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350 13. MULTILEVEL MODELS)sigma_actor ~ dcauchy(0,1),sigma_block ~ dcauchy(0,1)) ,data=list(pulled.left=d$pulled.left,prosoc.left=d$prosoc.left,condition=d$condition,actor=as.integer(d$actor),block_num=as.integer(d$block)) ,start=list(a=0,bp=0,bpc=0,sigma_actor=1,sigma_block=1,aj=rep(0,7),ak=rep(0,6)),warmup=1000 , iter=1e4Looking at estimates:R code13.17precis(m13.4)Mean StdDev lower 0.95 upper 0.95a 0.27 0.63 -0.99 1.52bp 0.77 0.25 0.31 1.26bpc -0.09 0.28 -0.63 0.44sigma_actor 2.16 0.84 0.94 3.76sigma_block 0.23 0.19 0.01 0.56aj[1] -0.98 0.66 -2.22 0.41aj[2] 4.22 1.51 1.73 7.31aj[3] -1.28 0.67 -2.65 -0.01aj[4] -1.28 0.66 -2.59 0.06aj[5] -0.98 0.66 -2.32 0.32aj[6] -0.03 0.66 -1.35 1.25aj[7] 1.50 0.71 0.15 2.93ak[1] -0.17 0.23 -0.68 0.18ak[2] 0.04 0.19 -0.34 0.46ak[3] 0.06 0.19 -0.31 0.49ak[4] 0.01 0.19 -0.39 0.40ak[5] -0.03 0.19 -0.44 0.33ak[6] 0.12 0.21 -0.26 0.57A lot of variation among chimpanzees (actor), as you saw in Chapter 11. But not much byexperiment block (block).13.4.1. Marginal posterior predictions. Simulating over varying intercepts.R code13.18post
13.4. CROSS-CLASSIFIED MODELS 351Density0.0 1.0 2.0 3.0blocksactors0 1 2 3 4 5 6 7sigma valueFIGURE 13.3. Posterior distributions of the standard deviations of varyingintercepts by actor (black) and experimental block (blue), for the modelm13.4.})post$a +rnorm(n,0,post$sigma_actor) +(post$bp + post$bpc*C)*P
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Statistical RethinkingA BAYESIAN CO
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4 CONTENTS5.5. Ordinary least squar
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PrefaceMasons, when they start upon
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HOW TO USE THIS BOOK 9least a minor
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HOW TO USE THIS BOOK 11than initial
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1 e Golem of PragueIn the 16th cent
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16 1. THE GOLEM OF PRAGUEconverses
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1.2. WRECKING PRAGUE 19model P 1B ,
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1.2. WRECKING PRAGUE 21e dominant r
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1.3. THREE TOOLS FOR GOLEM ENGINEER
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2 Small Worlds and Large WorldsWhen
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2.1. PROBABILITY IS JUST COUNTING 3
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2.2. COLOMBO’S FIRST BAYESIAN MOD
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W L W W W L W L W2.2. COLOMBO’S F
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2.3. COMPONENTS OF THE MODEL 41not
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2.3. COMPONENTS OF THE MODEL 43You
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2.3. COMPONENTS OF THE MODEL 45e ma
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2.4. MAKING THE MODEL GO 47other pr
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2.4. MAKING THE MODEL GO 495 points
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2.4. MAKING THE MODEL GO 51just the
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2.4. MAKING THE MODEL GO 53between
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2.6. PRACTICE 55Medium.2.6.5. m1. R
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2.6. PRACTICE 57implied by the equa
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3 Sampling the ImaginaryLots of boo
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3. SAMPLING THE IMAGINARY 61a probl
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3.2. SAMPLING TO SUMMARIZE 63plot(
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3.2. SAMPLING TO SUMMARIZE 65Densit
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3.2. SAMPLING TO SUMMARIZE 67In con
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3.2. SAMPLING TO SUMMARIZE 69Densit
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3.3. SAMPLING TO SIMULATE PREDICTIO
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3.5. PRACTICE 793.5. PracticeEasy.
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3.5. PRACTICE 813.5.17. Predict sec
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84 4. LINEAR MODELSFIGURE 4.1. e Pt
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86 4. LINEAR MODELSexperiment with
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88 4. LINEAR MODELS4.1.4.2. Epistem
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90 4. LINEAR MODELSe approach above
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92 4. LINEAR MODELS'data.frame': 54
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94 4. LINEAR MODELSe point isn’t
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96 4. LINEAR MODELShave the samples
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98 4. LINEAR MODELSere’s no troub
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100 4. LINEAR MODELS)Note the comma
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102 4. LINEAR MODELSpreviously obse
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104 4. LINEAR MODELS4.4. Adding a p
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106 4. LINEAR MODELS(1) What is the
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108 4. LINEAR MODELSdata(Howell1)d
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110 4. LINEAR MODELSRethinking: Wha
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112 4. LINEAR MODELSheight140 150 1
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116 4. LINEAR MODELSYou end up with
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118 4. LINEAR MODELS(1) Use link to
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122 4. LINEAR MODELSRethinking: Lin
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126 4. LINEAR MODELS4.7.1. e1. In t
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5 Multivariate Linear ModelsOne of
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5.1. SPURIOUS ASSOCIATION 131Divorc
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5.1. SPURIOUS ASSOCIATION 133But me
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5.1. SPURIOUS ASSOCIATION 135abmbas
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5.1. SPURIOUS ASSOCIATION 137this i
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5.1. SPURIOUS ASSOCIATION 139slower
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5.1. SPURIOUS ASSOCIATION 141Median
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5.1. SPURIOUS ASSOCIATION 143(a)(b)
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5.2. MASKED RELATIONSHIP 145N
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5.2. MASKED RELATIONSHIP 147a ~ dno
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5.2. MASKED RELATIONSHIP 149dcc$log
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5.3. WHEN ADDING VARIABLES HURTS 15
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5.4. CATEGORICAL VARIABLES 161$ wei
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5.4. CATEGORICAL VARIABLES 1635.4.2
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5.4. CATEGORICAL VARIABLES 165# sam
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168 5. MULTIVARIATE LINEAR MODELS5.
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170 5. MULTIVARIATE LINEAR MODELS5.
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6 Model Selection, Comparison, and
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6.1. THE PROBLEM WITH PARAMETERS 17
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6.2. INFORMATION THEORY AND MODEL P
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6.3. AKAIKE INFORMATION CRITERION 1
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6.4. DEVIANCE INFORMATION CRITERION
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6.5. USING AIC 203helps guard again
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6.5. USING AIC 205compare( m6.11 ,
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6.5. USING AIC 207e attitude this b
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6.5. USING AIC 209kcal.per.g0.5 0.7
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6.7. PRACTICE 211Consider by analog
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6.7. PRACTICE 2136.7.3. e deviance
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216 7. INTERACTIONSFIGURE 7.1. TOP:
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218 7. INTERACTIONSlog(rgdppc_2000)
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220 7. INTERACTIONSird, we may want
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222 7. INTERACTIONSlog GDP year 200
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226 7. INTERACTIONSInteraction mode
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228 7. INTERACTIONSthis model and t
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232 7. INTERACTIONSe main effect li
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234 7. INTERACTIONSbs -38.91 34.94s
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236 7. INTERACTIONSe primary reason
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238 7. INTERACTIONSNow for the plot
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240 7. INTERACTIONS7.4. Higher-orde
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8 Markov Chain Monte Carlo Estimati
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8.1. GOOD KING MARKOV AND HIS ISLAN
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8.2. MARKOV CHAIN MONTE CARLO 247fo
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8.2. MARKOV CHAIN MONTE CARLO 249No
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8.3. EASY HMC: MAP2STAN 251We’re
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8.3. EASY HMC: MAP2STAN 253$ cont_a
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8.3. EASY HMC: MAP2STAN 255mcmcpair
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8.3. EASY HMC: MAP2STAN 257FIGURE 8
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8.4. CARE AND FEEDING OF YOUR MARKO
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8.6. PRACTICE 265And since the chai
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268 9. BIG ENTROPY AND THE GENERALI
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270 9. BIG ENTROPY AND THE GENERALI
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10 Distance and DurationA curious t
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10.2. GAMMA 275can be quite complic
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278 11. COUNTING AND CLASSIFICATION
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Page 300 and 301: 300 11. COUNTING AND CLASSIFICATION
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Page 314 and 315: 314 12. MONSTERS AND MIXTURESResult
Page 316 and 317: 316 12. MONSTERS AND MIXTURESanswer
Page 318 and 319: 318 12. MONSTERS AND MIXTURESDensit
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Page 338 and 339: 338 13. MULTILEVEL MODELSrepeat obs
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Page 353 and 354: 14 Multilevel Models II: Slopes14.1
Page 355 and 356: 14.1. EVERYTHING CAN VARY AND PROBA
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Page 360 and 361: 360 15. MISSING DATA AND OTHER OPPO
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Page 382 and 383: 382 ENDNOTES12. For an autopsy of t
Page 384 and 385: 384 ENDNOTES45. Fisher (1925), in C
Page 386 and 387: 386 ENDNOTES77. See two famous edit
Page 388 and 389: 388 ENDNOTES113. Hurlbert (1984) is
Page 390 and 391: 390 BibliographyFrank, S. A. (2011)
Page 392 and 393: 392 BibliographyProulx, S. R. and A
Page 395 and 396: IndexAkaike (1973), 380, 383Akaike
Page 397: INDEX 397non-identifiability, 153Oc
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