.html" title="R Data Frames (15 problems)"><span class="progress-dot"></span>R Data Frames (15 problems)</a></li><li data-subkey="sec7sub3"><a 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d="M8 13.5v-4"/></svg></span><span class="tool-label">Sample Size (t Tests)</span></a></li><li><a href="/tools/sample-size-proportion-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2.5 2.5v11h11"/><path d="M6 13.5V9.5"/><path d="M11 13.5V5"/></svg></span><span class="tool-label">Sample Size (Proportions)</span></a></li><li><a href="/tools/sample-size-anova-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2.5 2.5v11h11"/><path d="M5.5 13.5V10"/><path d="M9 13.5V6"/><path d="M12.5 13.5V8"/></svg></span><span class="tool-label">Sample Size (ANOVA)</span></a></li><li><a href="/tools/survival-power-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2 3.5h3.5V7H9v3.5h3.5V13H14"/></svg></span><span class="tool-label">Survival Power</span></a></li><li><a href="/tools/type-i-ii-error-visualizer.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2 12c1.5 0 2-2 3.5-2S7 12 8 12s2-8 3.5-8S13 12 14.5 12"/><line x1="8" y1="2" x2="8" y2="14" stroke-dasharray="2 2"/></svg></span><span class="tool-label">Type I / II Error</span></a></li><li><a href="/tools/z-score-percentile.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2 13c2 0 3-1 4-3s1.5-6 2-6 .5 6 2 6 2.5 0 4 0"/><path d="M2 13.5h12"/></svg></span><span class="tool-label">Z-Score & Percentile</span></a></li><li><a href="/tools/normal-distribution-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M1.5 13c2 0 3-1 4-3s1.5-6 2.5-6 1.5 6 2.5 6 2-1 3.5-1"/><path d="M1.5 13.5h13"/><path d="M5.5 13C6.3 11 7 7 8 4C9 7 9.7 11 10.5 13Z" fill="currentColor" stroke="none" opacity="0.4"/></svg></span><span class="tool-label">Normal Distribution</span></a></li><li><a href="/tools/empirical-rule-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.3" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M1.5 12.5h13"/><path d="M2 12.5C5 12.5 5.2 4 8 4C10.8 4 11 12.5 14 12.5"/><path d="M5.6 12.5C6.5 10.8 7.2 7 8 4C8.8 7 9.5 10.8 10.4 12.5Z" fill="currentColor" stroke="none" opacity="0.32"/><path d="M5.6 12.5V10.2M10.4 12.5V10.2" stroke-dasharray="1.5 1.4"/><path d="M3.4 12.5V11M12.6 12.5V11" stroke-dasharray="1.5 1.4"/></svg></span><span class="tool-label">Empirical Rule</span></a></li><li><a href="/tools/equivalence-noninferiority-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M3 3.5v9M13 3.5v9"/><path d="M5.5 8h5"/><circle cx="8" cy="8" r="1.3" fill="currentColor" stroke="none"/></svg></span><span class="tool-label">Equivalence / NI</span></a></li><li><a href="/tools/outlier-detection-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><circle cx="5" cy="10" r="1" fill="currentColor" stroke="none"/><circle cx="7.5" cy="8.5" r="1" fill="currentColor" stroke="none"/><circle cx="5.5" cy="12.5" r="1" fill="currentColor" stroke="none"/><circle cx="12" cy="4" r="2.4"/></svg></span><span class="tool-label">Outlier Detection</span></a></li><li><a href="/tools/roc-auc-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2.5 13.5L13.5 2.5" stroke-dasharray="2 2"/><path d="M2.5 13.5C2.5 7 7 2.5 13.5 2.5"/></svg></span><span class="tool-label">ROC / AUC</span></a></li><li><a href="/tools/cronbachs-alpha-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2 4h5M2 8h5M2 12h5"/><path d="M7 4c3.5 0 3.5 4 6 4M7 12c3.5 0 3.5-4 6-4"/><circle cx="13" cy="8" r="1.2" fill="currentColor" stroke="none"/></svg></span><span class="tool-label">Cronbach's Alpha</span></a></li><li><a href="/tools/cohens-kappa-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="2.5" y="2.5" width="11" height="11" rx="1"/><path d="M6.17 2.5v11M9.83 2.5v11M2.5 6.17h11M2.5 9.83h11"/><circle cx="4.33" cy="4.33" r="1" fill="currentColor" stroke="none"/><circle cx="8" cy="8" r="1" fill="currentColor" stroke="none"/><circle cx="11.67" cy="11.67" r="1" fill="currentColor" stroke="none"/></svg></span><span class="tool-label">Cohen's Kappa</span></a></li><li><a href="/tools/icc-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2.5 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r=".9" fill="currentColor" stroke="none"/></svg></span><span class="tool-label">Correlation</span></a></li><li><a href="/tools/linear-regression-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><path d="M2.5 2v11.5h11"/><path d="M3.8 12.2 13.2 4.2"/><circle cx="5.2" cy="11.4" r=".9" fill="currentColor" stroke="none"/><circle cx="7.4" cy="8.6" r=".9" fill="currentColor" stroke="none"/><circle cx="9.4" cy="7.4" r=".9" fill="currentColor" stroke="none"/><circle cx="11.4" cy="4.8" r=".9" fill="currentColor" stroke="none"/></svg></span><span class="tool-label">Linear Regression</span></a></li><li><a href="/tools/prediction-interval-calculator.html"><span class="tool-icon"><svg viewBox="0 0 16 16" width="14" height="14" fill="none" stroke="currentColor" stroke-width="1.4" stroke-linecap="round" stroke-linejoin="round" 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<nav class="breadcrumb-nav" aria-label="Breadcrumb"><a href="/">Home</a> <span class="breadcrumb-sep">›</span> <span class="breadcrumb-current">Bayesian Factor Analysis in R with blavaan</span></nav>
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<h1>Bayesian Factor Analysis in R with blavaan</h1>
<p class="lead">Bayesian factor analysis uncovers the hidden factors behind a set of correlated measurements, and instead of a single number for each factor loading it hands you a full probability distribution, so you see both the estimate and how sure you can be about it. In R, the blavaan package fits these models with almost the same syntax as lavaan, so if you can write a classical factor model you can write a Bayesian one.</p>
<div class="post-byline" style="color:#6b7280;font-size:14px;margin:2px 0 4px 0;line-height:1.5;">By <strong>Selva Prabhakaran</strong> · August 2026</div><div class="post-verified" style="color:#9aa1ad;font-size:12.5px;margin:0 0 18px 0;">Code examples run against R 4.6.0</div>
<p>This tutorial builds the idea from the ground up. You will simulate data with a known hidden structure and run it right here on the page, watch a classical factor analysis recover that structure as bare point estimates, and then upgrade to blavaan to get the full posterior: loadings with <a class="auto-link" href="Credible-Intervals-vs-Confidence-Intervals.html" title="Credible vs Confidence Intervals in R">credible intervals</a>, convergence checks, and a look at how much your priors actually change the answer. The hands-on intuition uses base R, so nothing needs installing to follow along. The blavaan sections are marked to run in your own R install, because they lean on the Stan engine.</p>
<h2>What is factor analysis, and where do the hidden factors come from?</h2>
<p>Suppose you gave 250 students six short tests. You cannot measure "math ability" with a ruler, but if it exists, the math-flavored tests should rise and fall together, and so should the verbal ones. Factor analysis works backward from those correlations to the hidden abilities that could have produced them. Let us build exactly that situation, so we know the true answer before we look.</p>
<p>We will create two hidden factors, a math factor and a verbal factor, and let them be mildly correlated (real abilities usually are). Then we build six observed test scores: three driven mostly by math, three driven mostly by verbal, each with its own random noise. Because we made the data, we know the truth going in.</p>
<div class="webr-container" data-block-title="Simulate six scores from two hidden factors">
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<div class="webr-editor" data-language="r"><span class="cl"><span class="nf">set.seed</span>(<span class="m">2024</span>)</span>
<span class="cl">n <span class="o"><-</span> <span class="m">250</span></span>
<span class="cl">math <span class="o"><-</span> <span class="nf">rnorm</span>(n)</span>
<span class="cl">verbal <span class="o"><-</span> <span class="m">0.4</span> <span class="o">*</span> math <span class="o">+</span> <span class="nf">sqrt</span>(<span class="m">1</span> <span class="o">-</span> <span class="m">0.4</span><span class="o">^</span><span class="m">2</span>) <span class="o">*</span> <span class="nf">rnorm</span>(n) <span class="c1"># verbal correlates ~0.4 with math</span></span>
<span class="cl"></span>
<span class="cl">m1 <span class="o"><-</span> <span class="m">0.80</span> <span class="o">*</span> math <span class="o">+</span> <span class="nf">rnorm</span>(n, <span class="m">0</span>, <span class="m">0.6</span>)</span>
<span class="cl">m2 <span class="o"><-</span> <span class="m">0.70</span> <span class="o">*</span> math <span class="o">+</span> <span class="nf">rnorm</span>(n, <span class="m">0</span>, <span class="m">0.6</span>)</span>
<span class="cl">m3 <span class="o"><-</span> <span class="m">0.60</span> <span class="o">*</span> math <span class="o">+</span> <span class="nf">rnorm</span>(n, <span class="m">0</span>, <span class="m">0.6</span>)</span>
<span class="cl">v1 <span class="o"><-</span> <span class="m">0.80</span> <span class="o">*</span> verbal <span class="o">+</span> <span class="nf">rnorm</span>(n, <span class="m">0</span>, <span class="m">0.6</span>)</span>
<span class="cl">v2 <span class="o"><-</span> <span class="m">0.70</span> <span class="o">*</span> verbal <span class="o">+</span> <span class="nf">rnorm</span>(n, <span class="m">0</span>, <span class="m">0.6</span>)</span>
<span class="cl">v3 <span class="o"><-</span> <span class="m">0.60</span> <span class="o">*</span> verbal <span class="o">+</span> <span class="nf">rnorm</span>(n, <span class="m">0</span>, <span class="m">0.6</span>)</span>
<span class="cl"></span>
<span class="cl">scores <span class="o"><-</span> <span class="nf">data.frame</span>(m1, m2, m3, v1, v2, v3)</span>
<span class="cl"><span class="nf">dim</span>(scores)</span>
<span class="cl"><span class="c1">#> [1] 250 6</span></span>
<span class="cl"><span class="nf">round</span>(<span class="nf">head</span>(scores, <span class="m">3</span>), <span class="m">2</span>)</span>
<span class="cl"><span class="c1">#> m1 m2 m3 v1 v2 v3</span></span>
<span class="cl"><span class="c1">#> 1 1.25 0.56 0.56 1.86 2.91 1.35</span></span>
<span class="cl"><span class="c1">#> 2 -0.06 0.71 -0.02 0.92 0.13 0.11</span></span>
<span class="cl"><span class="c1">#> 3 0.39 1.08 -0.61 -0.62 1.06 0.01</span></span></div>
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<p>The block created a data frame of 250 rows and 6 columns, one column per test. Notice that the two factors themselves, <code>math</code> and <code>verbal</code>, are not in the data frame. That is the whole point: in real life you never observe the factor, only the noisy scores it produced. The diagram below shows the machine we just built.</p>
<p><img src="screenshots/Bayesian-Factor-Analysis-in-R-measurement-model.webp" alt="How factor analysis sees your data, with each hidden factor driving its own scores" class="img-responsive img-zoomable" loading="lazy" width="1328" height="1124" /></p>
<p><em>Figure 1: Each hidden factor drives its own set of observed scores, and the two factors can correlate.</em></p>
<p>If the hidden factors are real, their fingerprints show up as correlations. Scores driven by the same factor should correlate strongly with each other and weakly with scores from the other factor. Let us look at the <a class="auto-link" href="Correlation-Analysis-in-R.html" title="Correlation in R: Pearson vs Spearman vs Kendall — Compute, Test, and Visualise">correlation matrix</a> and check.</p>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="nf">round</span>(<span class="nf">cor</span>(scores), <span class="m">2</span>)</span>
<span class="cl"><span class="c1">#> m1 m2 m3 v1 v2 v3</span></span>
<span class="cl"><span class="c1">#> m1 1.00 0.66 0.67 0.33 0.36 0.28</span></span>
<span class="cl"><span class="c1">#> m2 0.66 1.00 0.61 0.28 0.36 0.23</span></span>
<span class="cl"><span class="c1">#> m3 0.67 0.61 1.00 0.28 0.32 0.26</span></span>
<span class="cl"><span class="c1">#> v1 0.33 0.28 0.28 1.00 0.59 0.52</span></span>
<span class="cl"><span class="c1">#> v2 0.36 0.36 0.32 0.59 1.00 0.47</span></span>
<span class="cl"><span class="c1">#> v3 0.28 0.23 0.26 0.52 0.47 1.00</span></span></div>
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<p>Read the matrix in two blocks. The top-left three-by-three corner (the m tests) shows correlations around 0.6, and so does the bottom-right corner (the v tests). The off-diagonal block linking m tests to v tests sits lower, around 0.3. That two-block pattern is the visible trace of two hidden factors. A quick heatmap makes the blocks jump out.</p>
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<div class="webr-editor" data-language="r"><span class="cl">cols <span class="o"><-</span> <span class="nf">colorRampPalette</span>(<span class="nf">c</span>(<span class="s">"white"</span>, <span class="s">"steelblue"</span>))(<span class="m">20</span>)</span>
<span class="cl"><span class="nf">image</span>(<span class="m">1</span><span class="o">:</span><span class="m">6</span>, <span class="m">1</span><span class="o">:</span><span class="m">6</span>, <span class="nf">cor</span>(scores)[, <span class="m">6</span><span class="o">:</span><span class="m">1</span>], col <span class="o">=</span> cols, axes <span class="o">=</span> <span class="kc">FALSE</span>,</span>
<span class="cl"> xlab <span class="o">=</span> <span class="s">""</span>, ylab <span class="o">=</span> <span class="s">""</span>, main <span class="o">=</span> <span class="s">"Correlations light up in two blocks"</span>)</span>
<span class="cl"><span class="nf">axis</span>(<span class="m">1</span>, at <span class="o">=</span> <span class="m">1</span><span class="o">:</span><span class="m">6</span>, labels <span class="o">=</span> <span class="nf">colnames</span>(scores))</span>
<span class="cl"><span class="nf">axis</span>(<span class="m">2</span>, at <span class="o">=</span> <span class="m">1</span><span class="o">:</span><span class="m">6</span>, labels <span class="o">=</span> <span class="nf">rev</span>(<span class="nf">colnames</span>(scores)))</span></div>
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<p>The darker the square, the stronger the correlation. Two dark blocks appear along the diagonal, one for the math tests and one for the verbal tests, with paler squares linking the two groups. Factor analysis is the formal tool that turns this eyeballed pattern into numbers.</p>
<div class="callout callout-insight"><div class="callout-label">Key Insight</div><div class="callout-body"><strong>Correlations are the clue; factors are the explanation.</strong> Factor analysis never measures the hidden abilities directly. It reads the pattern of correlations and works backward to the smallest set of hidden factors that could plausibly have produced that pattern.</div></div>
<p>The word "Bayesian" adds one more idea on top. A Bayesian analysis starts with a prior, a statement of what you believe before seeing the data, then updates it with the data to produce a posterior, a full distribution of plausible values. If that language is new, the <a href="MCMC-in-R.html">MCMC in R</a> and <a href="Grid-Approximation-in-R.html">Grid Approximation in R</a> tutorials build it from scratch. Here you only need the one-line version: Bayesian factor analysis returns a distribution for every loading, not a single number.</p>
<section class="tryit-block">
<p><strong>Try it:</strong> Confirm the block pattern yourself. Compute the correlation between two math tests (<code>m1</code> and <code>m2</code>) and between a math test and a verbal test (<code>m1</code> and <code>v1</code>), and see which is larger.</p>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Fill in the two cor() calls, then run.</span></span>
<span class="cl">ex_within <span class="o"><-</span> <span class="m">0</span> <span class="c1"># cor of m1 and m2 (same factor)</span></span>
<span class="cl">ex_between <span class="o"><-</span> <span class="m">0</span> <span class="c1"># cor of m1 and v1 (different factors)</span></span></div>
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<details>
<summary>Click to reveal solution</summary>
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<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">Compare two correlations solution</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl">ex_within <span class="o"><-</span> <span class="nf">cor</span>(scores<span class="o">$</span>m1, scores<span class="o">$</span>m2)</span>
<span class="cl">ex_between <span class="o"><-</span> <span class="nf">cor</span>(scores<span class="o">$</span>m1, scores<span class="o">$</span>v1)</span>
<span class="cl"><span class="nf">round</span>(<span class="nf">c</span>(within <span class="o">=</span> ex_within, between <span class="o">=</span> ex_between), <span class="m">2</span>)</span>
<span class="cl"><span class="c1">#> within between </span></span>
<span class="cl"><span class="c1">#> 0.66 0.33</span></span></div>
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<p><strong>Explanation:</strong> Two tests driven by the same factor correlate about twice as strongly (0.66) as two tests from different factors (0.33). That gap is exactly what factor analysis exploits.</p>
</details>
</section>
<h2>What does classical factor analysis give you, and what does it leave out?</h2>
<p>Before fitting anything, a factor analysis asks one question: how many factors? A common quick check counts how many <a class="auto-link" href="Eigenvalues-and-Eigenvectors-in-R.html" title="Eigenvalues & Eigenvectors in R: eigen(), Why They Power PCA & More">eigenvalues</a> of the correlation matrix exceed 1. Each eigenvalue measures how much shared variance one direction captures, and a value above 1 means that direction explains more than a single test's worth of variance. Let us compute them.</p>
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<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">Count the factors with eigenvalues</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl">ev <span class="o"><-</span> <span class="nf">eigen</span>(<span class="nf">cor</span>(scores))<span class="o">$</span>values</span>
<span class="cl"><span class="nf">round</span>(ev, <span class="m">2</span>)</span>
<span class="cl"><span class="c1">#> [1] 3.09 1.27 0.54 0.41 0.37 0.31</span></span></div>
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<p>Two eigenvalues sit above 1 (3.09 and 1.27) and the rest fall well below, so the data point clearly to two factors. That matches how we built it. Now we run a classical factor analysis. Base R ships <code>factanal()</code>, which fits a factor model by maximum likelihood and rotates the result so each test loads cleanly on one factor.</p>
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<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">Fit a classical factor analysis</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl">fa <span class="o"><-</span> <span class="nf">factanal</span>(scores, factors <span class="o">=</span> <span class="m">2</span>, rotation <span class="o">=</span> <span class="s">"promax"</span>)</span>
<span class="cl"><span class="nf">print</span>(fa<span class="o">$</span>loadings, cutoff <span class="o">=</span> <span class="m">0.3</span>)</span>
<span class="cl"><span class="c1">#> </span></span>
<span class="cl"><span class="c1">#> Loadings:</span></span>
<span class="cl"><span class="c1">#> Factor1 Factor2</span></span>
<span class="cl"><span class="c1">#> m1 0.842 </span></span>
<span class="cl"><span class="c1">#> m2 0.776 </span></span>
<span class="cl"><span class="c1">#> m3 0.800 </span></span>
<span class="cl"><span class="c1">#> v1 0.838 </span></span>
<span class="cl"><span class="c1">#> v2 0.686 </span></span>
<span class="cl"><span class="c1">#> v3 0.648 </span></span>
<span class="cl"><span class="c1">#> </span></span>
<span class="cl"><span class="c1">#> Factor1 Factor2</span></span>
<span class="cl"><span class="c1">#> SS loadings 1.961 1.593</span></span>
<span class="cl"><span class="c1">#> Proportion Var 0.327 0.265</span></span>
<span class="cl"><span class="c1">#> Cumulative Var 0.327 0.592</span></span></div>
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<p>The loadings table splits perfectly. The three m tests load on Factor1 (values around 0.8) and the three v tests load on Factor2, with the small cross-loadings hidden by the 0.3 cutoff. A loading is just the strength of the link between a test and its factor, on a scale where 1 is a perfect match and 0 is no relationship. Together the two factors explain about 59 percent of the total variance (the cumulative variance row).</p>
<p>This is a good result, and for many jobs it is enough. But look closely at what you got: one number per loading, and nothing else. There is no sense of how firm the 0.842 is. If you collected a fresh sample of 250 students, would it come back as 0.84, or could it be 0.72 or 0.95? The point estimate cannot say. The diagram below frames the gap this tutorial closes.</p>
<p><img src="screenshots/Bayesian-Factor-Analysis-in-R-point-vs-posterior.webp" alt="Classical CFA returns one number per loading while Bayesian CFA returns a full posterior" class="img-responsive img-zoomable" loading="lazy" width="1376" height="738" /></p>
<p><em>Figure 2: Classical CFA returns one number per loading; Bayesian CFA returns a full posterior with a <a class="auto-link" href="Bayesian-Linear-Regression-in-R.html" title="Bayesian Linear Regression in R: Get Uncertainty Estimates lm() Cannot Give You">credible interval</a>.</em></p>
<div class="callout callout-warning"><div class="callout-label">Warning</div><div class="callout-body"><strong>A single loading number hides how sure you are.</strong> Classical factor analysis hands you one value per loading with no built-in sense of how much it might wobble in a new sample. Two studies can both report a 0.84 loading while one is rock solid and the other is barely distinguishable from zero.</div></div>
<section class="tryit-block">
<p><strong>Try it:</strong> <code>factanal()</code> also reports uniquenesses, the share of each test's variance that its factor does not explain. Pull them out of the fitted object with <code>fa$uniquenesses</code> and find the largest one.</p>
<div class="webr-container" data-block-title="Your turn: find the largest uniqueness">
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<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># The uniquenesses live in fa$uniquenesses.</span></span>
<span class="cl"><span class="c1"># Round them, then find which test has the biggest.</span></span></div>
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<summary>Click to reveal solution</summary>
<div class="webr-container" data-block-title="Largest uniqueness solution">