About the Editors |
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xv | |
Notes on Contributors |
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xvii | |
Acknowledgments |
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xxi | |
Preface |
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xxiii | |
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Part I Fundamental Concepts of Direction Dependence |
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1 | (78) |
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1 From Correlation to Direction Dependence Analysis 1888-2018 |
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3 | (6) |
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3 | (1) |
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1.2 Correlation as a Symmetrical Concept of X and Y |
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4 | (1) |
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1.3 Correlation as an Asymmetrical Concept of X and Y |
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5 | (1) |
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1.4 Outlook and Conclusions |
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6 | (3) |
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6 | (3) |
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2 Direction Dependence Analysis: Statistical Foundations and Applications |
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9 | (38) |
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2.1 Some Origins of Direction Dependence Research |
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11 | (2) |
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2.2 Causation and Asymmetry of Dependence |
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13 | (1) |
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2.3 Foundations of Direction Dependence |
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14 | (15) |
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15 | (1) |
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2.3.2 DDA Component I: Distributional Properties of Observed Variables |
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16 | (3) |
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2.3.3 DDA Component II: Distributional Properties of Errors |
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19 | (1) |
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2.3.4 DDA Component III: Independence Properties |
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20 | (1) |
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2.3.5 Presence of Confounding |
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21 | (3) |
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2.3.6 An Integrated Framework |
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24 | (5) |
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2.4 Direction Dependence in Mediation |
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29 | (3) |
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2.5 Direction Dependence in Moderation |
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32 | (2) |
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2.6 Some Applications and Software Implementations |
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34 | (2) |
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2.7 Conclusions and Future Directions |
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36 | (11) |
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38 | (9) |
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3 The Use of Copulas for Directional Dependence Modeling |
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47 | (32) |
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3.1 Introduction and Definitions |
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47 | (4) |
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48 | (1) |
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3.1.2 Defining Directional Dependence |
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48 | (3) |
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3.2 Directional Dependence Between Two Numerical Variables |
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51 | (19) |
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52 | (7) |
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59 | (3) |
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3.2.3 An Alternative Approach to Directional Dependence |
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62 | (8) |
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3.3 Directional Association Between Two Categorical Variables |
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70 | (4) |
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3.4 Concluding Remarks and Future Directions |
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74 | (5) |
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75 | (4) |
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Part II Direction Dependence in Continuous Variables |
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79 | (104) |
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4 Asymmetry Properties of the Partial Correlation Coefficient: Foundations for Covariate Adjustment in Distribution-Based Direction Dependence Analysis |
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81 | (30) |
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4.1 Asymmetry Properties of the Partial Correlation Coefficient |
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84 | (2) |
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4.2 Direction Dependence Measures when Errors Are Non-Normal |
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86 | (3) |
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4.3 Statistical Inference on Direction Dependence |
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89 | (1) |
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4.4 Monte-Carlo Simulations |
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90 | (8) |
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4.4.1 Study I: Parameter Recovery |
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90 | (1) |
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91 | (1) |
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4.4.2 Study II: CI Coverage and Statistical Power |
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91 | (3) |
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4.4.2.1 Type I Error Coverage |
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94 | (1) |
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4.4.2.2 Statistical Power |
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94 | (4) |
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98 | (3) |
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101 | (10) |
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4.6.1 Relation to Causal Inference Methods |
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103 | (2) |
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105 | (6) |
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5 Recent Advances in Semi-Parametric Methods for Causal Discovery |
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111 | (20) |
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111 | (2) |
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5.2 Linear Non-Gaussian Methods |
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113 | (6) |
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113 | (2) |
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5.2.2 Hidden Common Causes |
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115 | (3) |
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118 | (1) |
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119 | (1) |
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5.2.5 Other Methodological Issues |
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119 | (1) |
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5.3 Nonlinear Bivariate Methods |
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119 | (6) |
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5.3.1 Additive Noise Models |
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120 | (1) |
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5.3.1.1 Post-Nonlinear Models |
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121 | (1) |
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5.3.1.2 Discrete Additive Noise Models |
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121 | (1) |
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5.3.2 Independence of Mechanism and Input |
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121 | (1) |
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5.3.2.1 Information-Geometric Approach for Causal Inference |
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122 | (1) |
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5.3.2.2 Causal Inference with Unsupervised Inverse Regression |
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123 | (1) |
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5.3.2.3 Approximation of Kolmogorov Complexities via the Minimum Description Length Principle |
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123 | (1) |
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5.3.2.4 Regression Error Based Causal Inference |
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124 | (1) |
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5.3.3 Applications to Multivariate Cases |
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125 | (1) |
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125 | (6) |
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126 | (5) |
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6 Assumption Checking for Directional Causality Analyses |
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131 | (36) |
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135 | (2) |
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136 | (1) |
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6.2 Assessment of Functional Form: Loess Regression |
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137 | (3) |
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6.3 Influential and Outlying Observations |
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140 | (1) |
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6.4 Directional Dependence Based on All Available Data |
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141 | (8) |
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6.4.1 Studentized Deleted Residuals |
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143 | (1) |
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143 | (1) |
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144 | (1) |
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145 | (1) |
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6.4.5 Results from Influence Diagnostics |
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145 | (3) |
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6.4.6 Directional Dependence Based on Factor Scores |
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148 | (1) |
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6.5 Directional Dependence Based on Latent Difference Scores |
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149 | (4) |
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6.6 Direction Dependence Based on State-Trait Models |
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153 | (3) |
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156 | (11) |
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163 | (4) |
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7 Complete Dependence: A Survey |
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167 | (16) |
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168 | (3) |
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7.2 Measure of Complete Dependence |
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171 | (6) |
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177 | (3) |
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7.4 Future Works and Open Problems |
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180 | (3) |
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181 | (2) |
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Part III Direction Dependence in Categorical Variables |
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183 | (82) |
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8 Locating Direction Dependence Using Log-Linear Modeling, Configural Frequency Analysis, and Prediction Analysis |
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185 | (34) |
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8.1 Specifying Directional Hypotheses in Categorical Variables |
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187 | (5) |
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8.2 Types of Directional Hypotheses |
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192 | (1) |
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8.2.1 Multiple Premises and Outcomes |
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192 | (1) |
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8.3 Analyzing Event-Based Directional Hypotheses |
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193 | (10) |
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8.3.1 Log-Linear Models of Direction Dependence |
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193 | (4) |
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8.3.1.1 Identification Issues |
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197 | (1) |
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8.3.2 Confirmatory Configural Frequency Analysis (CFA) of Direction Dependence |
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198 | (2) |
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8.3.3 Prediction Analysis of Cross-Classifications |
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200 | (2) |
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8.3.3.1 Descriptive Measures of Prediction Success |
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202 | (1) |
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203 | (6) |
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8.4.1 Log-Linear Analysis |
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205 | (1) |
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8.4.2 Configural Analysis |
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206 | (2) |
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8.4.3 Prediction Analysis |
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208 | (1) |
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8.5 Reversing Direction of Effect |
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209 | (3) |
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8.5.1 Log-Linear Modeling of the Re-Specified Hypotheses |
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209 | (1) |
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8.5.2 CFA of the Re-Specified Hypotheses |
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210 | (2) |
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8.5.3 PA of the Re-Specified Hypotheses |
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212 | (1) |
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212 | (7) |
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215 | (4) |
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9 Recent Developments on Asymmetric Association Measures for Contingency Tables |
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219 | (24) |
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219 | (1) |
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9.2 Measures on Two-Way Contingency Tables |
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220 | (5) |
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9.2.1 Functional Chi-Square Statistic |
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220 | (2) |
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9.2.2 Measures of Complete Dependence |
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222 | (1) |
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9.2.3 A Measure of Asymmetric Association Using Subcopula-Based Regression |
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223 | (2) |
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9.3 Asymmetric Measures of Three-Way Contingency Tables |
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225 | (12) |
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9.3.1 Measures of Complete Dependence for Three Way Contingency Table |
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225 | (7) |
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9.3.2 Subcopula Based Measure for Three Way Contingency Table |
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232 | (3) |
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235 | (2) |
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9.4 Simulation of Three-Way Contingency Tables |
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237 | (2) |
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9.5 Real Data of Three-Way Contingency Tables |
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239 | (4) |
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240 | (3) |
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10 Analysis of Asymmetric Dependence for Three-Way Contingency Tables Using the Subcopula Approach |
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243 | (22) |
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243 | (2) |
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10.2 Review on Subcopula Based Asymmetric Association Measure for Ordinal Two-Way Contingency Table |
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245 | (3) |
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10.3 Measure of Asymmetric Association for Ordinal Three-Way Contingency Tables via Subcopula Regression |
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248 | (5) |
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10.3.1 Subcopula Regression-Based Asymmetric Association Measures |
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248 | (3) |
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251 | (2) |
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253 | (7) |
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10.4.1 Sensitivity Analysis |
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253 | (4) |
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257 | (3) |
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260 | (5) |
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261 | (1) |
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10.A.1 The Proof of Proposition 10.1 |
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261 | (1) |
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262 | (3) |
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Part IV Applications and Software |
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265 | (114) |
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11 Distribution-Based Causal Inference: A Review and Practical Guidance for Epidemiologists |
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267 | (28) |
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267 | (1) |
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11.2 Direction of Dependence in Linear Regression |
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268 | (3) |
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11.3 Previous Epidemiologic Applications of Distribution-Based Causal Inference |
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271 | (2) |
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11.4 A Running Example: Re-Visiting the Case of Sleep Problems and Depression |
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273 | (1) |
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11.5 Evaluating the Assumptions in Practical Work |
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274 | (4) |
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275 | (1) |
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11.5.2 Testing Non-Normality |
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276 | (1) |
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11.5.3 Testing Independence |
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277 | (1) |
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11.6 Distribution-Based Causality Estimates for the Running Example |
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278 | (1) |
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11.7 Conducting Sensitivity Analyses |
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279 | (5) |
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11.7.1 Convergent Evidence from Multiple Estimators |
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279 | (1) |
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11.7.2 Simulation-Based Analysis of Robustness to Latent Confounding |
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279 | (2) |
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11.7.2.1 Obtain Data-Based Parameters |
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281 | (1) |
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11.7.2.2 Defining Parameters and Simulation Conditions |
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281 | (1) |
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11.7.2.3 Defining the Simulation Model |
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282 | (1) |
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11.7.2.4 Run Simulation and Interpret Results |
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283 | (1) |
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11.8 Simulation-Based Analysis of Statistical Power |
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284 | (4) |
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11.9 Triangulating Causal Inferences |
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288 | (3) |
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291 | (4) |
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292 | (3) |
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12 Determining Causality in Relation to Early Risk Factors for ADHD: The Case of Breastfeeding Duration |
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295 | (30) |
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298 | (6) |
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298 | (1) |
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12.1.1.1 Recruitment and Identification |
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298 | (1) |
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12.1.1.2 Parental Psychopathology |
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299 | (1) |
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12.1.1.3 Ethical Standards |
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300 | (1) |
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12.1.2 Exclusion Criteria |
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300 | (1) |
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12.1.2.1 Assessment of Breastfeeding Duration |
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300 | (1) |
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301 | (1) |
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12.1.3.1 Parental Education |
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301 | (1) |
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12.1.3.2 Primary Residence and Family Income |
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301 | (1) |
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12.1.3.3 Parental Occupational Status |
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301 | (1) |
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12.1.4 Data Reduction and Data Analysis |
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301 | (1) |
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301 | (1) |
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301 | (1) |
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302 | (2) |
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304 | (12) |
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12.2.1 Study Participant Demographic and Clinical Characteristics |
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304 | (12) |
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316 | (9) |
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317 | (1) |
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12.3.2 Question of Causality |
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317 | (1) |
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318 | (1) |
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318 | (7) |
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13 Direction of Effect Between Intimate Partner Violence and Mood Lability: A Granger Causality Model |
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325 | (26) |
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325 | (8) |
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13.1.1 Definitions and Frequency of IPV |
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326 | (3) |
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13.1.2 Depression, Mood and IPV |
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329 | (1) |
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13.1.2.1 Depression and IPV |
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329 | (1) |
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330 | (2) |
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332 | (1) |
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333 | (1) |
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333 | (1) |
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333 | (1) |
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13.2.2.1 Daily Diary Questions |
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333 | (1) |
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334 | (1) |
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334 | (7) |
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13.3.1 Data Consolidation |
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334 | (1) |
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13.3.2 Descriptive Statistics |
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335 | (1) |
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335 | (2) |
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13.3.4 Granger Causality Analyses |
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337 | (4) |
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341 | (10) |
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343 | (8) |
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14 On the Causal Relation of Academic Achievement and Intrinsic Motivation: An Application of Direction Dependence Analysis Using SPSS Custom Dialogs |
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351 | (28) |
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14.1 Direction of Dependence in Linear Regression |
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352 | (7) |
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14.1.1 Distributional Properties of x and y |
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353 | (1) |
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14.1.2 Distributional Properties of ex and ey |
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354 | (1) |
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14.1.3 Independence of Error Terms with Predictor Variable |
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355 | (1) |
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14.1.4 DDA in Confounded Models |
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356 | (1) |
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14.1.5 DDA in Multiple Linear Regression Models |
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356 | (3) |
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14.2 The Causal Relation of Intrinsic Motivation and Academic Achievement |
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359 | (4) |
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14.2.1 High School Longitudinal Study 2009 |
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360 | (3) |
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14.3 Direction Dependence Analysis Using SPSS |
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363 | (8) |
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14.3.1 Variable Distributions and Assumption Checks |
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363 | (3) |
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14.3.2 Residual Distributions |
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366 | (2) |
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14.3.3 Independence Properties |
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368 | (1) |
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14.3.4 Summary of DDA Results |
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369 | (2) |
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371 | (8) |
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14.4.1 Extensions and Future Work |
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372 | (1) |
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372 | (7) |
Author Index |
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379 | (16) |
Subject Index |
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395 | |