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Data Analysis Using Regression and Multilevel/Hierarchical Models (Paperback)

Andrew Gelman (Author), Jennifer Hill (Author)


Editorial Reviews
Review
"Data Analysis Using Regression and Multilevel/Hierarchical Models ... careful yet mathematically accessible style is generously illustrated with examples and graphical displays, making it ideal for either classroom use or self-study. It appears destined to adorn the shelves of a great many applied statisticians and social scientists for years to come."
Brad Carlin, University of Minnesota

"Gelman and Hill have written what may be the first truly modern book on modeling. Containing practical as well as methodological insights into both Bayesian and traditional approaches, Data Analysis Using Regression and Multilevel/Hierarchical Models provides useful guidance into the process of building and evaluating models. For the social scientist and other applied statisticians interested in linear and logistic regression, causal inference, and hierarchical models, it should prove invaluable either as a classroom text or as an addition to the research bookshelf."
Richard De Veaux, Williams College

"The theme of Gelman and Hill's engaging and nontechnical introduction to statistical modeling is 'Be flexible.' Using a broad array of examples written in R and WinBugs, the authors illustrate the many ways in which readers can build more flexibility into their predictive and causal models. This hands-on textbook is sure to become a popular choice in applied regression courses."
Donald Green, Yale University

"Simply put, Data Analysis Using Regression and Multilevel/Hierarchical Models is the best place to learn how to do serious empirical research. Gelman and Hill have written a much needed book that is sophisticated about research design without being technical. Data Analysis Using Regression and Multilevel/Hierarchical Models is destined to be a classic!"
Alex Tabarrok, George Mason University

"a detailed, carefully written exposition of the modelling challenge, using numerous convincing examples, and always paying careful attention to the practical aspects of modeling. I recommend it very warmly."
Journal of Applied Statistics

"Gelman and Hill's book is an excellent intermediate text that would be very useful for researchers interested in multilevel modeling... This book gives a wealth of information for anyone interested in multilevel modeling and seems destined to be a classic."
Brandon K. Vaughn, Journal of Eductional Measurement

"With their new book, Data Analysis Using Regression and Multilevel/Hierarchical Models, Drs. Gelman and Hill have raised the bar for what a book on applied statistical modeling should seek to accomplish. The book is extraordinarily broad in scope, modern in its approach and philosophy, and ambitious in its goals... I am tremendously impressed with this book and highly recommend it. Data Analysis Using Regression and Multilevel/Hierarchical Models deserves to be widely read by applied statisticians and practicing researchers, especially in the social sciences. Instructors considering textbooks for courses on the practice of statistical modeling should move this book to the top of their list."
Daniel B. Hall, Journal of the American Statistical Association

"Data Analysis Using Regression and Multilevel/Hierarchical Models is the book I wish I had in graduate school."
Timothy Hellwig, The Political Methodologist
Product Description
Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout. Author resource page: http://www.stat.columbia.edu/~gelman/arm/

Product Details Paperback: 648 pages Publisher: Cambridge University Press; 1 edition (December 18, 2006) Language: English ISBN-10: 052168689X ISBN-13: 978-0521686891

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关键词：Hierarchical Multilevel regression regressio Analysis accessible displays examples appears careful

Contents

List of examples page xvii

Preface xix

1 Why? 1

1.1 What is multilevel regression modeling? 1

1.2 Some examples from our own research 3

1.3 Motivations for multilevel modeling 6

1.4 Distinctive features of this book 8

1.5 Computing 9

2 Concepts and methods from basic probability and statistics 13

2.1 Probability distributions 13

2.2 Statistical inference 16

2.3 Classical confidence intervals 18

2.4 Classical hypothesis testing 20

2.5 Problems with statistical significance 22

2.6 55,000 residents desperately need your help! 23

2.7 Bibliographic note 26

2.8 Exercises 26

Part 1A: Single-level regression 29

3 Linear regression: the basics 31

3.1 One predictor 31

3.2 Multiple predictors 32

3.3 Interactions 34

3.4 Statistical inference 37

3.5 Graphical displays of data and fitted model 42

3.6 Assumptions and diagnostics 45

3.7 Prediction and validation 47

3.8 Bibliographic note 49

3.9 Exercises 49

4 Linear regression: before and after fitting the model 53

4.1 Linear transformations 53

4.2 Centering and standardizing, especially for models with interactions 55

4.3 Correlation and “regression to the mean” 57

4.4 Logarithmic transformations 59

4.5 Other transformations 65

4.6 Building regression models for prediction 68

4.7 Fitting a series of regressions 73

4.8 Bibliographic note 74

4.9 Exercises 74

5 Logistic regression 79

5.1 Logistic regression with a single predictor 79

5.2 Interpreting the logistic regression coefficients 81

5.3 Latent-data formulation 85

5.4 Building a logistic regression model: wells in Bangladesh 86

5.5 Logistic regression with interactions 92

5.6 Evaluating, checking, and comparing fitted logistic regressions 97

5.7 Average predictive comparisons on the probability scale 101

5.8 Identifiability and separation 104

5.9 Bibliographic note 105

5.10 Exercises 105

6 Generalized linear models 109

6.1 Introduction 109

6.2 Poisson regression, exposure, and overdispersion 110

6.3 Logistic-binomial model 116

6.4 Probit regression: normally distributed latent data 118

6.5 Multinomial regression 119

6.6 Robust regression using the t model 124

6.7 Building more complex generalized linear models 125

6.8 Constructive choice models 127

6.9 Bibliographic note 131

6.10 Exercises 132

Part 1B: Working with regression inferences 135

7 Simulation of probability models and statistical inferences 137

7.1 Simulation of probability models 137

7.2 Summarizing linear regressions using simulation: an informal
Bayesian approach 140

7.3 Simulation for nonlinear predictions: congressional elections 144

7.4 Predictive simulation for generalized linear models 148

7.5 Bibliographic note 151

7.6 Exercises 152

8 Simulation for checking statistical procedures and model fits 155

8.1 Fake-data simulation 155

8.2 Example: using fake-data simulation to understand residual plots 157

8.3 Simulating from the fitted model and comparing to actual data 158

8.4 Using predictive simulation to check the fit of a time-series model 163

8.5 Bibliographic note 165

8.6 Exercises 165

9 Causal inference using regression on the treatment variable 167

9.1 Causal inference and predictive comparisons 167

9.2 The fundamental problem of causal inference 170

9.3 Randomized experiments 172

9.4 Treatment interactions and poststratification 178

9.5 Observational studies 181

9.6 Understanding causal inference in observational studies 186

9.7 Do not control for post-treatment variables 188

9.8 Intermediate outcomes and causal paths 190

9.9 Bibliographic note 194

9.10 Exercises 194

10 Causal inference using more advanced models 199

10.1 Imbalance and lack of complete overlap 199

10.2 Subclassification: effects and estimates for different subpopulations 204

10.3 Matching: subsetting the data to get overlapping and balanced
treatment and control groups 206

10.4 Lack of overlap when the assignment mechanism is known:
regression discontinuity 212

10.5 Estimating causal effects indirectly using instrumental variables 215

10.6 Instrumental variables in a regression framework 220

10.7 Identification strategies that make use of variation within or between
groups 226

10.8 Bibliographic note 229

10.9 Exercises 231

Part 2A: Multilevel regression 235

11 Multilevel structures 237

11.1 Varying-intercept and varying-slope models 237

11.2 Clustered data: child support enforcement in cities 237

11.3 Repeated measurements, time-series cross sections, and other
non-nested structures 241

11.4 Indicator variables and fixed or random effects 244

11.5 Costs and benefits of multilevel modeling 246

11.6 Bibliographic note 247

11.7 Exercises 248

12 Multilevel linear models: the basics 251

12.1 Notation 251

12.2 Partial pooling with no predictors 252

12.3 Partial pooling with predictors 254

12.4 Quickly fitting multilevel models in R 259

12.5 Five ways to write the same model 262

12.6 Group-level predictors 265

12.7 Model building and statistical significance 270

12.8 Predictions for new observations and new groups 272

12.9 How many groups and how many observations per group are
needed to fit a multilevel model? 275

12.10 Bibliographic note 276

12.11 Exercises 277

13 Multilevel linear models: varying slopes, non-nested models, and other complexities 279

13.1 Varying intercepts and slopes 279

13.2 Varying slopes without varying intercepts 283

13.3 Modeling multiple varying coefficients using the scaled inverse-Wishart distribution 284

13.4 Understanding correlations between group-level intercepts and
slopes 287

13.5 Non-nested models 289

13.6 Selecting, transforming, and combining regression inputs 293

13.7 More complex multilevel models 297

13.8 Bibliographic note 297

13.9 Exercises 298

14 Multilevel logistic regression 301

14.1 State-level opinions from national polls 301

14.2 Red states and blue states: what’s the matter with Connecticut? 310

14.3 Item-response and ideal-point models 314

14.4 Non-nested overdispersed model for death sentence reversals 320

14.5 Bibliographic note 321

14.6 Exercises 322

15 Multilevel generalized linear models 325

15.1 Overdispersed Poisson regression: police stops and ethnicity 325

15.2 Ordered categorical regression: storable votes 331

15.3 Non-nested negative-binomial model of structure in social networks 332

15.4 Bibliographic note 342

15.5 Exercises 342

Part 2B: Fitting multilevel models 343

16 Multilevel modeling in Bugs and R: the basics 345

16.1 Why you should learn Bugs 345

16.2 Bayesian inference and prior distributions 345

16.3 Fitting and understanding a varying-intercept multilevel model
using R and Bugs 348

16.4 Step by step through a Bugs model, as called from R 353

16.5 Adding individual- and group-level predictors 359

16.6 Predictions for new observations and new groups 361

16.7 Fake-data simulation 363

16.8 The principles of modeling in Bugs 366

16.9 Practical issues of implementation 369

16.10 Open-ended modeling in Bugs 370

16.11 Bibliographic note 373

16.12 Exercises 373

17 Fitting multilevel linear and generalized linear models in Bugs and R 375

17.1 Varying-intercept, varying-slope models 375

17.2 Varying intercepts and slopes with group-level predictors 379

17.3 Non-nested models 380

17.4 Multilevel logistic regression 381

17.5 Multilevel Poisson regression 382

17.6 Multilevel ordered categorical regression 383

17.7 Latent-data parameterizations of generalized linear models 384

17.8 Bibliographic note 385

17.9 Exercises 385

18 Likelihood and Bayesian inference and computation 387

18.1 Least squares and maximum likelihood estimation 387

18.2 Uncertainty estimates using the likelihood surface 390

18.3 Bayesian inference for classical and multilevel regression 392

18.4 Gibbs sampler for multilevel linear models 397

18.5 Likelihood inference, Bayesian inference, and the Gibbs sampler:
the case of censored data 402

18.6 Metropolis algorithm for more general Bayesian computation 408

18.7 Specifying a log posterior density, Gibbs sampler, and Metropolis
algorithm in R 409

18.8 Bibliographic note 413

18.9 Exercises 413

19 Debugging and speeding convergence 415

19.1 Debugging and confidence building 415

19.2 General methods for reducing computational requirements 418

19.3 Simple linear transformations 419

19.4 Redundant parameters and intentionally nonidentifiable models 419

19.5 Parameter expansion: multiplicative redundant parameters 424

19.6 Using redundant parameters to create an informative prior

distribution for multilevel variance parameters 427

19.7 Bibliographic note 434

19.8 Exercises 434

Part 3: From data collection to model understanding to model checking 435

20 Sample size and power calculations 437

20.1 Choices in the design of data collection 437

20.2 Classical power calculations: general principles, as illustrated by
estimates of proportions 439

20.3 Classical power calculations for continuous outcomes 443

20.4 Multilevel power calculation for cluster sampling 447

20.5 Multilevel power calculation using fake-data simulation 449

20.6 Bibliographic note 454

20.7 Exercises 454

21 Understanding and summarizing the fitted models 457

21.1 Uncertainty and variability 457

21.2 Superpopulation and finite-population variances 459

21.3 Contrasts and comparisons of multilevel coefficients 462

21.4 Average predictive comparisons 466

21.5 R2 and explained variance 473

21.6 Summarizing the amount of partial pooling 477

21.7 Adding a predictor can increase the residual variance! 480

21.8 Multiple comparisons and statistical significance 481

21.9 Bibliographic note 484

21.10 Exercises 485

22 Analysis of variance 487

22.1 Classical analysis of variance 487

22.2 ANOVA and multilevel linear and generalized linear models 490

22.3 Summarizing multilevel models using ANOVA 492

22.4 Doing ANOVA using multilevel models 494

22.5 Adding predictors: analysis of covariance and contrast analysis 496

22.6 Modeling the variance parameters: a split-plot latin square 498

22.7 Bibliographic note 501

22.8 Exercises 501

23 Causal inference using multilevel models 503

23.1 Multilevel aspects of data collection 503

23.2 Estimating treatment effects in a multilevel observational study 506

23.3 Treatments applied at different levels 507

23.4 Instrumental variables and multilevel modeling 509

23.5 Bibliographic note 512

23.6 Exercises 512

24 Model checking and comparison 513

24.1 Principles of predictive checking 513

24.2 Example: a behavioral learning experiment 515

24.3 Model comparison and deviance 524

24.4 Bibliographic note 526

24.5 Exercises 527

25 Missing-data imputation 529

25.1 Missing-data mechanisms 530

25.2 Missing-data methods that discard data 531

25.3 Simple missing-data approaches that retain all the data 532

25.4 Random imputation of a single variable 533

25.5 Imputation of several missing variables 539

25.6 Model-based imputation 540

25.7 Combining inferences from multiple imputations 542

25.8 Bibliographic note 542

25.9 Exercises 543

Appendixes 545

A Six quick tips to improve your regression modeling 547

A.1 Fit many models 547

A.2 Do a little work to make your computations faster and more reliable 547

A.3 Graphing the relevant and not the irrelevant 548

A.4 Transformations 548

A.5 Consider all coefficients as potentially varying 549

A.6 Estimate causal inferences in a targeted way, not as a byproduct
of a large regression 549

B Statistical graphics for research and presentation 551

B.1 Reformulating a graph by focusing on comparisons 552

B.2 Scatterplots 553

B.3 Miscellaneous tips 559

B.4 Bibliographic note 562

B.5 Exercises 563

C Software 565

C.1 Getting started with R, Bugs, and a text editor 565

C.2 Fitting classical and multilevel regressions in R 565

C.3 Fitting models in Bugs and R 567

C.4 Fitting multilevel models using R, Stata, SAS, and other software 568

C.5 Bibliographic note 573

References 575

Author index 601

Subject index 607

good,thks!!!!

A very good book! thanks a lot