A one-of-a-kind guide to identifying and dealing with modern statistical developments in causality

Written by a group of well-known experts,Statistics and Causality: Methods for Applied Empirical Research focuses on the most up-to-date developments in statistical methods in respect to causality. Illustrating the properties of statistical methods to theories of causality, the book features a summary of the latest developments in methods for statistical analysis of causality hypotheses.

The book is divided into five accessible and independent parts. The first part introduces the foundations of causal structures and discusses issues associated with standard mechanistic and difference-making theories of causality. The second part features novel generalizations of methods designed to make statements concerning the direction of effects. The third part illustrates advances in Granger-causality testing and related issues. The fourth part focuses on counterfactual approaches and propensity score analysis. Finally, the fifth part presents designs for causal inference with an overview of the research designs commonly used in epidemiology.Statistics and Causality: Methods for Applied Empirical Research also includes:New statistical methodologies and approaches to causal analysis in the context of the continuing development of philosophical theories End-of-chapter bibliographies that provide references for further discussions and additional research topicsDiscussions on the use and applicability of software when appropriate

Statistics and Causality: Methods for Applied Empirical Research is an ideal reference for practicing statisticians, applied mathematicians, psychologists, sociologists, logicians, medical professionals, epidemiologists, and educators who want to learn more about new methodologies in causal analysis. The book is also an excellent textbook for graduate-level courses in causality and qualitative logic.

Wolfgang Wiedermann, PhD, is Assistant Professor in the Department of Educational, School, and Counseling Psychology at the University of Missouri, Columbia. His research interests include the development of methods for direction dependence analysis and causal inference, the development and evaluation of methods for person-oriented research, and methods for intensive longitudinal data.

Alexander von Eye, PhD, is Professor Emeritus of Psychology at Michigan State University. His research interests include statistical methods, categorical data analysis, and human development. Dr. von Eye is Section Editor for theEncyclopedia of Statistics in Behavioral Science and is the coauthor ofLog-Linear Modeling: Concepts, Interpretation, and Application, both published by Wiley.

List Of Contributors Xiii

Preface Xvii

Acknowledgments Xxv

Part I Bases Of Causality 1

1 Causation and the Aims of Inquiry 3
Ned Hall

1.1 Introduction, 3

1.2 The Aim of an Account of Causation, 4

1.2.1 The Possible Utility of a False Account, 4

1.2.2 Inquirys Aim, 5

1.2.3 Role of Intuitions, 6

1.3 The Good News, 7

1.3.1 The Core Idea, 7

1.3.2 Taxonomizing Conditions, 9

1.3.3 Unpacking Dependence, 10

1.3.4 The Good News, Amplified, 12

1.4 The Challenging News, 17

1.4.1 Multiple Realizability, 17

1.4.2 Protracted Causes, 18

1.4.3 Higher Level Taxonomies and Normal Conditions, 25

1.5 The Perplexing News, 26

1.5.1 The Centrality of Causal Process, 26

1.5.2 A Speculative Proposal, 28

2 Evidence and Epistemic Causality 31
Michael Wilde& Jon Williamson

2.1 Causality and Evidence, 31

2.2 The Epistemic Theory of Causality, 35

2.3 The Nature of Evidence, 38

2.4 Conclusion, 40

Part II Directionality Of Effects 43

3 Statistical Inference for Direction of Dependence in Linear Models 45
Yadolah Dodge& Valentin Rousson

3.1 Introduction, 45

3.2 Choosing the Direction of a Regression Line, 46

3.3 Significance Testing for the Direction of a Regression Line, 48

3.4 Lurking Variables and Causality, 54

3.4.1 Two Independent Predictors, 55

3.4.2 Confounding Variable, 55

3.4.3 Selection of a Subpopulation, 56

3.5 Brain and Body Data Revisited, 57

3.6 Conclusions, 60

4 Directionality of Effects in Causal Mediation Analysis 63
Wolfgang Wiedermann& Alexander von Eye

4.1 Introduction, 63

4.2 Elements of Causal Mediation Analysis, 66

4.3 Directionality of Effects in Mediation Models, 68

4.4 Testing Directionality Using Independence Properties of Competing Mediation Models, 71

4.4.1 Independence Properties of Bivariate Relations, 72

4.4.2 Independence Properties of the Multiple Variable Model, 74

4.4.3 Measuring and Testing Independence, 74

4.5 Simulating the Performance of Directionality Tests, 82

4.5.1 Results, 83

4.6 Empirical Data Example: Development of Numerical Cognition, 85

4.7 Discussion, 92

5 Direction of Effects in Categorical Variables: A Structural Perspective 107
Alexander von Eye& Wolfgang Wiedermann

5.1 Introduction, 107

5.2 Concepts of Independence in Categorical Data Analysis, 108

5.3 Direction Dependence in Bivariate Settings: Metric and Categorical Variables, 110

5.3.1 Simulating the Performance of Nonhierarchical Log-Linear Models, 114

5.4 Explaining the Structure of Cross-Classifications, 117

5.5 Data Example, 123

5.6 Discussion, 126

6 Directional Dependence Analysis Using SkewNormal Copula-Based Regression 131
Seongyong Kim& Daeyoung Kim

6.1 Introduction, 131

6.2 Copula-Based Regression, 133

6.2.1 Copula, 133

6.2.2 Copula-Based Regression, 134

6.3 Directional Dependence in the Copula-Based Regression, 136

6.4 SkewNormal Copula, 138

6.5 Inference of Directional Dependence Using SkewNormal Copula-Based Regression, 144

6.5.1 Estimation of Copula-Based Regression, 144

6.5.2 Detection of Directional Dependence and Computation of the Directional Dependence Measures, 146

6.6 Application, 147

6.7 Conclusion, 150

7 Non-Gaussian Structural Equation Models for Causal Discovery 153
Shohei Shimizu

7.1 Introduction, 153

7.2 Independent Component Analysis, 156

7.2.1 Model, 157

7.2.2 Identifiability, 157

7.2.3 Estimation, 158

7.3 Basic Linear Non-Gaussian Acyclic Model, 158

7.3.1 Model, 158

7.3.2 Identifiability, 160

7.3.3 Estimation, 162

7.4 LINGAM for Time Series, 167

7.4.1 Model, 167

7.4.2 Identifiability, 168

7.4.3 Estimation, 168

7.5 LINGAM with Latent Common Causes, 169

7.5.1 Model, 169

7.5.2 Identifiability, 171

7.5.3 Estimation, 174

7.6 Conclusion and Future Directions, 177

8 Nonlinear Functional Causal Models for Distinguishing Cause from Effect 185
Kun Zhang& Aapo Hyvärinen

8.1 Introduction, 185

8.2 Nonlinear Additive Noise Model, 188

8.2.1 Definition of Model, 188

8.2.2 Likelihood Ratio for Nonlinear Additive Models, 188

8.2.3 Information-Theoretic Interpretation, 189

8.2.4 Likelihood Ratio and Independence-Based Methods, 191

8.3 Post-Nonlinear Causal Model, 192

8.3.1 The Model, 192

8.3.2 Identifiability of Causal Direction, 193

8.3.3 Determination of Causal Direction Based on the PNL Causal Model, 193

8.4 On the Relationships Between Different Principles for Model Estimation, 194

8.5 Remark on General Nonlinear Causal Models, 196

8.6 Some Empirical Results, 197

8.7 Discussion and Conclusion, 198

Part III Granger Causality And Longitudinal Data Modeling 203

9 Alternative Forms of Granger Causality, Heterogeneity, and Nonstationarity 205
Peter C. M. Molenaar& Lawrence L. Lo

9.1 Introduction, 205

9.2 Some Initial Remarks on the Logic of Granger Causality Testing, 206

9.3 Preliminary Introduction to Time Series Analysis, 207

9.4 Overview of Granger Causality Testing in the Time Domain, 210

9.5 Granger Causality Testing in the Frequency Domain, 212

9.5.1 Two Equivalent Representations of a VAR(a), 212

9.5.2 Partial Directed Coherence (PDC) as a Frequency-Domain Index of Granger Causality, 213

9.5.3 Some Preliminary Comments, 214

9.5.4 Application to Simulated Data, 215

9.6 A New Data-Driven Solution to Granger Causality Testing, 216

9.6.1 Fitting a uSEM, 217

9.6.2 Extending the Fit of a uSEM, 217

9.6.3 Application of the Hybrid VAR Fit to Simulated Data, 218

9.7 Extensions to Nonstationary Series and Heterogeneous Replications, 221

9.7.1 Heterogeneous Replications, 221

9.7.2 Nonstationary Series, 222

9.8 Discussion and Conclusion, 224

10 Granger Meets Rasch: Investigating Granger Causation with Multidimensional Longitudinal Item Response Models 231
Ingrid Koller, Claus H. Carstensen, Wolfgang Wiedermann& Alexander von Eye

10.1 Introduction, 231

10.2 Granger Causation, 232

10.3 The Rasch Model, 234

10.4 Longitudinal Item Response Theory Models, 236

10.5 Data Example: Scientific Literacy in Preschool Children, 240

10.6 Discussion, 241

11 Granger Causality for Ill-Posed Problems: Ideas, Methods, and Application in Life Sciences 249
Katerina Hlavá cková-Schindler, Valeriya Naumova& Sergiy Pereverzyev Jr.

11.1 Introduction, 249

11.1.1 Causality Problems in Life Sciences, 250

11.1.2 Outline of the Chapter, 250

11.1.3 Notation, 251

11.2 Granger Causality and Multivariate Granger Causality, 251

11.2.1 Granger Causality, 252

11.2.2 Multivariate Granger Causality, 253

11.3 Gene Regulatory Networks, 254

11.4 Regularization of Ill-Posed Inverse Problems, 255

11.5 Multivariate Granger Causality Approaches Using𝓁1 and𝓁2

Penalties, 256

11.6 Applied Quality Measures, 262

11.7 Novel Regularization Techniques with a Case Study of Gene Regulatory Networks Reconstruction, 263

11.7.1 Optimal Graphical Lasso Granger Estimator, 263

11.7.2 Thresholding Strategy, 264

11.7.3 An Automatic Realization of the GLG-Method, 266

11.7.4 Granger Causality with Multi-Penalty Regularization, 266

11.7.5 Case Study of Gene Regulatory Network Reconstruction, 269

11.8 Conclusion, 271

12 Unmeasured Reciprocal Interactions: Specification and Fit Using Structural Equation Models 277
Phillip K. Wood

12.1 Introduction, 277

12.2 Types of Reciprocal Relationship Models, 278

12.2.1 Cross-Lagged Panel Approaches, 278

12.2.2 Granger Causality, 279

12.2.3 Epistemic Causality, 280

12.2.4 Reciprocal Causality, 281

12.3 Unmeasured Reciprocal and Autocausal Effects, 286

12.3.1 Bias in Standardized Regression Weight, 288

12.3.2 Autocausal Effects, 289

12.3.3 Instrumental Variables, 291

12.4 Longitudinal Data Settings, 293

12.4.1 Monte Carlo Simulation, 293

12.4.2 Real-World Data Examples, 302

12.5 Discussion, 304

Part IV Counterfactual Approaches And Propensity Score Analysis 309

13 Log-Linear Causal Analysis of Cross-Classified Categorical Data 311
Kazuo Yamaguchi

13.1 Introduction, 311

13.2 Propensity Score Methods and the Collapsibility Problem for the Logit Model, 313

13.3 Theorem On Standardization and the Lack of Collapsibility of the Logit Model, 316

13.4 The Problem of Zero-Sample Estimates of Conditional Probabilities and the Use of Semiparametric Models to Solve the Problem, 318

13.4.1 The Problem of Zero-Sample Estimates of Conditional Probabilities, 318

13.4.2 Method for Obtaining Adjusted Two-Way Frequency Data for the Analysis of Association between X and Y, 319

13.4.3 Method for Obtaining an Adjusted Three-Way Frequency Table for the Analysis of Conditional Association, 320

13.5 Estimation of Standard Errors in the Analysis of Association with Adjusted Contingency Table Data, 322

13.6 Illustrative Application, 323

13.6.1 Data, 323

13.6.2 Software, 324

13.6.3 Analysis, 324

13.7 Conclusion, 326

14 Design- and Model-Based Analysis of Propensity Score Designs 333
Peter M. Steiner

14.1 Introduction, 333

14.2 Causal Models and Causal Estimands, 334

14.3 Design- and Model-Based Inference with Randomized Experiments, 336

14.3.1 Design-Based Formulation, 337

14.3.2 Model-Based Formulation, 338

14.4 Design- and Model-Based Inferences with PS Designs, 339

14.4.1 Propensity Score Designs, 340

14.4.2 Design- versus Model-Based Formulations of PS Designs, 344

14.4.3 Other Propensity Score Techniques, 346

14.5 Statistical Issues with PS Designs in Practice, 347

14.5.1 Choice of a Specific PS Design, 347

14.5.2 Estimation of Propensity Scores, 350

14.5.3 Estimating and Testing the Treatment Effect, 353

14.6 Discussion, 355

15 Adjustment when Covariates are Fallible 363
Steffi Pohl, Marie-Ann Sengewald& Rolf Steyer

15.1 Introduction, 363

15.2 Theoretical Framework, 364

15.2.1 Definition of Causal Effects, 365

15.2.2 Identification of Causal Effects, 366

15.2.3 Adjusting for Latent or Fallible Covariates, 367

15.3 The Impact of Measurement Error in Covariates on Causal Effect Estimation, 369

15.3.1 Theoretical Impact of One Fallible Covariate, 369

15.3.2 Investigation of the Impact of Fallible Covariates in Simulation Studies, 370

15.3.3 Investigation of the Impact of Fallible Covariates in an Empirical Study, 370

15.4 Approaches Accounting for Latent Covariates, 372

15.4.1 Latent Covariates in Propensity Score Methods, 373

15.4.2 Latent Covariates in ANCOVA Models, 374

15.4.3 Performance of the Approaches in an Empirical Study, 374

15.5 The Impact of Additional Covariates on the Biasing Effect of a Fallible Covariate, 375

15.5.1 Investigation of the Impact of Additional Covariates in an Empirical Study, 376

15.5.2 Investigation of the Impact of Additional Covariates in Simulation Studies, 378

15.6 Discussion, 379

16 Latent Class Analysis with Causal Inference: The Effect of Adolescent Depression on Young Adult Substance Use Profile 385
Stephanie T. Lanza, Megan S. Schuler& Bethany C. Bray

16.1 Introduction, 385

16.2 Latent Class Analysis, 387

16.2.1 LCA With Covariates, 387

16.3 Propensity Score Analysis, 389

16.3.1 Inverse Propensity Weights (IPWs), 390

16.4 Empirical Demonstration, 391

16.4.1 The Causal Question: A Moderated Average Causal Effect, 391

16.4.2 Participants, 391

16.4.3 Measures, 391

16.4.4 Analytic Strategy for LCA With Causal Inference, 394

16.4.5 Results From Empirical Demonstration, 394

16.5 Discussion, 398

16.5.1 Limitations, 399

Part V Designs For Causal Inference 405

17 Can We Establish Causality with Statistical Analyses? The Example of Epidemiology 407
Ulrich Frick& Jürgen Rehm

17.1 Why a Chapter on Design?, 407

17.2 The Epidemiological Theory of Causality, 408

17.3 Cohort and Case-Control Studies, 411

17.4 Improving Control in Epidemiological Research, 414

17.4.1 Measurement, 414

17.4.2 Mendelian Randomization, 416

17.4.3 Surrogate Endpoints (Experimental), 419

17.4.4 Other Design Measures to Increase Control, 420

17.4.5 Methods of Analysis, 421

17.5 Conclusion: Control in Epidemiological Research Can Be Improved, 424

Index 433

List Of Contributors Xiii

Preface Xvii

Acknowledgments Xxv

Part I Bases Of Causality 1

1 Causation and the Aims of Inquiry 3

Ned Hall

1.1 Introduction, 3

1.2 The Aim of an Account of Causation, 4

1.2.1 The Possible Utility of a False Account, 4

1.2.2 Inquirys Aim, 5

1.2.3 Role of Intuitions, 6

1.3 The Good News, 7

1.3.1 The Core Idea, 7

1.3.2 Taxonomizing Conditions, 9

1.3.3 Unpacking Dependence, 10

1.3.4 The Good News, Amplified, 12

1.4 The Challenging News, 17

1.4.1 Multiple Realizability, 17

1.4.2 Protracted Causes, 18

1.4.3 Higher Level Taxonomies and Normal Conditions, 25

1.5 The Perplexing News, 26

1.5.1 The Centrality of Causal Process, 26

1.5.2 A Speculative Proposal, 28

2 Evidence and Epistemic Causality 31

Michael Wilde& Jon Williamson

2.1 Causality and Evidence, 31

2.2 The Epistemic Theory of Causality, 35

2.3 The Nature of Evidence, 38

2.4 Conclusion, 40

Part II Directionality Of Effects 43

3 Statistical Inference for Direction of Dependence in Linear Models 45

Yadolah Dodge& Valentin Rousson

3.1 Introduction, 45

3.2 Choosing the Direction of a Regression Line, 46

3.3 Significance Testing for the Direction of a Regression Line, 48

3.4 Lurking Variables and Causality, 54

3.4.1 Two Independent Predictors, 55

3.4.2 Confounding Variable, 55

3.4.3 Selection of a Subpopulation, 56

3.5 Brain and Body Data Revisited, 57

3.6 Conclusions, 60

4 Directionality of Effects in Causal Mediation Analysis 63

Wolfgang Wiedermann& Alexander von Eye

4.1 Introduction, 63

4.2 Elements of Causal Mediation Analysis, 66

4.3 Directionality of Effects in Mediation Models, 68

4.4 Testing Directionality Using Independence Properties of Competing Mediation Models, 71

4.4.1 Independence Properties of Bivariate Relations, 72

4.4.2 Independence Properties of the Multiple Variable Model, 74

4.4.3 Measuring and Testing Independence, 74

4.5 Simulating the Performance of Directionality Tests, 82

4.5.1 Results, 83

4.6 Empirical Data Example: Development of Numerical Cognition, 85

4.7 Discussion, 92

5 Direction of Effects in Categorical Variables: A Structural Perspective 107

Alexander von Eye& Wolfgang Wiedermann

5.1 Introduction, 107

5.2 Concepts of Independence in Categorical Data Analysis, 108

5.3 Direction Dependence in Bivariate Settings: Metric and Categorical Variables, 110

5.3.1 Simulating the Performance of Nonhierarchical Log-Linear Models, 114

5.4 Explaining the Structure of Cross-Classifications, 117

5.5 Data Example, 123

5.6 Discussion, 126

6 Directional Dependence Analysis Using SkewNormal Copula-Based Regression 131

Seongyong Kim& Daeyoung Kim

6.1 Introduction, 131

6.2 Copula-Based Regression, 133

6.2.1 Copula, 133

6.2.2 Copula-Based Regression, 134

6.3 Directional Dependence in the Copula-Based Regression, 136

6.4 SkewNormal Copula, 138

6.5 Inference of Directional Dependence Using SkewNormal Copula-Based Regression, 144

6.5.1 Estimation of Copula-Based Regression, 144

6.5.2 Detection of Directional Dependence and Computation of the Directional Dependence Measures, 146

6.6 Application, 147

6.7 Conclusion, 150

7 Non-Gaussian Structural Equation Models for Causal Discovery 153

Shohei Shimizu

7.1 Introduction, 153

7.2 Independent Component Analysis, 156

7.2.1 Model, 157

7.2.2 Identifiability, 157

7.2.3 Estimation, 158

7.3 Basic Linear Non-Gaussian Acyclic Model, 158

7.3.1 Model, 158

7.3.2 Identifiability, 160

7.3.3 Estimation, 162

7.4 LINGAM for Time Series, 167

7.4.1 Model, 167

7.4.2 Identifiability, 168

7.4.3 Estimation, 168

7.5 LINGAM with Latent Common Causes, 169

7.5.1 Model, 169

7.5.2 Identifiability, 171

7.5.3 Estimation, 174

7.6 Conclusion and Future Directions, 177

8 Nonlinear Functional Causal Models for Distinguishing Cause from Effect 185

Kun Zhang& Aapo Hyvärinen

8.1 Introduction, 185

8.2 Nonlinear Additive Noise Model, 188

8.2.1 Definition of Model, 188

8.2.2 Likelihood Ratio for Nonlinear Additive Models, 188

8.2.3 Information-Theoretic Interpretation, 189

8.2.4 Likelihood Ratio and Independence-Based Methods, 191

8.3 Post-Nonlinear Causal Model, 192

8.3.1 The Model, 192

8.3.2 Identifiability of Causal Direction, 193

8.3.3 Determination of Causal Direction Based on the PNL Causal Model, 193

8.4 On the Relationships Between Different Principles for Model Estimation, 194

8.5 Remark on General Nonlinear Causal Models, 196

8.6 Some Empirical Results, 197

8.7 Discussion and Conclusion, 198

Part III Granger Causality And Longitudinal Data Modeling 203

9 Alternative Forms of Granger Causality, Heterogeneity, and Nonstationarity 205

Peter C. M. Molenaar& Lawrence L. Lo

9.1 Introduction, 205

9.2 Some Initial Remarks on the Logic of Granger Causality Testing, 206

9.3 Preliminary Introduction to Time Series Analysis, 207

9.4 Overview of Granger Causality Testing in the Time Domain, 210

9.5 Granger Causality Testing in the Frequency Domain, 212

9.5.1 Two Equivalent Representations of a VAR(a), 212

9.5.2 Partial Directed Coherence (PDC) as a Frequency-Domain Index of Granger Causality, 213

9.5.3 Some Preliminary Comments, 214

9.5.4 Application to Simulated Data, 215

9.6 A New Data-Driven Solution to Granger Causality Testing, 216

9.6.1 Fitting a uSEM, 217

9.6.2 Extending the Fit of a uSEM, 217

9.6.3 Application of the Hybrid VAR Fit to Simulated Data, 218

9.7 Extensions to Nonstationary Series and Heterogeneous Replications, 221

9.7.1 Heterogeneous Replications, 221

9.7.2 Nonstationary Series, 222

9.8 Discussion and Conclusion, 224

10 Granger Meets Rasch: Investigating Granger Causation with Multidimensional Longitudinal Item Response Models 231

Ingrid Koller, Claus H. Carstensen, Wolfgang Wiedermann& Alexander von Eye

10.1 Introduction, 231

10.2 Granger Causation, 232

10.3 The Rasch Model, 234

10.4 Longitudinal Item Response Theory Models, 236

10.5 Data Example: Scientific Literacy in Preschool Children, 240

10.6 Discussion, 241

11 Granger Causality for Ill-Posed Problems: Ideas, Methods, and Application in Life Sciences 249

Katerina Hlavá cková-Schindler, Valeriya Naumova& Sergiy Pereverzyev Jr.

11.1 Introduction, 249

11.1.1 Causality Problems in Life Sciences, 250

11.1.2 Outline of the Chapter, 250

11.1.3 Notation, 251

11.2 Granger Causality and Multivariate Granger Causality, 251

11.2.1 Granger Causality, 252

11.2.2 Multivariate Granger Causality, 253

11.3 Gene Regulatory Networks, 254

11.4 Regularization of Ill-Posed Inverse Problems, 255

11.5 Multivariate Granger Causality Approaches Using𝓁1 and𝓁2

Penalties, 256

11.6 Applied Quality Measures, 262

11.7 Novel Regularization Techniques with a Case Study of Gene Regulatory Networks Reconstruction, 263

11.7.1 Optimal Graphical Lasso Granger Estimator, 263

11.7.2 Thresholding Strategy, 264

11.7.3 An Automatic Realization of the GLG-Method, 266

11.7.4 Granger Causality with Multi-Penalty Regularization, 266

11.7.5 Case Study of Gene Regulatory Network Reconstruction, 269

11.8 Conclusion, 271

12 Unmeasured Reciprocal Interactions: Specification and Fit Using Structural Equation Models 277

Phillip K. Wood

12.1 Introduction, 277

12.2 Types of Reciprocal Relationship Models, 278

12.2.1 Cross-Lagged Panel Approaches, 278

12.2.2 Granger Causality, 279

12.2.3 Epistemic Causality, 280

12.2.4 Reciprocal Causality, 281

12.3 Unmeasured Reciprocal and Autocausal Effects, 286

12.3.1 Bias in Standardized Regression Weight, 288

12.3.2 Autocausal Effects, 289

12.3.3 Instrumental Variables, 291

12.4 Longitudinal Data Settings, 293

12.4.1 Monte Carlo Simulation, 293

12.4.2 Real-World Data Examples, 302

12.5 Discussion, 304

Part IV Counterfactual Approaches And Propensity Score Analysis 309

13 Log-Linear Causal Analysis of Cross-Classified Categorical Data 311

Kazuo Yamaguchi

13.1 Introduction, 311

13.2 Propensity Score Methods and the Collapsibility Problem for the Logit Model, 313

13.3 Theorem On Standardization and the Lack of Collapsibility of the Logit Model, 316

13.4 The Problem of Zero-Sample Estimates of Conditional Probabilities and the Use of Semiparametric Models to Solve the Problem, 318

13.4.1 The Problem of Zero-Sample Estimates of Conditional Probabilities, 318

13.4.2 Method for Obtaining Adjusted Two-Way Frequency Data for the Analysis of Association between X and Y, 319

13.4.3 Method for Obtaining an Adjusted Three-Way Frequency Table for the Analysis of Conditional Association, 320

13.5 Estimation of Standard Errors in the Analysis of Association with Adjusted Contingency Table Data, 322

13.6 Illustrative Application, 323

13.6.1 Data, 323

13.6.2 Software, 324

13.6.3 Analysis, 324

13.7 Conclusion, 326

14 Design- and Model-Based Analysis of Propensity Score Designs 333

Peter M. Steiner

14.1 Introduction, 333

14.2 Causal Models and Causal Estimands, 334

14.3 Design- and Model-Based Inference with Randomized Experiments, 336

14.3.1 Design-Based Formulation, 337

14.3.2 Model-Based Formulation, 338

14.4 Design- and Model-Based Inferences with PS Designs, 339

14.4.1 Propensity Score Designs, 340

14.4.2 Design- versus Model-Based Formulations of PS Designs, 344

14.4.3 Other Propensity Score Techniques, 346

14.5 Statistical Issues with PS Designs in Practice, 347

14.5.1 Choice of a Specific PS Design, 347

14.5.2 Estimation of Propensity Scores, 350

14.5.3 Estimating and Testing the Treatment Effect, 353

14.6 Discussion, 355

15 Adjustment when Covariates are Fallible 363

Steffi Pohl, Marie-Ann Sengewald& Rolf Steyer

15.1 Introduction, 363

15.2 Theoretical Framework, 364

15.2.1 Definition of Causal Effects, 365

15.2.2 Identification of Causal Effects, 366

15.2.3 Adjusting for Latent or Fallible Covariates, 367

15.3 The Impact of Measurement Error in Covariates on Causal Effect Estimation, 369

15.3.1 Theoretical Impact of One Fallible Covariate, 369

15.3.2 Investigation of the Impact of Fallible Covariates in Simulation Studies, 370

15.3.3 Investigation of the Impact of Fallible Covariates in an Empirical Study, 370

15.4 Approaches Accounting for Latent Covariates, 372

15.4.1 Latent Covariates in Propensity Score Methods, 373

15.4.2 Latent Covariates in ANCOVA Models, 374

15.4.3 Performance of the Approaches in an Empirical Study, 374

15.5 The Impact of Additional Covariates on the Biasing Effect of a Fallible Covariate, 375

15.5.1 Investigation of the Impact of Additional Covariates in an Empirical Study, 376

15.5.2 Investigation of the Impact of Additional Covariates in Simulation Studies, 378

15.6 Discussion, 379

16 Latent Class Analysis with Causal Inference: The Effect of Adolescent Depression on Young Adult Substance Use Profile 385

Stephanie T. Lanza, Megan S. Schuler& Bethany C. Bray

16.1 Introduction, 385

16.2 Latent Class Analysis, 387

16.2.1 LCA With Covariates, 387

16.3 Propensity Score Analysis, 389

16.3.1 Inverse Propensity Weights (IPWs), 390

16.4 Empirical Demonstration, 391

16.4.1 The Causal Question: A Moderated Average Causal Effect, 391

16.4.2 Participants, 391

16.4.3 Measures, 391

16.4.4 Analytic Strategy for LCA With Causal Inference, 394

16.4.5 Results From Empirical Demonstration, 394

16.5 Discussion, 398

16.5.1 Limitations, 399

Part V Designs For Causal Inference 405

17 Can We Establish Causality with Statistical Analyses? The Example of Epidemiology 407

Ulrich Frick& Jürgen Rehm

17.1 Why a Chapter on Design?, 407

17.2 The Epidemiological Theory of Causality, 408

17.3 Cohort and Case-Control Studies, 411

17.4 Improving Control in Epidemiological Research, 414

17.4.1 Measurement, 414

17.4.2 Mendelian Randomization, 416

17.4.3 Surrogate Endpoints (Experimental), 419

17.4.4 Other Design Measures to Increase Control, 420

17.4.5 Methods of Analysis, 421

17.5 Conclusion: Control in Epidemiological Research Can Be Improved, 424

Index 433