Statistics and Causality

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 1.3 The Good News, 7 1.4 The Challenging News, 17 1.5 The Perplexing News, 26 2 Evidence and Epistemic Causality 31 Michael Wilde and 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 and 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 3.5 Brain and Body Data Revisited, 57 3.6 Conclusions, 60 4 Directionality of Effects in Causal Mediation Analysis 63 Wolfgang Wiedermann and 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 4.5 Simulating the Performance of Directionality Tests, 82 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 and 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 5.4 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 and Daeyoung Kim 6.1 Introduction, 131 6.2 Copula-Based Regression, 133 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 6.6 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 7.3 Basic Linear Non-Gaussian Acyclic Model, 158 7.4 LINGAM for Time Series, 167 7.5 LINGAM with Latent Common Causes, 169 7.6 Conclusion and Future Directions, 177 8 Nonlinear Functional Causal Models for Distinguishing Cause from Effect 185 Kun Zhang and Aapo Hyvärinen 8.1 Introduction, 185 8.2 Nonlinear Additive Noise Model, 188 8.3 Post-Nonlinear Causal Model, 192 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 PARTIII GRANGER CAUSALITY AND LONGITUDINAL DATA MODELING 203 9 Alternative Forms of Granger Causality, Heterogeneity, and Nonstationarity 205 Peter C. M. Molenaar and 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 9.6 A New Data-Driven Solution to Granger Causality Testing, 216 9.7 Extensions to Nonstationary Series and Heterogeneous Replications, 221 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 and 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 Katrina Hlav ková-Schindler, Valeriya Naumova and Sergiy Pereverzyev Jr. 11.1 Introduction, 249 11.2 Granger Causality and Multivariate Granger Causality, 251 11.3 Gene Regulatory Networks, 254 11.4 Regularization of Ill-Posed Inverse Problems, 255 11.5 Multivariate Granger Causality Approaches Using l1 and l2 Penalties, 256 11.6 Applied Quality Measures, 262 11.7 Novel Regularization Techniques with a Case Study of Gene Regulatory Networks Reconstruction, 263 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 12.3 Unmeasured Reciprocal and Autocausal Effects, 286 12.4 Longitudinal Data Settings, 293 12.5 Discussion, 304 PARTIV 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 13.5 Estimation of Standard Errors in the Analysis of Association with Adjusted Contingency Table Data, 322 13.6 Illustrative Application, 323 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 14.4 Design- and Model-Based Inferences with PS Designs, 339 14.5 Statistical Issues with PS Designs in Practice, 347 14.6 Discussion, 355 15 Adjustment when Covariates are Fallible 363 Steffi Pohl, Marie-Ann Sengewald and Rolf Steyer 15.1 Introduction, 363 15.2 Theoretical Framework, 364 15.3 The Impact of Measurement Error in Covariates on Causal Effect Estimation, 369 15.4 Approaches Accounting for Latent Covariates, 372 15.5 The Impact of Additional Covariates on the Biasing Effect of a Fallible Covariate, 375 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 and Bethany C. Bray 16.1 Introduction, 385 16.2 Latent Class Analysis, 387 16.3 Propensity Score Analysis, 389 16.4 Empirical Demonstration, 391 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 and 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 17.5 Conclusion: Control in Epidemiological Research Can Be Improved, 424 INDEX 433