**Statistical Models: Theory and Practice 2nd Edition by David A. Freedman, ISBN-13: 978-0521743853**

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- Publisher: Cambridge University Press; 2nd edition (April 27, 2009)
- Language: English
- 458 pages
- ISBN-10: 0521743850
- ISBN-13: 978-0521743853

**Explains the basic ideas of association and regression, taking you through the current models that link these ideas to causality.**

This lively and engaging textbook explains the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. The author, David A. Freedman, explains the basic ideas of association and regression, and takes you through the current models that link these ideas to causality. The focus is on applications of linear models, including generalized least squares and two-stage least squares, with probits and logits for binary variables. The bootstrap is developed as a technique for estimating bias and computing standard errors. Careful attention is paid to the principles of statistical inference. There is background material on study design, bivariate regression, and matrix algebra. To develop technique, there are computer labs with sample computer programs. The book is rich in exercises, most with answers. Target audiences include advanced undergraduates and beginning graduate students in statistics, as well as students and professionals in the social and health sciences. The discussion in the book is organized around published studies, as are many of the exercises. Relevant journal articles are reprinted at the back of the book. Freedman makes a thorough appraisal of the statistical methods in these papers and in a variety of other examples. He illustrates the principles of modeling, and the pitfalls. The discussion shows you how to think about the critical issues – including the connection (or lack of it) between the statistical models and the real phenomena.

**Features of the book:**

• authoritative guidance from a well-known author with wide experience in teaching, research, and consulting

• careful analysis of statistical issues in substantive applications

• no-nonsense, direct style

• versatile structure, enabling the text to be used as a text in a course, or read on its own • text that has been thoroughly class-tested at **Berkeley**

• background material on regression and matrix algebra

• plenty of exercises, most with solutions

• extra material for instructors, including data sets and code for lab projects (available from Cambridge University Press)

• many new exercises and examples

• reorganized, restructured, and revised chapters to aid teaching and understanding

**Table of Contents:**

Foreword to the Revised Edition xi

Preface xiii

1 Observational Studies and Experiments

1.1 Introduction 1

1.2 The HIP trial 4

1.3 Snow on cholera 6

1.4 Yule on the causes of poverty 9

Exercise set A 13

1.5 End notes 14

2 The Regression Line

2.1 Introduction 18

2.2 The regression line 18

2.3 Hooke’s law 22

Exercise set A 23

2.4 Complexities 23

2.5 Simple vs multiple regression 26

Exercise set B 26

2.6 End notes 28

3 Matrix Algebra

3.1 Introduction 29

Exercise set A 30

3.2 Determinants and inverses 31

Exercise set B 33

3.3 Random vectors 35

Exercise set C 35

3.4 Positive definite matrices 36

Exercise set D 37

3.5 The normal distribution 38

Exercise set E 39

3.6 If you want a book on matrix algebra 40

4 Multiple Regression

4.1 Introduction 41

Exercise set A 44

4.2 Standard errors 45

Things we don’t need 49

Exercise set B 49

4.3 Explained variance in multiple regression 51

Association or causation? 53

Exercise set C 53

4.4 What happens to OLS if the assumptions break down? 53

4.5 Discussion questions 53

4.6 End notes 59

5 Multiple Regression: Special Topics

5.1 Introduction 61

5.2 OLS is BLUE 61

Exercise set A 63

5.3 Generalized least squares 63

Exercise set B 65

5.4 Examples on GLS 65

Exercise set C 66

5.5 What happens to GLS if the assumptions break down? 68

5.6 Normal theory 68

Statistical significance 70

Exercise set D 71

5.7 The F-test 72

“The” F-test in applied work 73

Exercise set E 74

5.8 Data snooping 74

Exercise set F 76

5.9 Discussion questions 76

5.10 End notes 78

6 Path Models

6.1 Stratification 81

Exercise set A 86

6.2 Hooke’s law revisited 87

Exercise set B 88

6.3 Political repression during the McCarthy era 88

Exercise set C 90

6.4 Inferring causation by regression 91

Exercise set D 93

6.5 Response schedules for path diagrams 94

Selection vs intervention 101

Structural equations and stable parameters 101

Ambiguity in notation 102

Exercise set E 102

6.6 Dummy variables 103

Types of variables 104

6.7 Discussion questions 105

6.8 End notes 112

7 Maximum Likelihood

7.1 Introduction 115

Exercise set A 119

7.2 Probit models 121

Why not regression? 123

The latent-variable formulation 123

Exercise set B 124

Identification vs estimation 125

What if the Ui are N(μ, σ2)? 126

Exercise set C 127

7.3 Logit models 128

Exercise set D 128

7.4 The effect of Catholic schools 130

Latent variables 132

Response schedules 133

The second equation 134

Mechanics: bivariate probit 136

Why a model rather than a cross-tab? 138

Interactions 138

More on table 3 in Evans and Schwab 139

More on the second equation 139

Exercise set E 140

7.5 Discussion questions 141

7.6 End notes 150

8 The Bootstrap

8.1 Introduction 155

Exercise set A 166

8.2 Bootstrapping a model for energy demand 167

Exercise set B 173

8.3 End notes 174

9 Simultaneous Equations

9.1 Introduction 176

Exercise set A 181

9.2 Instrumental variables 181

Exercise set B 184

9.3 Estimating the butter model 184

Exercise set C 185

9.4 What are the two stages? 186

Invariance assumptions 187

9.5 A social-science example: education and fertility 187

More on Rindfuss et al 191

9.6 Covariates 192

9.7 Linear probability models 193

The assumptions 194

The questions 195

Exercise set D 196

9.8 More on IVLS 197

Some technical issues 197

Exercise set E 198

Simulations to illustrate IVLS 199

9.9 Discussion questions 200

9.10 End notes 207

10 Issues in Statistical Modeling

10.1 Introduction 209

The bootstrap 211

The role of asymptotics 211

Philosophers’ stones 211

The modelers’ response 212

10.2 Critical literature 212

10.3 Response schedules 217

10.4 Evaluating the models in chapters 7–9 217

10.5 Summing up 218

References 219

Answers to Exercises 235

The Computer Labs 294

Appendix: Sample MATLAB Code 310

Reprints

Gibson on McCarthy 315

Evans and Schwab on Catholic Schools 343

Rindfuss et al on Education and Fertility 377

Schneider et al on Social Capital 402

Index 431

* David A. Freedman *is Professor of Statistics at the

*. He has also taught in Athens, Caracas, Jerusalem, Kuwait, London, Mexico City, and*

**University of California, Berkeley***. He has written several previous books, including a widely used elementary text. He is one of the leading researchers in probability and statistics, with 200 papers in the professional literature. He is a member of the American Academy of Arts and Sciences. In 2003, he received the John J. Carty Award for the Advancement of Science from the National Academy of Sciences, recognizing his ‘profound contributions to the theory and practice of statistics’. Freedman has consulted for the Carnegie Commission, the City of San Francisco, and the Federal Reserve, as well as several departments of the US government. He has testified as an expert witness on statistics in law cases that involve employment discrimination, fair loan practices, duplicate signatures on petitions, railroad taxation, ecological inference, flight patterns of golf balls, price scanner errors, sampling techniques, and census adjustment.*

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