Statistics and Causality

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 the Encyclopedia of Statistics in Behavioral Science and is the coauthor of Log-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 Hyvrinen 8.1 Introduction