Analysis Techniques for non-Experimental Data: An Introduction

Preface v
List of Figures xiii
List of Tables xvii

1 Introduction 1
1.1 Causality 1
1.2 Investigating causality: the classic experiment 6
1.3 Why an experiment is not always possible 12
1.4 Methodological problems in non-experimental studies 20
1.5 About this book 25
1.5.1 The dataset 27
1.5.2 SPSS and Stata 28
1.5.3 Symbols 31

2 Regression Analysis 33
2.1 Multiple regression 33
2.1.1 The multiple regression model 33
2.1.2 Model fit 37
2.1.3 Choosing predictors 38
2.1.4 Tests 40
2.2 Assumptions 41
2.3 Regression with a dichotomous dependent variable: logistic regression 42
2.4 Regression with a dependent count variable 50
2.4.1 Poisson regression 52
2.4.2 Negative binomial regression 59
2.4.3 The zero-inflated extension to a model 63
2.5 Regression models for dependent variables with other distributions 65
2.6 Some more statistics basics 66
2.6.1 Variance and bias 67
2.6.2 Consistency and efficiency of estimators 69

3 Propensity score matching 71
3.1 Matching 71
3.1.1 A precursor to propensity score matching: Mahalanobis metric
matching 73
3.2 Propensity score matching 76
3.2.1 Choices when matching respondents 78
3.3 Matching methods 78
3.3.1 Nearest neighbour matching 79
3.3.2 Caliper and radius matching 81
3.3.3 Stratification or interval matching 82
3.3.4 Kernel matching 84
3.3.5 Performance of (different) matching methods 87
3.4 Controlling for robustness and sensitivity analysis 88
3.5 Conditions for propensity score matching 89
3.5.1 Large sample size 89
3.5.2 A sufficiently large area of common support 90
3.5.3 Not too many missing values 90
3.5.4 The correct functional form of the logistic regression model 91
3.5.5 No remaining unobserved bias 92
3.6 Example: Treatment and sex offending recidivism 92
3.7 Propensity score analyse in SPSS 93
3.7.1 Step 1: logistic regression 96
3.7.2 Step 2: matching 99
3.7.3 Step 3: analysis of the matched groups 100
3.8 Propensity score analysis with Stata: caliper matching 102
3.9 Propensity score analyse with Stata: kernel matching 108
3.10 Software 110
3.11 Extensions 110
3.12 Further reading 112

4 Instrumental variables 113
4.1 Introduction 113
4.2 Instrumental variables 116
4.2.1 The instrumental variable method 116
4.2.2 Solution for distorting variables 118
4.2.3 Solution for simultaneous causality 123
4.2.4 Solution for measurement error in the intervention variable 127
4.2.5 Weak instruments 132
4.2.6 What to consider when using instrumental variables 133
4.3 Example: Probation and general recidivism 134
4.3.1 Choosing an instrumental variable 137
4.3.2 The instrumental variables model 141
4.3.3 Instrumental variables using SPSS 142
4.3.4 Instrumental variables with Stata 145
4.4 Software 147
4.5 Advantages and limitations 150
4.6 Further reading 151

5 The regression discontinuity design 155
5.1 The regression discontinuity design 155
5.2 Illustration of the regression discontinuity design 157
5.3 Example: Treatment and number of arrests 165
5.3.1 The underlying continuum 167
5.3.2 Regression discontinuity design using SPSS 167
5.3.3 Regression discontinuity design with Stata 177
5.4 Strengths and weaknesses of the regression discontinuity design 178
5.5 Further reading 179

6 Fixed effects panel models 181
6.1 Introduction 181
6.2 Analysis method for longitudinal data 181
6.3 A naive analysis of panel data 184
6.4 The fixed effects panel model 186
6.5 Software 192
6.6 Example: Effects of marriage, parenthood, and work on criminal behaviour
194
6.6.1 Period effects: Two-way fixed effects panel models 197
6.6.2 A random effects panel model 198
6.6.3 Fixed effects versus random effects panel models 202
6.7 Limitations of fixed effects panel models 203
6.8 Final points 205
6.9 Further reading 206

7 Trajectory models 207
7.1 The trajectory model 208
7.2 A closer look at the trajectory model 212
7.2.1 Trajectory model example 213
7.3 Model selection 216
7.4 Posterior probabilities of group membership 218
7.5 Adding independent variables to the trajectory model 220
7.5.1 Statistical predictors 220
7.5.2 Time-varying covariates 221
7.6 Censoring, missing data and exposure 222
7.7 Example: The influence of employment on criminal behaviour 223
7.7.1 The trajectory model 224
7.7.2 The trajectory model with covariates 230
7.8 Strengths and limitations 233
7.9 Further reading 235

8 Final remarks 237

Appendix A Complete SPSS syntax 245
Appendix B Complete Stata syntax 253

Bibliography 263
Subject index 270