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1 Observational Studies and Experiments1.1 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 18

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 29

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 41

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 Topics5.1 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 81

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 115

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 155

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 176

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 209

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 315

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