Statistics and Causality E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 881

Veröffentlichungsjahr: 2016

Beschreibung

>STATISTICS AND CAUSALITY 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 topics * Discussions 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.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

List of Contributors

Preface

References

Acknowledgments

Part I Bases of Causality

Chapter 1: Causation and the Aims of Inquiry

1.1 Introduction

1.2 The Aim of an Account of Causation

1.3 The Good News

1.4 The Challenging News

1.5 The Perplexing News

References

Chapter 2: Evidence and Epistemic Causality

2.1 Causality and Evidence

2.2 The Epistemic Theory of Causality

2.3 The Nature of Evidence

2.4 Conclusion

References

Part II: Directionality of Effects

Chapter 3: Statistical Inference for Direction of Dependence in Linear Models

3.1 Introduction

3.2 Choosing the Direction of a Regression Line

3.3 Significance Testing for the Direction of a Regression Line

3.4 Lurking Variables and Causality

3.5 Brain and Body Data Revisited

3.6 Conclusions

References

Chapter 4: Directionality of Effects in Causal Mediation Analysis

4.1 Introduction

4.2 Elements of Causal Mediation Analysis

4.3 Directionality of Effects in Mediation Models

4.4 Testing Directionality Using Independence Properties of Competing Mediation Models

4.5 Simulating the Performance of Directionality Tests

4.6 Empirical Data Example: Development of Numerical Cognition

4.7 Discussion

Appendix A: Dependence Property of the Predictor–Outcome Relation

Appendix B: Dependence Properties in the Multiple Variable Model

References

Chapter 5: Direction of Effects in Categorical Variables: a Structural Perspective

5.1 Introduction

5.2 Concepts of Independence in Categorical Data Analysis

5.3 Direction Dependence in Bivariate Settings: Metric And Categorical Variables

5.4 Explaining The Structure of Cross-Classifications

5.5 Data Example

5.6 Discussion

References

Chapter 6: Directional Dependence Analysis Using Skew–Normal Copula-Based Regression

6.1 Introduction

6.2 Copula-Based Regression

6.3 Directional Dependence in the Copula-Based Regression

6.4 Skew–Normal Copula

6.5 Inference of Directional Dependence Using Skew–Normal Copula-Based Regression

6.6 Application

6.7 Conclusion

References

Chapter 7: Non-Gaussian Structural Equation Models for Causal Discovery

7.1 Introduction

7.2 Independent Component Analysis

7.3 Basic Linear Non-Gaussian Acyclic Model

7.4 LiNGAM For Time Series

7.5 LiNGAM With Latent Common Causes

7.6 Conclusion and Future Directions

References

Code Availability

Chapter 8: Nonlinear Functional Causal Models for Distinguishing Cause from Effect

8.1 Introduction

8.2 Nonlinear Additive Noise Model

8.3 Post-Nonlinear Causal Model

8.4 On the Relationships Between Different Principles for Model Estimation

8.5 Remark on General Nonlinear Causal Models

8.6 Some Empirical Results

8.7 Discussion and Conclusion

References

Part III: Granger Causality and Longitudinal Data Modeling

Chapter 9: Alternative Forms of Granger Causality, Heterogeneity, and Nonstationarity

9.1 Introduction

9.2 Some Initial Remarks on the Logic of Granger Causality Testing

9.3 Preliminary Introduction to Time Series Analysis

9.4 Overview of Granger Causality Testing in the Time Domain

9.5 Granger Causality Testing in the Frequency Domain

9.6 A New Data-Driven Solution to Granger Causality Testing

9.7 Extensions to Nonstationary Series and Heterogeneous Replications

9.8 Discussion and Conclusion

References

Appendix

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

10.1 Introduction

10.2 Granger Causation

10.3 The Rasch Model

10.4 Longitudinal Item Response Theory Models

10.5 Data Example: Scientific Literacy in Preschool Children

10.6 Discussion

References

Appendix

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

11.1 Introduction

11.2 Granger Causality and Multivariate Granger Causality

11.3 Gene Regulatory Networks

11.4 Regularization of Ill-Posed Inverse Problems

11.5 Multivariate Granger Causality Approaches Using ℓ

1

and ℓ

2

Penalties

11.6 Applied Quality Measures

11.7 Novel Regularization Techniques With a Case Study of Gene Regulatory Networks Reconstruction

11.8 Conclusion

Acknowledgments

References

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

12.1 Introduction

12.2 Types of Reciprocal Relationship Models

12.3 Unmeasured Reciprocal and Autocausal Effects

12.4 Longitudinal Data Settings

12.5 Discussion

Acknowledgments

References

Part IV: Counterfactual Approaches and Propensity Score Analysis

Chapter 13: Log-Linear Causal Analysis of Cross-Classified Categorical Data

13.1 Introduction

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

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

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

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

13.6 Illustrative Application

13.7 Conclusion

References

Appendix A: A Proof of the Theorem

Appendix B: Iterative Proportional Adjustment Procedures that Purge the Interaction Effects of V and X on Y

Chapter 14: Design- and Model-Based Analysis of Propensity Score Designs

14.1 Introduction

14.2 Causal Models and Causal Estimands

14.3 Design- and Model-Based Inference With Randomized Experiments

14.4 Design- and Model-Based Inferences With PS Designs

14.5 Statistical Issues With PS Designs in Practice

14.6 Discussion

Acknowledgments

References

Chapter 15: Adjustment when Covariates are Fallible

15.1 Introduction

15.2 Theoretical Framework

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

15.4 Approaches Accounting for Latent Covariates

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

15.6 Discussion

References

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

16.1 Introduction

16.2 Latent Class Analysis

16.3 Propensity Score Analysis

16.4 Empirical Demonstration

16.5 Discussion

Acknowledgments

References

Appendix

Part V: Designs for Causal Inference

Chapter 17: Can We Establish Causality With Statistical Analyses? The Example of Epidemiology

17.1 Why a Chapter On Design?

17.2 The Epidemiological Theory of Causality

17.3 Cohort and Case-Control Studies

17.4 Improving Control in Epidemiological Research

17.5 Conclusion: Control in Epidemiological Research Can Be Improved

References

Index

End User License Agreement

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Guide

Cover

Table of Contents

Begin Reading

List of Illustrations

Chapter 2: Evidence and Epistemic Causality

Figure 2.1 Trihoral relationships involving Canterbury (C), London (L), Gatwick (G), Dunkirk (D), Paris (P), and Orléans (O).

Chapter 3: Statistical Inference for Direction of Dependence in Linear Models

Figure 3.1 Estimated probability to conclude model (3.1) using tests based on skewness for , (shown respectively in panels (a), (b), (c), and (d)) and various values of , with Procedure A (Conditions 1–4), Procedure B (Conditions 1 and 4), and Procedure C (only Condition 4). A horizontal line at 5% is plotted as reference line. The numbers plotted refer to the probabilities reached with Procedure A.

Figure 3.2 Estimated probability to conclude model (3.1) using tests based on kurtosis for , (shown respectively in panels (a), (b), (c), and (d)) and various values of , with Procedure A (Conditions 1–4), Procedure B (Conditions 1 and 4), and Procedure C (only Condition 4). A horizontal line at 5% is plotted as reference line. The numbers plotted refer to the probabilities reached with Procedure A.

Figure 3.3 Estimated probability to conclude model (3.1) using tests based on kurtosis for , (shown respectively in panels (a), (b), (c), and (d)) and various values of , with Procedure A (Conditions 1–4), Procedure B (Conditions 1 and 4), and Procedure C (only Condition 4). A horizontal line at 5% is plotted as reference line. The numbers plotted refer to the probabilities reached with Procedure A.

Figure 3.4 Log body versus log brain for nine groups of species collected by Crile and Quiring (1940), together with Spearman's rho correlation, sample size , and -value associated to Spearman's test.

Figure 3.5 BCa bootstrap confidence intervals at the 95% level for the difference in absolute skewness (left panels), respectively, in absolute excess kurtosis (right panels), for nine groups of species, when calculated using all observations (top panels) and after removing 15 outliers (bottom panels). Estimated differences are plotted with a triangle when significant, with a circle when not significant.

Chapter 4: Directionality of Effects in Causal Mediation Analysis

Figure 4.1 Path diagrams for two mediation models with reversed causal directions.

Figure 4.2 Theoretical (solid lines) and empirical values (data points) of for as a function of , , and .

Figure 4.3 Theoretical (solid lines) and empirical values (data points) of for as a function of , , and .

Figure 4.4 Theoretical (solid lines) and empirical values (data points) of for as a function of , , and .

Figure 4.5 Type I error rates of the Pearson correlation test as a function of , , and . The dashed lines give Bradley's (1978) liberal robustness interval (2.5–7.5%); , , and .

Figure 4.6 Type I error rates of the Spearman correlation test as a function of , , and . The dashed lines give Bradley's (1978) liberal robustness interval (2.5–7.5%); , , and .

Figure 4.7 Type I error rates of the normal scores correlation test as a function of , , and . The dashed lines give Bradley's (1978) liberal robustness interval (2.5–7.5%); , , and .

Figure 4.8 Empirical power rates of the Pearson correlation test as a function of , , and ; , , and .

Figure 4.9 Empirical power rates of the Spearman correlation test as a function of , , and ; , , and .

Figure 4.10 Empirical power rates of the normal scores correlation test as a function of , , and ; , , and .

Figure 4.11 Pearson, Spearman, and normal scores correlations of estimated regression residuals and squared values of the corresponding predictor (Error bars give the 95% nonparametric bootstrap confidence interval).

Chapter 5: Direction of Effects in Categorical Variables: a Structural Perspective

Figure 5.1 Kernel density plots of (skewness = 2.81) and (skewness = 1.55).

Figure 5.2 Observed relative frequencies for and as a function of and .

Figure 5.3 Observed power for the model selection procedure, the two LR tests, the main effects and , and the interaction effect of the true model (for simplicity, we omitted the subscripts of the terms).

Figure 5.4 Power set of the three variables, , , and, (presented in the form of a Hasse diagram).

Figure 5.5 Hasse diagram of the power set of the two predictors, , , and the outcome variable .

Chapter 6: Directional Dependence Analysis Using Skew–Normal Copula-Based Regression

Figure 6.1 (=(0,0), ==1, =0.5, =(0,0)): (a) contour plot for ; (b) and (c) contour plots of the copula for and its copula density; (d) conditional distributions of the copula for , (left) and (right) where with the line types and colors range from solid/black (0.05) to dotdash/dark gray (0.5) to dotted/dim gray (0.95).

Figure 6.2 (=(0,0), ==1, =0.5, =(2,-4) ) - (a) contour plot for ; (b) and (c) contour plots of the copula for and its copula density; (d) conditional distributions of the copula for , (left) and (right) where with the line types and colors range from solid/black (0.05) to dotdash/dark gray (0.5) to dotted/dim gray (0.95).

Figure 6.3 (=(0,0), ==1, =0.5, =(-4,4) ) - (a) contour plot for ; (b) and (c) contour plots of the copula for and its copula density; (d) conditional distributions of the copula for , (left) and (right) where with the line types and colors range from solid/black (0.05) to dotdash/dark gray (0.5) to dotted/dim gray (0.95).

Figure 6.4 (a) Scatter plot of component scores of VAAA and PAAP and a fitted skew–normal density; (b) Q–Q plot.

Figure 6.5 Parametric estimation: (a) conditional regression plot, versus ; (b) copula-based regression estimate for VAAA, (solid line); (c) copula-based regression estimate for PAAP, (solid line).

Figure 6.6 Semiparametric estimation: (a) conditional regression plot, versus ; (b) copula-based regression estimate for VAAA, (solid line); (c) copula-based regression estimate for PAAP, (solid line).

Chapter 7: Non-Gaussian Structural Equation Models for Causal Discovery

Figure 7.1 Which of these two models, with opposing directions of causation, is better? The errors and may be dependent.

Figure 7.2 Which of the two models with opposing directions of causation is better? Here, the errors and are independent, which implies that Models 1 and 2 have no latent common causes.

Figure 7.3 Causal graphs of basic causal discovery models with no latent common causes.

Figure 7.4 Different causal directions give different data distributions.

Figure 7.5 An example of a causal graph for a cyclic SEM and its corresponding connection strength matrix.

Figure 7.6 A causal graph of LiNGAM for time series.

Figure 7.7 A causal LiNGAM graph with latent common causes and .

Figure 7.8 A causal graph to illustrate the idea of independent latent common causes.

Figure 7.9 The associated causal graphs of Models 1 and 2. For simplicity, only one latent common cause is shown in the causal graph.

Figure 7.10 Different causal directions give different data distributions.

Figure 7.11 LiNGAM with latent common causes ().

Figure 7.12 LiNGAM with observation-specific intercepts and ().

Chapter 8: Nonlinear Functional Causal Models for Distinguishing Cause from Effect

Figure 8.1 Illustration of the effect of the assumptions of linearity and Gaussianity on the identifiability. On the left, we have data generated for the causal direction , and on the right, data generated for the causal direction . The rows correspond to different models: (a) linear Gaussian model, (b) linear non-Gaussian model, (c) the nonlinear model, with two squaring nonlinearity in both directions, (d) the nonlinear model, with cubic root nonlinearity and cubic nonlinearity.

Chapter 9: Alternative Forms of Granger Causality, Heterogeneity, and Nonstationarity

Figure 9.1 Representation of the model described in Equation 9.15. Time-domain representation of the model with instantaneous effects (a) and corresponding frequency domain representation (b). Time-domain representation of the equivalent VAR(2) model (c) with corresponding frequency-domain representation (d).

Figure 9.2 Time-domain representation of the hybrid VAR(1) model given by Equation 9.17.

Figure 9.3 Hybrid VAR fit estimates for model given by Equation 9.17.

Figure 9.4 Standard VAR fit estimates for model given by Eq. 9.17.

Figure 9.5 Structural VAR fit estimates for model given by Equation 9.17.

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

Figure 10.1 Path diagrams for two linear autoregressive models, the right panel assumes that Granger-causes .

Figure 10.2 Path diagrams (upper panel) and the associated scoring matrices (lower panel) for the between item multidimensional model (left panel) and the within item multidimensional model (right panel).

Figure 10.3 Path diagrams for Embretson's MRMLC (left panel) and for Andersen's MRMRT (right panel).

Figure 10.4 An example of melting and knowledge of science from the SNAKE study.

Figure 10.5 Path diagrams for the two linear autoregressive models. Correlation and regression parameters are displayed for each path (the standard errors are given in parentheses; .

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

Figure 11.1 Causal structure from biological experiments for 19 selected genes.

Figure 11.2 The horizontal coordinate indicates the 48 time measurements and the vertical coordinate indicates 19 genes ordered. The color of the pixel corresponds to the value determined by the color scale on the right-hand side.

Figure 11.3 The considered gene regulatory network (a) and its reconstructions with LG3 (b) and MPR (c) in the circular layout.

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

Figure 12.1 Cross-lagged panel correlation model.

Figure 12.2 Reciprocal and autocausal effects models and bias of univariate regression. (a) Reciprocal effect with instrumental variable. (b) Autocausal effect. (c) Estimation of autocausal effect using phantom variable. (d) Bias of bivariate regression.

Figure 12.3 Autocausal model and estimates for drinking data. (a) Model parameters. (b) Unstandardized (fixed parameter). (c) Standardized (fixed parameter).

Figure 12.4 Examples of reciprocal and circular models. (a) Reciprocal model. (b) Circular model.

Figure 12.5 Autocausal effects for longitudinal data. (a) Model parameters. (b) Hypothetical values (autocauses set to equality).

Figure 12.6 Longitudinal growth model with autocausal effects Monte Carlo values.

Chapter 15: Adjustment when Covariates are Fallible

Figure 15.1 Design of the four-arm within-study comparison

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

Figure 16.1 Boxplots showing overlap of propensity score distributions for adolescent depression risk groups.

Chapter 17: Can We Establish Causality With Statistical Analyses? The Example of Epidemiology

Figure 17.1 Principle of Mendelian randomization: example of clarifying the causal direction between low cholesterol and cancer.

Figure 17.2 Principle of Mendelian randomization: example of clarifying the causal direction between low average volume of drinking and ischemic heart disease.

Figure 17.3 Principle of propensity score. (a) Risk of spousal violence from a traditional multivariate modeling perspective without PS. (b) Impact of arresting the offender calculated using PS.

List of Tables

Chapter 4: Directionality of Effects in Causal Mediation Analysis

Table 4.1 Linear Regression Results for Two Competing Mediation Models

Chapter 5: Direction of Effects in Categorical Variables: a Structural Perspective

Table 5.1 Empirical Type I Error Rates of Model Goodness of Fit Tests and the Selection Procedure Based on the Combined Model Fit Decisions

Table 5.2 Cross-Classification of , , and : Observed Frequencies and Predicted Frequencies, Estimated under Two Log-Linear Models

Chapter 6: Directional Dependence Analysis Using Skew–Normal Copula-Based Regression

Table 6.1 Estimates for Directional Dependence Measures and the 95% Nonparametric Bootstrap BCa Interval for (Number of Nonparametric Bootstrap Samples = 999)

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

Table 10.1 Scoring Matrix and Design Matrix for the Joint MRMLC and MRCML Models (see also Wang

et al.

, 1998)

Table 10.2 Scoring Matrix and Design Matrix for the Combination of MRMRT with MRCML Model for the Investigation of Granger Causation

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

Table 11.1 Quality Measures for the Considered Methods. The Number of the Causal Links in the Considered Gene Regulatory Network from Figure 11.1 Is 95. This Number Can Be Seen as the Maximal Possible Value for TP

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

Table 12.1 Monte Carlo Results for Detection of Unincluded Reciprocal Effects

Table 12.2 Example Mplus Model for Estimated Autocausal Effects

Table 12.3 Estimated Parameters Associated with Longitudinal Data on Alcohol Consumption and General Distress

Chapter 13: Log-Linear Causal Analysis of Cross-Classified Categorical Data

Table 13.1 Three Hypothetical Data Sets

Table 13.2 Analysis of Data Sets in Table 13.1

Table 13.3 Unweighted and Adjusted Frequencies of Happiness

Table 13.4 Multinomial Logit Models

Chapter 14: Design- and Model-Based Analysis of Propensity Score Designs

Table 14.1 Parametric Design-Based Analysis of PS Designs

Table 14.2 Model-Based Analysis of PS Designs

Chapter 15: Adjustment when Covariates are Fallible

Table 15.1 Correlation Between the Covariates and the Outcome Variable

Y

, the Treatment Variable

X

and the Fallible Covariate

(Pretest Eng)

Table 15.2 Difference in the Estimated Bias Using Manifest or Latent English Pretest Scores and Including Additional Relevant or Irrelevant Covariates in the Model

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

Table 16.1 Balance Table Showing Means/Proportions for Each Depression Risk Exposure Group and Standardized Mean Difference (Unweighted and Weighted) for All Potential Confounders

Table 16.2 Model Fit Statistics (Weighted) for Models With Measurement Parameters Freely Estimated and Constrained to Be Equal Across Gender

Table 16.3 The Four-Class Model of Young Adult Substance Use With Measurement Constrained to Be Equal Across Gender

Table 16.4 Average Causal Effect of Adolescent Depression Risk on Adult Substance Use Class

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Statistics and Causality

Methods for Applied Empirical Research

Edited by

Wolfgang Wiedermann

Alexander von Eye

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List of Contributors

Bethany C. BrayThe Methodology Center and The College of Health and Human Development, The Pennsylvania State University, University Park, PA, USA

Claus H. Carstensen Psychology and Methods of Educational Research, University of Bamberg, Bamberg, Germany

Yadolah Dodge Institute of Statistics, University of Neuchâtel, Neuchâtel, Switzerland

Ulrich Frick Department of Applied Psychology, HSD University of Applied Sciences, Cologne, Germany and Swiss Research Institute on Public Health and Addiction, University of Zurich, Zurich, Switzerland and Psychiatric University Hospital, University of Regensburg, Regensburg, Germany