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 XiiiPreface XviiAcknowledgments XxvPart I Bases Of Causality 11 Causation and the Aims of Inquiry 3Ned Hall1.1 Introduction, 31.2 The Aim of an Account of Causation, 41.2.1 The Possible Utility of a False Account, 41.2.2 Inquiry’s Aim, 51.2.3 Role of “Intuitions”, 61.3 The Good News, 71.3.1 The Core Idea, 71.3.2 Taxonomizing “Conditions”, 91.3.3 Unpacking “Dependence”, 101.3.4 The Good News, Amplified, 121.4 The Challenging News, 171.4.1 Multiple Realizability, 171.4.2 Protracted Causes, 181.4.3 Higher Level Taxonomies and “Normal” Conditions, 251.5 The Perplexing News, 261.5.1 The Centrality of “Causal Process”, 261.5.2 A Speculative Proposal, 282 Evidence and Epistemic Causality 31Michael Wilde & Jon Williamson2.1 Causality and Evidence, 312.2 The Epistemic Theory of Causality, 352.3 The Nature of Evidence, 382.4 Conclusion, 40Part II Directionality Of Effects 433 Statistical Inference for Direction of Dependence in Linear Models 45Yadolah Dodge & Valentin Rousson3.1 Introduction, 453.2 Choosing the Direction of a Regression Line, 463.3 Significance Testing for the Direction of a Regression Line, 483.4 Lurking Variables and Causality, 543.4.1 Two Independent Predictors, 553.4.2 Confounding Variable, 553.4.3 Selection of a Subpopulation, 563.5 Brain and Body Data Revisited, 573.6 Conclusions, 604 Directionality of Effects in Causal Mediation Analysis 63Wolfgang Wiedermann & Alexander von Eye4.1 Introduction, 634.2 Elements of Causal Mediation Analysis, 664.3 Directionality of Effects in Mediation Models, 684.4 Testing Directionality Using Independence Properties of Competing Mediation Models, 714.4.1 Independence Properties of Bivariate Relations, 724.4.2 Independence Properties of the Multiple Variable Model, 744.4.3 Measuring and Testing Independence, 744.5 Simulating the Performance of Directionality Tests, 824.5.1 Results, 834.6 Empirical Data Example: Development of Numerical Cognition, 854.7 Discussion, 925 Direction of Effects in Categorical Variables: A Structural Perspective 107Alexander von Eye & Wolfgang Wiedermann5.1 Introduction, 1075.2 Concepts of Independence in Categorical Data Analysis, 1085.3 Direction Dependence in Bivariate Settings: Metric and Categorical Variables, 1105.3.1 Simulating the Performance of Nonhierarchical Log-Linear Models, 1145.4 Explaining the Structure of Cross-Classifications, 1175.5 Data Example, 1235.6 Discussion, 1266 Directional Dependence Analysis Using Skew–Normal Copula-Based Regression 131Seongyong Kim & Daeyoung Kim6.1 Introduction, 1316.2 Copula-Based Regression, 1336.2.1 Copula, 1336.2.2 Copula-Based Regression, 1346.3 Directional Dependence in the Copula-Based Regression, 1366.4 Skew–Normal Copula, 1386.5 Inference of Directional Dependence Using Skew–Normal Copula-Based Regression, 1446.5.1 Estimation of Copula-Based Regression, 1446.5.2 Detection of Directional Dependence and Computation of the Directional Dependence Measures, 1466.6 Application, 1476.7 Conclusion, 1507 Non-Gaussian Structural Equation Models for Causal Discovery 153Shohei Shimizu7.1 Introduction, 1537.2 Independent Component Analysis, 1567.2.1 Model, 1577.2.2 Identifiability, 1577.2.3 Estimation, 1587.3 Basic Linear Non-Gaussian Acyclic Model, 1587.3.1 Model, 1587.3.2 Identifiability, 1607.3.3 Estimation, 1627.4 LINGAM for Time Series, 1677.4.1 Model, 1677.4.2 Identifiability, 1687.4.3 Estimation, 1687.5 LINGAM with Latent Common Causes, 1697.5.1 Model, 1697.5.2 Identifiability, 1717.5.3 Estimation, 1747.6 Conclusion and Future Directions, 1778 Nonlinear Functional Causal Models for Distinguishing Cause from Effect 185Kun Zhang & Aapo Hyvärinen8.1 Introduction, 1858.2 Nonlinear Additive Noise Model, 1888.2.1 Definition of Model, 1888.2.2 Likelihood Ratio for Nonlinear Additive Models, 1888.2.3 Information-Theoretic Interpretation, 1898.2.4 Likelihood Ratio and Independence-Based Methods, 1918.3 Post-Nonlinear Causal Model, 1928.3.1 The Model, 1928.3.2 Identifiability of Causal Direction, 1938.3.3 Determination of Causal Direction Based on the PNL Causal Model, 1938.4 On the Relationships Between Different Principles for Model Estimation, 1948.5 Remark on General Nonlinear Causal Models, 1968.6 Some Empirical Results, 1978.7 Discussion and Conclusion, 198Part III Granger Causality And Longitudinal Data Modeling 2039 Alternative Forms of Granger Causality, Heterogeneity, and Nonstationarity 205Peter C. M. Molenaar & Lawrence L. Lo9.1 Introduction, 2059.2 Some Initial Remarks on the Logic of Granger Causality Testing, 2069.3 Preliminary Introduction to Time Series Analysis, 2079.4 Overview of Granger Causality Testing in the Time Domain, 2109.5 Granger Causality Testing in the Frequency Domain, 2129.5.1 Two Equivalent Representations of a VAR(a), 2129.5.2 Partial Directed Coherence (PDC) as a Frequency-Domain Index of Granger Causality, 2139.5.3 Some Preliminary Comments, 2149.5.4 Application to Simulated Data, 2159.6 A New Data-Driven Solution to Granger Causality Testing, 2169.6.1 Fitting a uSEM, 2179.6.2 Extending the Fit of a uSEM, 2179.6.3 Application of the Hybrid VAR Fit to Simulated Data, 2189.7 Extensions to Nonstationary Series and Heterogeneous Replications, 2219.7.1 Heterogeneous Replications, 2219.7.2 Nonstationary Series, 2229.8 Discussion and Conclusion, 22410 Granger Meets Rasch: Investigating Granger Causation with Multidimensional Longitudinal Item Response Models 231Ingrid Koller, Claus H. Carstensen, Wolfgang Wiedermann & Alexander von Eye10.1 Introduction, 23110.2 Granger Causation, 23210.3 The Rasch Model, 23410.4 Longitudinal Item Response Theory Models, 23610.5 Data Example: Scientific Literacy in Preschool Children, 24010.6 Discussion, 24111 Granger Causality for Ill-Posed Problems: Ideas, Methods, and Application in Life Sciences 249Katerina Hlavá ˇ cková-Schindler, Valeriya Naumova & ˇ Sergiy Pereverzyev Jr.11.1 Introduction, 24911.1.1 Causality Problems in Life Sciences, 25011.1.2 Outline of the Chapter, 25011.1.3 Notation, 25111.2 Granger Causality and Multivariate Granger Causality, 25111.2.1 Granger Causality, 25211.2.2 Multivariate Granger Causality, 25311.3 Gene Regulatory Networks, 25411.4 Regularization of Ill-Posed Inverse Problems, 25511.5 Multivariate Granger Causality Approaches Using 𝓁1 and 𝓁2Penalties, 25611.6 Applied Quality Measures, 26211.7 Novel Regularization Techniques with a Case Study of Gene Regulatory Networks Reconstruction, 26311.7.1 Optimal Graphical Lasso Granger Estimator, 26311.7.2 Thresholding Strategy, 26411.7.3 An Automatic Realization of the GLG-Method, 26611.7.4 Granger Causality with Multi-Penalty Regularization, 26611.7.5 Case Study of Gene Regulatory Network Reconstruction, 26911.8 Conclusion, 27112 Unmeasured Reciprocal Interactions: Specification and Fit Using Structural Equation Models 277Phillip K. Wood12.1 Introduction, 27712.2 Types of Reciprocal Relationship Models, 27812.2.1 Cross-Lagged Panel Approaches, 27812.2.2 Granger Causality, 27912.2.3 Epistemic Causality, 28012.2.4 Reciprocal Causality, 28112.3 Unmeasured Reciprocal and Autocausal Effects, 28612.3.1 Bias in Standardized Regression Weight, 28812.3.2 Autocausal Effects, 28912.3.3 Instrumental Variables, 29112.4 Longitudinal Data Settings, 29312.4.1 Monte Carlo Simulation, 29312.4.2 Real-World Data Examples, 30212.5 Discussion, 304Part IV Counterfactual Approaches And Propensity Score Analysis 30913 Log-Linear Causal Analysis of Cross-Classified Categorical Data 311Kazuo Yamaguchi13.1 Introduction, 31113.2 Propensity Score Methods and the Collapsibility Problem for the Logit Model, 31313.3 Theorem On Standardization and the Lack of Collapsibility of the Logit Model, 31613.4 The Problem of Zero-Sample Estimates of Conditional Probabilities and the Use of Semiparametric Models to Solve the Problem, 31813.4.1 The Problem of Zero-Sample Estimates of Conditional Probabilities, 31813.4.2 Method for Obtaining Adjusted Two-Way Frequency Data for the Analysis of Association between X and Y, 31913.4.3 Method for Obtaining an Adjusted Three-Way Frequency Table for the Analysis of Conditional Association, 32013.5 Estimation of Standard Errors in the Analysis of Association with Adjusted Contingency Table Data, 32213.6 Illustrative Application, 32313.6.1 Data, 32313.6.2 Software, 32413.6.3 Analysis, 32413.7 Conclusion, 32614 Design- and Model-Based Analysis of Propensity Score Designs 333Peter M. Steiner14.1 Introduction, 33314.2 Causal Models and Causal Estimands, 33414.3 Design- and Model-Based Inference with Randomized Experiments, 33614.3.1 Design-Based Formulation, 33714.3.2 Model-Based Formulation, 33814.4 Design- and Model-Based Inferences with PS Designs, 33914.4.1 Propensity Score Designs, 34014.4.2 Design- versus Model-Based Formulations of PS Designs, 34414.4.3 Other Propensity Score Techniques, 34614.5 Statistical Issues with PS Designs in Practice, 34714.5.1 Choice of a Specific PS Design, 34714.5.2 Estimation of Propensity Scores, 35014.5.3 Estimating and Testing the Treatment Effect, 35314.6 Discussion, 35515 Adjustment when Covariates are Fallible 363Steffi Pohl, Marie-Ann Sengewald & Rolf Steyer15.1 Introduction, 36315.2 Theoretical Framework, 36415.2.1 Definition of Causal Effects, 36515.2.2 Identification of Causal Effects, 36615.2.3 Adjusting for Latent or Fallible Covariates, 36715.3 The Impact of Measurement Error in Covariates on Causal Effect Estimation, 36915.3.1 Theoretical Impact of One Fallible Covariate, 36915.3.2 Investigation of the Impact of Fallible Covariates in Simulation Studies, 37015.3.3 Investigation of the Impact of Fallible Covariates in an Empirical Study, 37015.4 Approaches Accounting for Latent Covariates, 37215.4.1 Latent Covariates in Propensity Score Methods, 37315.4.2 Latent Covariates in ANCOVA Models, 37415.4.3 Performance of the Approaches in an Empirical Study, 37415.5 The Impact of Additional Covariates on the Biasing Effect of a Fallible Covariate, 37515.5.1 Investigation of the Impact of Additional Covariates in an Empirical Study, 37615.5.2 Investigation of the Impact of Additional Covariates in Simulation Studies, 37815.6 Discussion, 37916 Latent Class Analysis with Causal Inference: The Effect of Adolescent Depression on Young Adult Substance Use Profile 385Stephanie T. Lanza, Megan S. Schuler & Bethany C. Bray16.1 Introduction, 38516.2 Latent Class Analysis, 38716.2.1 LCA With Covariates, 38716.3 Propensity Score Analysis, 38916.3.1 Inverse Propensity Weights (IPWs), 39016.4 Empirical Demonstration, 39116.4.1 The Causal Question: A Moderated Average Causal Effect, 39116.4.2 Participants, 39116.4.3 Measures, 39116.4.4 Analytic Strategy for LCA With Causal Inference, 39416.4.5 Results From Empirical Demonstration, 39416.5 Discussion, 39816.5.1 Limitations, 399Part V Designs For Causal Inference 40517 Can We Establish Causality with Statistical Analyses? The Example of Epidemiology 407Ulrich Frick & Jürgen Rehm17.1 Why a Chapter on Design?, 40717.2 The Epidemiological Theory of Causality, 40817.3 Cohort and Case-Control Studies, 41117.4 Improving Control in Epidemiological Research, 41417.4.1 Measurement, 41417.4.2 Mendelian Randomization, 41617.4.3 Surrogate Endpoints (Experimental), 41917.4.4 Other Design Measures to Increase Control, 42017.4.5 Methods of Analysis, 42117.5 Conclusion: Control in Epidemiological Research Can Be Improved, 424Index 433List Of Contributors XiiiPreface XviiAcknowledgments XxvPart I Bases Of Causality 11 Causation and the Aims of Inquiry 3Ned Hall1.1 Introduction, 31.2 The Aim of an Account of Causation, 41.2.1 The Possible Utility of a False Account, 41.2.2 Inquiry’s Aim, 51.2.3 Role of “Intuitions”, 61.3 The Good News, 71.3.1 The Core Idea, 71.3.2 Taxonomizing “Conditions”, 91.3.3 Unpacking “Dependence”, 101.3.4 The Good News, Amplified, 121.4 The Challenging News, 171.4.1 Multiple Realizability, 171.4.2 Protracted Causes, 181.4.3 Higher Level Taxonomies and “Normal” Conditions, 251.5 The Perplexing News, 261.5.1 The Centrality of “Causal Process”, 261.5.2 A Speculative Proposal, 282 Evidence and Epistemic Causality 31Michael Wilde & Jon Williamson2.1 Causality and Evidence, 312.2 The Epistemic Theory of Causality, 352.3 The Nature of Evidence, 382.4 Conclusion, 40Part II Directionality Of Effects 433 Statistical Inference for Direction of Dependence in Linear Models 45Yadolah Dodge & Valentin Rousson3.1 Introduction, 453.2 Choosing the Direction of a Regression Line, 463.3 Significance Testing for the Direction of a Regression Line, 483.4 Lurking Variables and Causality, 543.4.1 Two Independent Predictors, 553.4.2 Confounding Variable, 553.4.3 Selection of a Subpopulation, 563.5 Brain and Body Data Revisited, 573.6 Conclusions, 604 Directionality of Effects in Causal Mediation Analysis 63Wolfgang Wiedermann & Alexander von Eye4.1 Introduction, 634.2 Elements of Causal Mediation Analysis, 664.3 Directionality of Effects in Mediation Models, 684.4 Testing Directionality Using Independence Properties of Competing Mediation Models, 714.4.1 Independence Properties of Bivariate Relations, 724.4.2 Independence Properties of the Multiple Variable Model, 744.4.3 Measuring and Testing Independence, 744.5 Simulating the Performance of Directionality Tests, 824.5.1 Results, 834.6 Empirical Data Example: Development of Numerical Cognition, 854.7 Discussion, 925 Direction of Effects in Categorical Variables: A Structural Perspective 107Alexander von Eye & Wolfgang Wiedermann5.1 Introduction, 1075.2 Concepts of Independence in Categorical Data Analysis, 1085.3 Direction Dependence in Bivariate Settings: Metric and Categorical Variables, 1105.3.1 Simulating the Performance of Nonhierarchical Log-Linear Models, 1145.4 Explaining the Structure of Cross-Classifications, 1175.5 Data Example, 1235.6 Discussion, 1266 Directional Dependence Analysis Using Skew–Normal Copula-Based Regression 131Seongyong Kim & Daeyoung Kim6.1 Introduction, 1316.2 Copula-Based Regression, 1336.2.1 Copula, 1336.2.2 Copula-Based Regression, 1346.3 Directional Dependence in the Copula-Based Regression, 1366.4 Skew–Normal Copula, 1386.5 Inference of Directional Dependence Using Skew–Normal Copula-Based Regression, 1446.5.1 Estimation of Copula-Based Regression, 1446.5.2 Detection of Directional Dependence and Computation of the Directional Dependence Measures, 1466.6 Application, 1476.7 Conclusion, 1507 Non-Gaussian Structural Equation Models for Causal Discovery 153Shohei Shimizu7.1 Introduction, 1537.2 Independent Component Analysis, 1567.2.1 Model, 1577.2.2 Identifiability, 1577.2.3 Estimation, 1587.3 Basic Linear Non-Gaussian Acyclic Model, 1587.3.1 Model, 1587.3.2 Identifiability, 1607.3.3 Estimation, 1627.4 LINGAM for Time Series, 1677.4.1 Model, 1677.4.2 Identifiability, 1687.4.3 Estimation, 1687.5 LINGAM with Latent Common Causes, 1697.5.1 Model, 1697.5.2 Identifiability, 1717.5.3 Estimation, 1747.6 Conclusion and Future Directions, 1778 Nonlinear Functional Causal Models for Distinguishing Cause from Effect 185Kun Zhang & Aapo Hyvärinen8.1 Introduction, 1858.2 Nonlinear Additive Noise Model, 1888.2.1 Definition of Model, 1888.2.2 Likelihood Ratio for Nonlinear Additive Models, 1888.2.3 Information-Theoretic Interpretation, 1898.2.4 Likelihood Ratio and Independence-Based Methods, 1918.3 Post-Nonlinear Causal Model, 1928.3.1 The Model, 1928.3.2 Identifiability of Causal Direction, 1938.3.3 Determination of Causal Direction Based on the PNL Causal Model, 1938.4 On the Relationships Between Different Principles for Model Estimation, 1948.5 Remark on General Nonlinear Causal Models, 1968.6 Some Empirical Results, 1978.7 Discussion and Conclusion, 198Part III Granger Causality And Longitudinal Data Modeling 2039 Alternative Forms of Granger Causality, Heterogeneity, and Nonstationarity 205Peter C. M. Molenaar & Lawrence L. Lo9.1 Introduction, 2059.2 Some Initial Remarks on the Logic of Granger Causality Testing, 2069.3 Preliminary Introduction to Time Series Analysis, 2079.4 Overview of Granger Causality Testing in the Time Domain, 2109.5 Granger Causality Testing in the Frequency Domain, 2129.5.1 Two Equivalent Representations of a VAR(a), 2129.5.2 Partial Directed Coherence (PDC) as a Frequency-Domain Index of Granger Causality, 2139.5.3 Some Preliminary Comments, 2149.5.4 Application to Simulated Data, 2159.6 A New Data-Driven Solution to Granger Causality Testing, 2169.6.1 Fitting a uSEM, 2179.6.2 Extending the Fit of a uSEM, 2179.6.3 Application of the Hybrid VAR Fit to Simulated Data, 2189.7 Extensions to Nonstationary Series and Heterogeneous Replications, 2219.7.1 Heterogeneous Replications, 2219.7.2 Nonstationary Series, 2229.8 Discussion and Conclusion, 22410 Granger Meets Rasch: Investigating Granger Causation with Multidimensional Longitudinal Item Response Models 231Ingrid Koller, Claus H. Carstensen, Wolfgang Wiedermann & Alexander von Eye10.1 Introduction, 23110.2 Granger Causation, 23210.3 The Rasch Model, 23410.4 Longitudinal Item Response Theory Models, 23610.5 Data Example: Scientific Literacy in Preschool Children, 24010.6 Discussion, 24111 Granger Causality for Ill-Posed Problems: Ideas, Methods, and Application in Life Sciences 249Katerina Hlavá ˇ cková-Schindler, Valeriya Naumova & ˇ Sergiy Pereverzyev Jr.11.1 Introduction, 24911.1.1 Causality Problems in Life Sciences, 25011.1.2 Outline of the Chapter, 25011.1.3 Notation, 25111.2 Granger Causality and Multivariate Granger Causality, 25111.2.1 Granger Causality, 25211.2.2 Multivariate Granger Causality, 25311.3 Gene Regulatory Networks, 25411.4 Regularization of Ill-Posed Inverse Problems, 25511.5 Multivariate Granger Causality Approaches Using 𝓁1 and 𝓁2Penalties, 25611.6 Applied Quality Measures, 26211.7 Novel Regularization Techniques with a Case Study of Gene Regulatory Networks Reconstruction, 26311.7.1 Optimal Graphical Lasso Granger Estimator, 26311.7.2 Thresholding Strategy, 26411.7.3 An Automatic Realization of the GLG-Method, 26611.7.4 Granger Causality with Multi-Penalty Regularization, 26611.7.5 Case Study of Gene Regulatory Network Reconstruction, 26911.8 Conclusion, 27112 Unmeasured Reciprocal Interactions: Specification and Fit Using Structural Equation Models 277Phillip K. Wood12.1 Introduction, 27712.2 Types of Reciprocal Relationship Models, 27812.2.1 Cross-Lagged Panel Approaches, 27812.2.2 Granger Causality, 27912.2.3 Epistemic Causality, 28012.2.4 Reciprocal Causality, 28112.3 Unmeasured Reciprocal and Autocausal Effects, 28612.3.1 Bias in Standardized Regression Weight, 28812.3.2 Autocausal Effects, 28912.3.3 Instrumental Variables, 29112.4 Longitudinal Data Settings, 29312.4.1 Monte Carlo Simulation, 29312.4.2 Real-World Data Examples, 30212.5 Discussion, 304Part IV Counterfactual Approaches And Propensity Score Analysis 30913 Log-Linear Causal Analysis of Cross-Classified Categorical Data 311Kazuo Yamaguchi13.1 Introduction, 31113.2 Propensity Score Methods and the Collapsibility Problem for the Logit Model, 31313.3 Theorem On Standardization and the Lack of Collapsibility of the Logit Model, 31613.4 The Problem of Zero-Sample Estimates of Conditional Probabilities and the Use of Semiparametric Models to Solve the Problem, 31813.4.1 The Problem of Zero-Sample Estimates of Conditional Probabilities, 31813.4.2 Method for Obtaining Adjusted Two-Way Frequency Data for the Analysis of Association between X and Y, 31913.4.3 Method for Obtaining an Adjusted Three-Way Frequency Table for the Analysis of Conditional Association, 32013.5 Estimation of Standard Errors in the Analysis of Association with Adjusted Contingency Table Data, 32213.6 Illustrative Application, 32313.6.1 Data, 32313.6.2 Software, 32413.6.3 Analysis, 32413.7 Conclusion, 32614 Design- and Model-Based Analysis of Propensity Score Designs 333Peter M. Steiner14.1 Introduction, 33314.2 Causal Models and Causal Estimands, 33414.3 Design- and Model-Based Inference with Randomized Experiments, 33614.3.1 Design-Based Formulation, 33714.3.2 Model-Based Formulation, 33814.4 Design- and Model-Based Inferences with PS Designs, 33914.4.1 Propensity Score Designs, 34014.4.2 Design- versus Model-Based Formulations of PS Designs, 34414.4.3 Other Propensity Score Techniques, 34614.5 Statistical Issues with PS Designs in Practice, 34714.5.1 Choice of a Specific PS Design, 34714.5.2 Estimation of Propensity Scores, 35014.5.3 Estimating and Testing the Treatment Effect, 35314.6 Discussion, 35515 Adjustment when Covariates are Fallible 363Steffi Pohl, Marie-Ann Sengewald & Rolf Steyer15.1 Introduction, 36315.2 Theoretical Framework, 36415.2.1 Definition of Causal Effects, 36515.2.2 Identification of Causal Effects, 36615.2.3 Adjusting for Latent or Fallible Covariates, 36715.3 The Impact of Measurement Error in Covariates on Causal Effect Estimation, 36915.3.1 Theoretical Impact of One Fallible Covariate, 36915.3.2 Investigation of the Impact of Fallible Covariates in Simulation Studies, 37015.3.3 Investigation of the Impact of Fallible Covariates in an Empirical Study, 37015.4 Approaches Accounting for Latent Covariates, 37215.4.1 Latent Covariates in Propensity Score Methods, 37315.4.2 Latent Covariates in ANCOVA Models, 37415.4.3 Performance of the Approaches in an Empirical Study, 37415.5 The Impact of Additional Covariates on the Biasing Effect of a Fallible Covariate, 37515.5.1 Investigation of the Impact of Additional Covariates in an Empirical Study, 37615.5.2 Investigation of the Impact of Additional Covariates in Simulation Studies, 37815.6 Discussion, 37916 Latent Class Analysis with Causal Inference: The Effect of Adolescent Depression on Young Adult Substance Use Profile 385Stephanie T. Lanza, Megan S. Schuler & Bethany C. Bray16.1 Introduction, 38516.2 Latent Class Analysis, 38716.2.1 LCA With Covariates, 38716.3 Propensity Score Analysis, 38916.3.1 Inverse Propensity Weights (IPWs), 39016.4 Empirical Demonstration, 39116.4.1 The Causal Question: A Moderated Average Causal Effect, 39116.4.2 Participants, 39116.4.3 Measures, 39116.4.4 Analytic Strategy for LCA With Causal Inference, 39416.4.5 Results From Empirical Demonstration, 39416.5 Discussion, 39816.5.1 Limitations, 399Part V Designs For Causal Inference 40517 Can We Establish Causality with Statistical Analyses? The Example of Epidemiology 407Ulrich Frick & Jürgen Rehm17.1 Why a Chapter on Design?, 40717.2 The Epidemiological Theory of Causality, 40817.3 Cohort and Case-Control Studies, 41117.4 Improving Control in Epidemiological Research, 41417.4.1 Measurement, 41417.4.2 Mendelian Randomization, 41617.4.3 Surrogate Endpoints (Experimental), 41917.4.4 Other Design Measures to Increase Control, 42017.4.5 Methods of Analysis, 42117.5 Conclusion: Control in Epidemiological Research Can Be Improved, 424Index 433