MSA/pca.html at main · yilewang/MSA

History

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

<!DOCTYPE html>

<head>

<title>Chapter 4 Principal Component Analysis | Multivariate Statistical Analysis Cookbook with R</title>

code.sourceCode > span { display: inline-block; line-height: 1.25; }

code.sourceCode > span { color: inherit; text-decoration: inherit; }

code.sourceCode > span:empty { height: 1.2em; }

.sourceCode { overflow: visible; }

code.sourceCode { white-space: pre; position: relative; }

pre.sourceCode { margin: 0; }

@media screen {

div.sourceCode { overflow: auto; }

}

@media print {

code.sourceCode { white-space: pre-wrap; }

code.sourceCode > span { text-indent: -5em; padding-left: 5em; }

}

pre.numberSource code

{ counter-reset: source-line 0; }

pre.numberSource code > span

{ position: relative; left: -4em; counter-increment: source-line; }

pre.numberSource code > span > a:first-child::before

{ content: counter(source-line);

position: relative; left: -1em; text-align: right; vertical-align: baseline;

border: none; display: inline-block;

-webkit-touch-callout: none; -webkit-user-select: none;

-khtml-user-select: none; -moz-user-select: none;

-ms-user-select: none; user-select: none;

padding: 0 4px; width: 4em;

color: #aaaaaa;

}

pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa; padding-left: 4px; }

div.sourceCode

{ }

@media screen {

code.sourceCode > span > a:first-child::before { text-decoration: underline; }

}

code span.al { color: #ff0000; font-weight: bold; } /* Alert */

code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */

code span.at { color: #7d9029; } /* Attribute */

code span.bn { color: #40a070; } /* BaseN */

code span.bu { } /* BuiltIn */

code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */

code span.ch { color: #4070a0; } /* Char */

code span.cn { color: #880000; } /* Constant */

code span.co { color: #60a0b0; font-style: italic; } /* Comment */

code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */

code span.do { color: #ba2121; font-style: italic; } /* Documentation */

code span.dt { color: #902000; } /* DataType */

code span.dv { color: #40a070; } /* DecVal */

code span.er { color: #ff0000; font-weight: bold; } /* Error */

code span.ex { } /* Extension */

code span.fl { color: #40a070; } /* Float */

code span.fu { color: #06287e; } /* Function */

code span.im { } /* Import */

code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */

code span.kw { color: #007020; font-weight: bold; } /* Keyword */

code span.op { color: #666666; } /* Operator */

code span.ot { color: #007020; } /* Other */

code span.pp { color: #bc7a00; } /* Preprocessor */

code span.sc { color: #4070a0; } /* SpecialChar */

code span.ss { color: #bb6688; } /* SpecialString */

code span.st { color: #4070a0; } /* String */

code span.va { color: #19177c; } /* Variable */

code span.vs { color: #4070a0; } /* VerbatimString */

code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */

</style>

</head>

<body>

<li class="chapter" data-level="1" data-path="intro.html"><a href="intro.html">1 Introduction</a><ul>

<li class="chapter" data-level="1.1" data-path="intro.html"><a href="intro.html#main-packages">1.1 Main Packages</a></li>

<li class="chapter" data-level="1.2" data-path="intro.html"><a href="intro.html#msa-introduction">1.2 MSA Introduction</a></li>

</ul></li>

<li class="chapter" data-level="2" data-path="Functions.html"><a href="Functions.html">2 Functions Introduction</a><ul>

<li class="chapter" data-level="2.1" data-path="Functions.html"><a href="Functions.html#Scree">2.1 Plotting Scree plot</a></li>

<li class="chapter" data-level="2.2" data-path="Functions.html"><a href="Functions.html#Permutation">2.2 Plotting Permutation test results</a></li>

<li class="chapter" data-level="2.3" data-path="Functions.html"><a href="Functions.html#Heatmap">2.3 Plotting Heatmap</a></li>

<li class="chapter" data-level="2.4" data-path="Functions.html"><a href="Functions.html#FactorScores">2.4 Plotting Row Factor Scores</a></li>

<li class="chapter" data-level="2.5" data-path="Functions.html"><a href="Functions.html#CFactorScore">2.5 Plotting Column Plot</a></li>

<li class="chapter" data-level="2.6" data-path="Functions.html"><a href="Functions.html#Loading">2.6 Plotting Loading Plot</a></li>

<li class="chapter" data-level="2.7" data-path="Functions.html"><a href="Functions.html#Contribution">2.7 Plotting Contribution Barplot</a></li>

<li class="chapter" data-level="2.8" data-path="Functions.html"><a href="Functions.html#binshelper">2.8 Bins Helper Functions</a></li>

<li class="chapter" data-level="2.9" data-path="Functions.html"><a href="Functions.html#plotting-latent-variable-plot">2.9 Plotting Latent Variable Plot</a></li>

<li class="chapter" data-level="2.10" data-path="Functions.html"><a href="Functions.html#plotting-partial-factor-scores">2.10 Plotting Partial Factor Scores</a></li>

</ul></li>

<li class="chapter" data-level="3" data-path="Data-Intro.html"><a href="Data-Intro.html">3 Data Introduction</a><ul>

<li class="chapter" data-level="3.1" data-path="Data-Intro.html"><a href="Data-Intro.html#collect">3.1 Main data set: Collective Action Data Set</a></li>

<li class="chapter" data-level="3.2" data-path="Data-Intro.html"><a href="Data-Intro.html#sausage">3.2 Low Income Sausage</a></li>

<li class="chapter" data-level="3.3" data-path="Data-Intro.html"><a href="Data-Intro.html#wines">3.3 Wines</a></li>

</ul></li>

<li class="chapter" data-level="4" data-path="pca.html"><a href="pca.html">4 Principal Component Analysis</a><ul>

<li class="chapter" data-level="4.1" data-path="pca.html"><a href="pca.html#introduction-of-pca">4.1 Introduction of PCA</a></li>

<li class="chapter" data-level="4.2" data-path="pca.html"><a href="pca.html#computing">4.2 Computing</a></li>

<li class="chapter" data-level="4.3" data-path="pca.html"><a href="pca.html#heatmap">4.3 Heatmap</a></li>

<li class="chapter" data-level="4.4" data-path="pca.html"><a href="pca.html#pcaScree">4.4 Scree Plot</a></li>

<li class="chapter" data-level="4.5" data-path="pca.html"><a href="pca.html#factor-scores">4.5 Factor Scores</a></li>

<li class="chapter" data-level="4.6" data-path="pca.html"><a href="pca.html#loading">4.6 Loading</a></li>

<li class="chapter" data-level="4.7" data-path="pca.html"><a href="pca.html#contriution-and-bootstrap-ratio-barplots">4.7 Contriution and Bootstrap Ratio Barplots</a></li>

<li class="chapter" data-level="4.8" data-path="pca.html"><a href="pca.html#conclusion">4.8 Conclusion</a></li>

</ul></li>

<li class="chapter" data-level="5" data-path="ca.html"><a href="ca.html">5 Correspondence Analysis</a><ul>

<li class="chapter" data-level="5.1" data-path="ca.html"><a href="ca.html#introduction-of-ca">5.1 Introduction of CA</a></li>

<li class="chapter" data-level="5.2" data-path="ca.html"><a href="ca.html#computation">5.2 Computation</a></li>

<li class="chapter" data-level="5.3" data-path="ca.html"><a href="ca.html#heatmap-1">5.3 Heatmap</a></li>

<li class="chapter" data-level="5.4" data-path="ca.html"><a href="ca.html#computation-1">5.4 Computation</a></li>

<li class="chapter" data-level="5.5" data-path="ca.html"><a href="ca.html#scree-plot">5.5 Scree Plot</a></li>

<li class="chapter" data-level="5.6" data-path="ca.html"><a href="ca.html#symmetric-asymmetric-plots">5.6 Symmetric & Asymmetric Plots</a></li>

<li class="chapter" data-level="5.7" data-path="ca.html"><a href="ca.html#contribution-and-bootstrap-ratio-barplot">5.7 Contribution and Bootstrap Ratio Barplot</a></li>

</ul></li>

<li class="chapter" data-level="6" data-path="dica.html"><a href="dica.html">6 Discriminant Correspondence Analysis</a><ul>

<li class="chapter" data-level="6.1" data-path="dica.html"><a href="dica.html#introdcution-of-dica">6.1 Introdcution of DiCA</a></li>

<li class="chapter" data-level="6.2" data-path="dica.html"><a href="dica.html#histgram-of-binning-variables">6.2 Histgram of Binning Variables</a></li>

<li class="chapter" data-level="6.3" data-path="dica.html"><a href="dica.html#heatmap-2">6.3 Heatmap</a></li>

<li class="chapter" data-level="6.4" data-path="dica.html"><a href="dica.html#scree-plot-1">6.4 Scree Plot</a></li>

<li class="chapter" data-level="6.5" data-path="dica.html"><a href="dica.html#factor-scores-1">6.5 Factor Scores</a></li>

<li class="chapter" data-level="6.6" data-path="dica.html"><a href="dica.html#confusion-matrix">6.6 Confusion Matrix</a></li>

<li class="chapter" data-level="6.7" data-path="dica.html"><a href="dica.html#contribution-and-bootstrap-ratio-barplots">6.7 Contribution and Bootstrap Ratio Barplots</a></li>

</ul></li>

<li class="chapter" data-level="7" data-path="bada.html"><a href="bada.html">7 Barycentric Discriminant Analysis</a><ul>

<li class="chapter" data-level="7.1" data-path="bada.html"><a href="bada.html#introduction-of-bada">7.1 Introduction of BADA</a></li>

<li class="chapter" data-level="7.2" data-path="bada.html"><a href="bada.html#computation-2">7.2 Computation</a></li>

<li class="chapter" data-level="7.3" data-path="bada.html"><a href="bada.html#heatmap-3">7.3 Heatmap</a></li>

<li class="chapter" data-level="7.4" data-path="bada.html"><a href="bada.html#scree">7.4 Scree</a></li>

<li class="chapter" data-level="7.5" data-path="bada.html"><a href="bada.html#factor-scores-2">7.5 Factor Scores</a></li>

<li class="chapter" data-level="7.6" data-path="bada.html"><a href="bada.html#loading-1">7.6 Loading</a></li>

<li class="chapter" data-level="7.7" data-path="bada.html"><a href="bada.html#confusion-matrix-1">7.7 Confusion Matrix</a></li>

<li class="chapter" data-level="7.8" data-path="bada.html"><a href="bada.html#contribution-and-bootstrap-ratio-barplot-1">7.8 Contribution and Bootstrap Ratio Barplot</a></li>

</ul></li>

<li class="chapter" data-level="8" data-path="mca.html"><a href="mca.html">8 Multiple Corresponding Analysis</a><ul>

<li class="chapter" data-level="8.1" data-path="mca.html"><a href="mca.html#introduction-of-mca">8.1 Introduction of MCA</a></li>

<li class="chapter" data-level="8.2" data-path="mca.html"><a href="mca.html#histgram-of-binning-variables-1">8.2 Histgram of Binning Variables</a></li>

<li class="chapter" data-level="8.3" data-path="mca.html"><a href="mca.html#computation-3">8.3 Computation</a></li>

<li class="chapter" data-level="8.4" data-path="mca.html"><a href="mca.html#heatmap-4">8.4 Heatmap</a></li>

<li class="chapter" data-level="8.5" data-path="mca.html"><a href="mca.html#scree-plot-2">8.5 Scree Plot</a></li>

<li class="chapter" data-level="8.6" data-path="mca.html"><a href="mca.html#row-factor-scores">8.6 Row Factor Scores</a></li>

<li class="chapter" data-level="8.7" data-path="mca.html"><a href="mca.html#important-variables-line-plots">8.7 Important Variables Line Plots</a></li>

<li class="chapter" data-level="8.8" data-path="mca.html"><a href="mca.html#contribution-and-bootstrap-ratio-barplots-1">8.8 Contribution and Bootstrap Ratio Barplots</a></li>

</ul></li>

<li class="chapter" data-level="9" data-path="pls.html"><a href="pls.html">9 Partial Least Square</a><ul>

<li class="chapter" data-level="9.1" data-path="pls.html"><a href="pls.html#introduction-of-pls-c">9.1 Introduction of PLS-C</a></li>

<li class="chapter" data-level="9.2" data-path="pls.html"><a href="pls.html#computation-4">9.2 Computation</a></li>

<li class="chapter" data-level="9.3" data-path="pls.html"><a href="pls.html#heatmap-5">9.3 Heatmap</a></li>

<li class="chapter" data-level="9.4" data-path="pls.html"><a href="pls.html#scree-plot-3">9.4 Scree Plot</a></li>

<li class="chapter" data-level="9.5" data-path="pls.html"><a href="pls.html#latent-variables">9.5 Latent Variables</a></li>

<li class="chapter" data-level="9.6" data-path="pls.html"><a href="pls.html#salience">9.6 Salience</a></li>

<li class="chapter" data-level="9.7" data-path="pls.html"><a href="pls.html#bootstrap-ratio-barplot">9.7 Bootstrap Ratio Barplot</a></li>

</ul></li>

<li class="chapter" data-level="10" data-path="distatis.html"><a href="distatis.html">10 DiSTATIS</a><ul>

<li class="chapter" data-level="10.1" data-path="distatis.html"><a href="distatis.html#introduction-of-distatis">10.1 Introduction of DiSTATIS</a></li>

<li class="chapter" data-level="10.2" data-path="distatis.html"><a href="distatis.html#computation-5">10.2 Computation</a></li>

<li class="chapter" data-level="10.3" data-path="distatis.html"><a href="distatis.html#heatmap-6">10.3 HeatMap</a></li>

<li class="chapter" data-level="10.4" data-path="distatis.html"><a href="distatis.html#scree-plot-4">10.4 Scree Plot</a></li>

<li class="chapter" data-level="10.5" data-path="distatis.html"><a href="distatis.html#global-factor-scores">10.5 Global Factor Scores</a></li>

<li class="chapter" data-level="10.6" data-path="distatis.html"><a href="distatis.html#partial-factor-scores">10.6 Partial Factor Scores</a></li>

<li class="chapter" data-level="10.7" data-path="distatis.html"><a href="distatis.html#vocabulary-graphs">10.7 Vocabulary graphs</a></li>

<li class="chapter" data-level="10.8" data-path="distatis.html"><a href="distatis.html#contribution-barplots">10.8 Contribution Barplots</a></li>

</ul></li>

<li class="chapter" data-level="11" data-path="mfa.html"><a href="mfa.html">11 Multiple Factor Analysis</a><ul>

<li class="chapter" data-level="11.1" data-path="mfa.html"><a href="mfa.html#introduction-of-mfa">11.1 Introduction of MFA</a></li>

<li class="chapter" data-level="11.2" data-path="mfa.html"><a href="mfa.html#computation-6">11.2 Computation</a></li>

<li class="chapter" data-level="11.3" data-path="mfa.html"><a href="mfa.html#heatmap-7">11.3 Heatmap</a></li>

<li class="chapter" data-level="11.4" data-path="mfa.html"><a href="mfa.html#scree-plot-5">11.4 Scree Plot</a></li>

<li class="chapter" data-level="11.5" data-path="mfa.html"><a href="mfa.html#global-factor-scores-1">11.5 Global Factor Scores</a></li>

<li class="chapter" data-level="11.6" data-path="mfa.html"><a href="mfa.html#partial-factor-scores-1">11.6 Partial Factor Scores</a></li>

<li class="chapter" data-level="11.7" data-path="mfa.html"><a href="mfa.html#contribution-barplots-1">11.7 Contribution Barplots</a></li>

</ul></li>

<li class="chapter" data-level="12.1" data-path="end.html"><a href="end.html#final-conclusion">12.1 Final Conclusion</a></li>

<li class="chapter" data-level="12.2" data-path="end.html"><a href="end.html#appreciation">12.2 Appreciation</a></li>

</ul></li>

<li><a href="https://github.com/rstudio/bookdown/_book" target="blank">Published with bookdown</a></li>

</ul>

</nav>

</div>

<h1>

<a href="./">Multivariate Statistical Analysis Cookbook with R</a>

</h1>

</div>

<h1>Chapter 4 Principal Component Analysis</h1>

<h2>4.1 Introduction of PCA</h2>

In the first statistical method, I will start from Principal Component Analysis (PCA).PCA is a common analysis I used for data exploration and dimensionality reduction. I aim to use PCA to extract important information , and find the similarity from sets of variables I have. Since the origin of PCA can be traced to concepts of Correlation and Linear Analysis, I can see large overlap between PCA and other linear methods. However, the uniqueness of the PCA relies on its calculation process: its goal is to convert the original data table (information) into new orthogonal variables. These new orthogonal variables will have same numbers with the original data table but generally the first few variables will explain most of the total variance for the whole data table, which I called them principal components in our analysis. Generating these new principal components will be beneficial for us to know the what’s dominant features in our data set and get rid of these noisy ones. Let’s me give an example: In questionnaire study, sometimes I will ask questions with high similarity:

1. Do you like pet?

2. Do you enjoying playing with your pet in your spare time?

</blockquote>

If I am a dog person, I will definitely answer “yes” at the first question and “My pleasure” at the second one. Reversely, If I am allergic to dog’s hair and was bitten by a dog during my childhood, I may answer “No” and “Absolutely No” at the two questions. I bet 99% people will have consistent answers for the two questions.

Except questionnaire study, there are many other place I might need to reduce the similarity and extract the most important information from our data set. In neuroimaging study, sometimes I will need to find out which brain regions will have similar activation; In real life research, after collecting hundreds of participants’ data, I want to know if male/female, or young/aged will have significant separation on some biological characteristics. PCA will be a good fit to reduce these kinds of redundancy. By looking into the <code>Scree Plot</code><a href="Functions.html#Scree">2.1</a>, I can know how many variables explain much more variance than others. By looking into the <code>Loading</code><a href="Functions.html#Loading">2.6</a>, I can know the relationship among different column variables. By looking into the <code>Factor Scores</code><a href="Functions.html#FactorScores">2.4</a> and <code>Contribution Barplot</code><a href="Functions.html#Contribution">2.7</a>, I can know which component are more closely associated with the separation of different groups. I will introduce these concepts in details in the following content.

Overall, PCA is a powerful statistical tool which is designed to help us find out the connections between variables and observation, and connection among multiple variables in single numeric data table (In the following chapter, I will mention more about the multiple data tables).

</div>

<h2>4.2 Computing</h2>

The first step I need to do is to run PCA analysis. In this part, I will use some trick to make my computational life easier. All important matrix will be stored as a short character for convenience.

<ul>

<li>fs: factor scores</li>

<li>eigs: eigenvalue</li>

<li>tau: represents how many varience explained by the factor</li>

<li>p.vals: the p value for the scree plot, which can tell us that what’s the significant components in our results.</li>

<li>boot.ratios: it is bootstrap ratio matrix helps us to generate bootstrap barplot in the end.</li>

<li>cj: contribution ratio for the column variables</li>

<li>fj: factor scores of column variables</li>

</ul>

<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb24-1"></a>res.PCA <- epPCA(DATA = exp.neg[7:35], center = TRUE,

<a href="pca.html#cb24-2"></a> scale = 'SS1',

<a href="pca.html#cb24-3"></a> DESIGN = exp.neg$group, graphs = FALSE)

<a href="pca.html#cb24-4"></a>res.PCA.inference <- epPCA.inference.battery(DATA = exp.neg[7:35],

<a href="pca.html#cb24-5"></a> center = TRUE,

<a href="pca.html#cb24-6"></a> scale = 'SS1',

<a href="pca.html#cb24-7"></a> DESIGN = exp.neg$group,

<a href="pca.html#cb24-8"></a> graphs = FALSE)

<a href="pca.html#cb24-9"></a>fs <- res.PCA$ExPosition.Data$fi

<a href="pca.html#cb24-10"></a>eigs <- res.PCA$ExPosition.Data$eigs

<a href="pca.html#cb24-11"></a>tau <- res.PCA$ExPosition.Data$t

<a href="pca.html#cb24-12"></a>p.eigs <- res.PCA.inference$Inference.Data$components$p.vals

<a href="pca.html#cb24-13"></a>eigs.permu <- res.PCA.inference$Inference.Data$components$eigs.perm

<a href="pca.html#cb24-14"></a>boot.ratios <- res.PCA.inference$Inference.Data$fj.boots$tests$boot.ratios

<a href="pca.html#cb24-15"></a>cj <- res.PCA$ExPosition.Data$cj

</div>

<h2>4.3 Heatmap</h2>

In the heatmap part, the input data is XTX, which represent the co-variance Matrix or the correlation matrix in PCA. From the heatmap, I can know that some variables are closely correlated with each other, such as game performance, time usage, personality trait and attitude toward global environment. The heatmap can give us a hint about the following PCA results.

<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb25-1"></a># plot

<a href="pca.html#cb25-2"></a>pca.xtx <- as.matrix(t(scale(exp.neg[,7:35],

<a href="pca.html#cb25-3"></a> center = TRUE,

<a href="pca.html#cb25-4"></a> scale = TRUE)) %*% scale(exp.neg[,7:35],

<a href="pca.html#cb25-5"></a> center = TRUE,

<a href="pca.html#cb25-6"></a> scale = TRUE))

<a href="pca.html#cb25-7"></a>plot.heatmap(DATA = pca.xtx,

<a href="pca.html#cb25-8"></a> xcol = m.color.design,

<a href="pca.html#cb25-9"></a> ycol = m.color.design,

<a href="pca.html#cb25-10"></a> textsize = 3)</code></pre></div>

<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb26-1"></a>pheatmap(mat=pca.xtx, cluster_rows = FALSE,

<a href="pca.html#cb26-2"></a> cluster_cols = FALSE )</code></pre></div>

</div>

<h2>4.4 Scree Plot</h2>

For the scree plot and permutation test, I can know how many components are statistically significant in our study, and whether the results is stable. Permutation test is designed for a NS test, to test the null hypothesis. By repeatedly sampling from data (putting it back, compared to bootstrap ratio), it will generate a new frequency distribution about the overall probability of outcome I observed. By comparing the value in the distribution range, I can know how confident I are to reject the null hypothesis and how much probability I have to make the typeI error. From the results below, I conclude that

<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb27-1"></a>plot.scree(eigs, p.eigs)</code></pre></div>

<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb28-1"></a>plot.permutation(eigs.perm = eigs.permu,

<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb29-1"></a>plot.permutation(eigs.perm = eigs.permu,

</div>

<h2>4.5 Factor Scores</h2>

The factor scores is the most important part in our PCA analysis. As you can see, with the help of the function, things become such easy to have our factor scores plot. In the two plot below, I can know that they are separated with each other in great extend. The dimension 2 perfectly distinguishes Hig social intelligence and High general intelligence participants with Low social intelligence and Low general intelligence ones. The interesting thing is that it looks like a gradient distribution: HIGH_HIGH at the top, LOW_LOW at the bottom, and HIGH_LOW in the middle. From the factor scores plot, I can also know that high social intelligence is closer to double high participants. However, the Dimension 1 and Dimension 3 are not much informative for us from the plots.

<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb30-1"></a>plot.fs(exp.neg$group,

<a href="pca.html#cb30-2"></a> fs=fs,

<a href="pca.html#cb30-3"></a> eigs=eigs,

<a href="pca.html#cb30-4"></a> tau=tau,

<a href="pca.html#cb30-5"></a> d = 1,

<a href="pca.html#cb30-6"></a> mode="CI",

<a href="pca.html#cb30-7"></a> method = "PCA")</code></pre></div>

<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb31-1"></a>plot.fs(exp.neg$group,

<a href="pca.html#cb31-2"></a> fs=fs,

<a href="pca.html#cb31-3"></a> eigs=eigs,

<a href="pca.html#cb31-4"></a> tau=tau,

<a href="pca.html#cb31-5"></a> d = 2,

<a href="pca.html#cb31-6"></a> mode="CI",

<a href="pca.html#cb31-7"></a> method = "PCA")</code></pre></div>

</div>

<h2>4.6 Loading</h2>

From the loading plot, I can see that they are some determined factors associated more with dimension 2: The SAT results and empathy are related with dimension 2, which represents that the two aspects are important for the separation of the groups.

<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb32-1"></a>plot.loading(exp.neg[,7:35],

<a href="pca.html#cb32-2"></a> col=m.color.design,

<a href="pca.html#cb32-3"></a> fs=fs,

<a href="pca.html#cb32-4"></a> eigs=eigs,

<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb33-1"></a>plot.loading(exp.neg[,7:35],

<a href="pca.html#cb33-2"></a> col=m.color.design,

<a href="pca.html#cb33-3"></a> fs=fs,

<a href="pca.html#cb33-4"></a> eigs=eigs,

</div>

<h2>4.7 Contriution and Bootstrap Ratio Barplots</h2>

From the contribution and bootstrap ratio barplots, I can know that the first component is closely related with participants’ game performance. SAT results and empathy related ability are significantly contributing to component2, which aligns with the conclusion of the published article.

<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a href="pca.html#cb34-1"></a>plot.cb(cj=cj,

<a href="pca.html#cb34-2"></a> fj=fj,

<a href="pca.html#cb34-3"></a> col = m.color.design,

<a href="pca.html#cb34-4"></a> boot.ratios = boot.ratios,

<a href="pca.html#cb34-5"></a> signifOnly = TRUE,

<a href="pca.html#cb34-6"></a> fig = 3,

<a href="pca.html#cb34-7"></a> horizontal = TRUE,

<a href="pca.html#cb34-8"></a> colrow = "col")</code></pre></div>

</div>

<h2>4.8 Conclusion</h2>

It is easy to observe that they are connection between the game performance results and some personality or attitude variables. However, it is worth to mention that currently the separation doesn’t represent that I have already had the evidence the collective action will be affected by social intelligence and general intelligence. Please remember our group variable is GPA and Emotion Processing Ability, the two variables are naturally correlated with the previous two aspects. I need more evidence on other variables to prove that I are right.

</div>

</section>

</div>

</div>

gitbook.require(["gitbook"], function(gitbook) {

gitbook.start({

"sharing": {

"github": false,

"facebook": true,

"twitter": true,

"linkedin": false,

"weibo": false,

"instapaper": false,

"vk": false,

"all": ["facebook", "twitter", "linkedin", "weibo", "instapaper"]

"fontsettings": {

"theme": "white",

"family": "sans",

"size": 2

"edit": {

"link": "https://github.com/rstudio/bookdown/_book/edit/master/04-PCA.Rmd",

"text": "Edit"

"history": {

"link": null,

"text": null

"view": {

"link": null,

"text": null

"download": ["MSA.pdf", "MSA.epub"],

"toc": {

"collapse": "subsection"

}

});

</script>

</body>

</html>

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

pca.html

pca.html

Files

pca.html

Latest commit

History

pca.html

File metadata and controls