Statistics and Causality
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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 Inquiry's 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 Skew-Normal 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 Skew-Normal Copula, 138
6.5 Inference of Directional Dependence Using Skew-Normal 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 Using ¿¿¿¿1 and ¿¿¿¿2
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 Inquiry's 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 Skew-Normal 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 Skew-Normal Copula, 138
6.5 Inference of Directional Dependence Using Skew-Normal 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 Using ¿¿¿¿1 and ¿¿¿¿2
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
