CONTENTS
Preface xi
Audience xi
Teaching strategy xii
How to use this book xii
Installing the rethinking R package xvi
Acknowledgments xvi
Chapter 1. The Golem of Prague 1
Statistical golems 1
Statistical rethinking 4
Three tools for golem engineering 10
Summary 16
Chapter 2. Small Worlds and Large Worlds 19
The garden of forking data 20
Building a model 28
Components of the model 32
Making the model go 37
Summary 45
Practice 45
Chapter 3. Sampling the Imaginary 49
Sampling from a grid-approximate posterior 52
Sampling to summarize 53
Sampling to simulate prediction 61
Summary 68
Practice 69
Chapter 4. Linear Models 71
Why normal distributions are normal 72
A language for describing models 77
A Gaussian model of height 78
Adding a predictor 92
Polynomial regression 110
Summary 115
Practice 115
Chapter 5. Multivariate Linear Models 119
Spurious association 121
Masked relationship 135
When adding variables hurts 141
Categorical variables 152
Ordinary least squares and 1m 159
Summary 162
Practice 162
Chapter 6. Overfitting, Regularization, and Information Criteria 165
The problem with parameters 167
Information theory and model performance 174
Regularization 186
Information criteria 188
Using information criteria 195
Summary 205
Practice 205
Chapter 7. Interactions 209
Building an interaction 211
Symmetry of the linear interaction 223
Continuous interactions 225
Interactions in design formulas 235
Summary 236
Practice 236
Chapter 8. Markov Chain Monte Carlo 241
Good King Markov and His island kingdom 242
Markov chain Monte Carlo 245
Easy HMC: map2stan 247
Care and feeding of your Markov chain 255
Summary 263
Practice 263
Chapter 9. Big Entropy and the Generalized Linear Model 267
Maximum entropy 268
Generalized linear models 280
Maximum entropy priors 288
Summary 289
Chapter 10. Counting and Classification 291
Binomial regression 292
Poisson regression 311
Other count regressions 322
Summary 328
Practice 329
Chapter 11. Monsters and Mixtures 331
Ordered categorical outcomes 331
Zero-inflated outcomes 342
Over-dispersed outcomes 346
Summary , 351
Practice 352
Chapter 12. Multilevel Models 355
Example: Multilevel tadpoles 357
Varying effects and the under fitting/overfitting trade-off 364
More than one type of cluster 370
Multilevel posterior predictions 376
Summary 384
Practice 384
Chapter 13. Adventures in Covariance 387
Varying slopes by construction 389
Example: Admission decisions and gender 398
Example: Cross-classified chimpanzees with varying slopes 403
Continuous categories and the Gaussian process 410
Summary 419
Practice 419
Chapter 14. Missing Data and Other Opportunities 423
Measurement error 424
Missing data 431
Summary 439
Practice 439
Chapter 15. Horoscopes 441
Endnotes 445
Bibliography 457
Citation index 465
Topic index 467