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Direction Dependence in Statistical Modeling: Methods of Analysis [Kõva köide]

Edited by (Michigan State University, USA), Edited by , Edited by , Edited by
  • Formaat: Hardback, 432 pages, kõrgus x laius x paksus: 234x158x25 mm, kaal: 794 g
  • Ilmumisaeg: 28-Jan-2021
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119523079
  • ISBN-13: 9781119523079
Teised raamatud teemal:
  • Formaat: Hardback, 432 pages, kõrgus x laius x paksus: 234x158x25 mm, kaal: 794 g
  • Ilmumisaeg: 28-Jan-2021
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1119523079
  • ISBN-13: 9781119523079
Teised raamatud teemal:
"This edited book examines current methods for the statistical analysis of hypotheses that are compatible with direction dependence. The proposed book is divided in four parts, each consisting of two or more chapters, for a total of 14 chapters. The first part of this book introduces the fundamental concepts of direction dependence in statistical models. The authors provide a historical view on the origins of studying the direction of dependence in a regression line. Various classes of copulas with directional dependence properties are introduced. In addition, an introduction into copula regression functions and concomitants of order statistics in directional dependence modeling is given. Part II of the proposed book is devoted to recent developments andadvances in direction dependence modeling of continuous variables and contains six chapters. The author demonstrates the benefits of incorporating concepts of direction dependence to identify causal models. Part III of the proposed volume introduces direction dependence methods for the categorical variable case. Finally, Part IV of the proposed book is devoted to substantive theory and real-world applications and consists of four chapters. The author introduces custom dialogs and macros in SPSS to make direction dependence analysis accessible to applied empirical researchers."--

This edited book examines current methods for the statistical analysis of hypotheses that are compatible with direction dependence. The proposed book is divided in four parts, each consisting of two or more chapters, for a total of 14 chapters. The first part of this book introduces the fundamental concepts of direction dependence in statistical models. The authors provide a historical view on the origins of studying the direction of dependence in a regression line. Various classes of copulas with directional dependence properties are introduced. In addition, an introduction into copula regression functions and concomitants of order statistics in directional dependence modeling is given. Part II of the proposed book is devoted to recent developments and advances in direction dependence modeling of continuous variables and contains six chapters. The author demonstrates the benefits of incorporating concepts of direction dependence to identify causal models. Part III of the proposed volume introduces direction dependence methods for the categorical variable case. Finally, Part IV of the proposed book is devoted to substantive theory and real-world applications and consists of four chapters. The author introduces custom dialogs and macros in SPSS to make direction dependence analysis accessible to applied empirical researchers.

About the Editors xv
Notes on Contributors xvii
Acknowledgments xxi
Preface xxiii
Part I Fundamental Concepts of Direction Dependence
1(78)
1 From Correlation to Direction Dependence Analysis 1888-2018
3(6)
Yadolah Dodge
Valentin Rousson
1.1 Introduction
3(1)
1.2 Correlation as a Symmetrical Concept of X and Y
4(1)
1.3 Correlation as an Asymmetrical Concept of X and Y
5(1)
1.4 Outlook and Conclusions
6(3)
References
6(3)
2 Direction Dependence Analysis: Statistical Foundations and Applications
9(38)
Wolfgang Wiedemann
Xintong Li
Alexander von Eye
2.1 Some Origins of Direction Dependence Research
11(2)
2.2 Causation and Asymmetry of Dependence
13(1)
2.3 Foundations of Direction Dependence
14(15)
2.3.1 Data Requirements
15(1)
2.3.2 DDA Component I: Distributional Properties of Observed Variables
16(3)
2.3.3 DDA Component II: Distributional Properties of Errors
19(1)
2.3.4 DDA Component III: Independence Properties
20(1)
2.3.5 Presence of Confounding
21(3)
2.3.6 An Integrated Framework
24(5)
2.4 Direction Dependence in Mediation
29(3)
2.5 Direction Dependence in Moderation
32(2)
2.6 Some Applications and Software Implementations
34(2)
2.7 Conclusions and Future Directions
36(11)
References
38(9)
3 The Use of Copulas for Directional Dependence Modeling
47(32)
Engin A. Sungur
3.1 Introduction and Definitions
47(4)
3.1.1 Why Copulas?
48(1)
3.1.2 Defining Directional Dependence
48(3)
3.2 Directional Dependence Between Two Numerical Variables
51(19)
3.2.1 Asymmetric Copulas
52(7)
3.2.2 Regression Setting
59(3)
3.2.3 An Alternative Approach to Directional Dependence
62(8)
3.3 Directional Association Between Two Categorical Variables
70(4)
3.4 Concluding Remarks and Future Directions
74(5)
References
75(4)
Part II Direction Dependence in Continuous Variables
79(104)
4 Asymmetry Properties of the Partial Correlation Coefficient: Foundations for Covariate Adjustment in Distribution-Based Direction Dependence Analysis
81(30)
Wolfgang Wiedemann
4.1 Asymmetry Properties of the Partial Correlation Coefficient
84(2)
4.2 Direction Dependence Measures when Errors Are Non-Normal
86(3)
4.3 Statistical Inference on Direction Dependence
89(1)
4.4 Monte-Carlo Simulations
90(8)
4.4.1 Study I: Parameter Recovery
90(1)
4.4.1.1 Results
91(1)
4.4.2 Study II: CI Coverage and Statistical Power
91(3)
4.4.2.1 Type I Error Coverage
94(1)
4.4.2.2 Statistical Power
94(4)
4.5 Data Example
98(3)
4.6 Discussion
101(10)
4.6.1 Relation to Causal Inference Methods
103(2)
References
105(6)
5 Recent Advances in Semi-Parametric Methods for Causal Discovery
111(20)
Shohei Shimizu
Patrick Blobaum
5.1 Introduction
111(2)
5.2 Linear Non-Gaussian Methods
113(6)
5.2.1 LiNGAM
113(2)
5.2.2 Hidden Common Causes
115(3)
5.2.3 Time Series
118(1)
5.2.4 Multiple Data Sets
119(1)
5.2.5 Other Methodological Issues
119(1)
5.3 Nonlinear Bivariate Methods
119(6)
5.3.1 Additive Noise Models
120(1)
5.3.1.1 Post-Nonlinear Models
121(1)
5.3.1.2 Discrete Additive Noise Models
121(1)
5.3.2 Independence of Mechanism and Input
121(1)
5.3.2.1 Information-Geometric Approach for Causal Inference
122(1)
5.3.2.2 Causal Inference with Unsupervised Inverse Regression
123(1)
5.3.2.3 Approximation of Kolmogorov Complexities via the Minimum Description Length Principle
123(1)
5.3.2.4 Regression Error Based Causal Inference
124(1)
5.3.3 Applications to Multivariate Cases
125(1)
5.4 Conclusion
125(6)
References
126(5)
6 Assumption Checking for Directional Causality Analyses
131(36)
Phillip K. Wood
6.1 Epistemic Causality
135(2)
6.1.1 Example Data Set
136(1)
6.2 Assessment of Functional Form: Loess Regression
137(3)
6.3 Influential and Outlying Observations
140(1)
6.4 Directional Dependence Based on All Available Data
141(8)
6.4.1 Studentized Deleted Residuals
143(1)
6.4.2 Lever
143(1)
6.4.3 DFFITS
144(1)
6.4.4 DFBETA
145(1)
6.4.5 Results from Influence Diagnostics
145(3)
6.4.6 Directional Dependence Based on Factor Scores
148(1)
6.5 Directional Dependence Based on Latent Difference Scores
149(4)
6.6 Direction Dependence Based on State-Trait Models
153(3)
6.7 Discussion
156(11)
References
163(4)
7 Complete Dependence: A Survey
167(16)
Santi Tasena
7.1 Basic Properties
168(3)
7.2 Measure of Complete Dependence
171(6)
7.3 Example Calculation
177(3)
7.4 Future Works and Open Problems
180(3)
References
181(2)
Part III Direction Dependence in Categorical Variables
183(82)
8 Locating Direction Dependence Using Log-Linear Modeling, Configural Frequency Analysis, and Prediction Analysis
185(34)
Alexander von Eye
Wolfgang Wiedemann
8.1 Specifying Directional Hypotheses in Categorical Variables
187(5)
8.2 Types of Directional Hypotheses
192(1)
8.2.1 Multiple Premises and Outcomes
192(1)
8.3 Analyzing Event-Based Directional Hypotheses
193(10)
8.3.1 Log-Linear Models of Direction Dependence
193(4)
8.3.1.1 Identification Issues
197(1)
8.3.2 Confirmatory Configural Frequency Analysis (CFA) of Direction Dependence
198(2)
8.3.3 Prediction Analysis of Cross-Classifications
200(2)
8.3.3.1 Descriptive Measures of Prediction Success
202(1)
8.4 Data Example
203(6)
8.4.1 Log-Linear Analysis
205(1)
8.4.2 Configural Analysis
206(2)
8.4.3 Prediction Analysis
208(1)
8.5 Reversing Direction of Effect
209(3)
8.5.1 Log-Linear Modeling of the Re-Specified Hypotheses
209(1)
8.5.2 CFA of the Re-Specified Hypotheses
210(2)
8.5.3 PA of the Re-Specified Hypotheses
212(1)
8.6 Discussion
212(7)
References
215(4)
9 Recent Developments on Asymmetric Association Measures for Contingency Tables
219(24)
Xiaonan Zhu
Zheng Wei
Tonghui Wang
9.1 Introduction
219(1)
9.2 Measures on Two-Way Contingency Tables
220(5)
9.2.1 Functional Chi-Square Statistic
220(2)
9.2.2 Measures of Complete Dependence
222(1)
9.2.3 A Measure of Asymmetric Association Using Subcopula-Based Regression
223(2)
9.3 Asymmetric Measures of Three-Way Contingency Tables
225(12)
9.3.1 Measures of Complete Dependence for Three Way Contingency Table
225(7)
9.3.2 Subcopula Based Measure for Three Way Contingency Table
232(3)
9.3.3 Estimation
235(2)
9.4 Simulation of Three-Way Contingency Tables
237(2)
9.5 Real Data of Three-Way Contingency Tables
239(4)
References
240(3)
10 Analysis of Asymmetric Dependence for Three-Way Contingency Tables Using the Subcopula Approach
243(22)
Daeyoung Kim
Zheng Wei
10.1 Introduction
243(2)
10.2 Review on Subcopula Based Asymmetric Association Measure for Ordinal Two-Way Contingency Table
245(3)
10.3 Measure of Asymmetric Association for Ordinal Three-Way Contingency Tables via Subcopula Regression
248(5)
10.3.1 Subcopula Regression-Based Asymmetric Association Measures
248(3)
10.3.2 Estimation
251(2)
10.4 Numerical Examples
253(7)
10.4.1 Sensitivity Analysis
253(4)
10.4.2 Data Analysis
257(3)
10.5 Conclusion
260(5)
10.A Appendix
261(1)
10.A.1 The Proof of Proposition 10.1
261(1)
References
262(3)
Part IV Applications and Software
265(114)
11 Distribution-Based Causal Inference: A Review and Practical Guidance for Epidemiologists
267(28)
Tom Rosenstrom
Regina Garcia-Velazquez
11.1 Introduction
267(1)
11.2 Direction of Dependence in Linear Regression
268(3)
11.3 Previous Epidemiologic Applications of Distribution-Based Causal Inference
271(2)
11.4 A Running Example: Re-Visiting the Case of Sleep Problems and Depression
273(1)
11.5 Evaluating the Assumptions in Practical Work
274(4)
11.5.1 Testing Linearity
275(1)
11.5.2 Testing Non-Normality
276(1)
11.5.3 Testing Independence
277(1)
11.6 Distribution-Based Causality Estimates for the Running Example
278(1)
11.7 Conducting Sensitivity Analyses
279(5)
11.7.1 Convergent Evidence from Multiple Estimators
279(1)
11.7.2 Simulation-Based Analysis of Robustness to Latent Confounding
279(2)
11.7.2.1 Obtain Data-Based Parameters
281(1)
11.7.2.2 Defining Parameters and Simulation Conditions
281(1)
11.7.2.3 Defining the Simulation Model
282(1)
11.7.2.4 Run Simulation and Interpret Results
283(1)
11.8 Simulation-Based Analysis of Statistical Power
284(4)
11.9 Triangulating Causal Inferences
288(3)
11.10 Conclusion
291(4)
References
292(3)
12 Determining Causality in Relation to Early Risk Factors for ADHD: The Case of Breastfeeding Duration
295(30)
Joel T. Nigg
Diane D. Stadler
Alexander von Eye
Wolfgang Wiedemann
12.1 Method
298(6)
12.1.1 Participants
298(1)
12.1.1.1 Recruitment and Identification
298(1)
12.1.1.2 Parental Psychopathology
299(1)
12.1.1.3 Ethical Standards
300(1)
12.1.2 Exclusion Criteria
300(1)
12.1.2.1 Assessment of Breastfeeding Duration
300(1)
12.1.3 Covariates
301(1)
12.1.3.1 Parental Education
301(1)
12.1.3.2 Primary Residence and Family Income
301(1)
12.1.3.3 Parental Occupational Status
301(1)
12.1.4 Data Reduction and Data Analysis
301(1)
12.1.4.1 Parental ADHD
301(1)
12.1.4.2 Data Reduction
301(1)
12.1.4.3 Data Analysis
302(2)
12.2 Results
304(12)
12.2.1 Study Participant Demographic and Clinical Characteristics
304(12)
12.3 Discussion
316(9)
12.3.1 Limitations
317(1)
12.3.2 Question of Causality
317(1)
Acknowledgments
318(1)
References
318(7)
13 Direction of Effect Between Intimate Partner Violence and Mood Lability: A Granger Causality Model
325(26)
G. Anne Bogat
Alytia A. Levendosky
Jade E. Kobayashi
Alexander von Eye
13.1 Introduction
325(8)
13.1.1 Definitions and Frequency of IPV
326(3)
13.1.2 Depression, Mood and IPV
329(1)
13.1.2.1 Depression and IPV
329(1)
13.1.2.2 Mood and IPV
330(2)
13.1.3 Summary
332(1)
13.2 Methods
333(1)
13.2.1 Participants
333(1)
13.2.2 Measures
333(1)
13.2.2.1 Daily Diary Questions
333(1)
13.2.3 Procedures
334(1)
13.3 Results
334(7)
13.3.1 Data Consolidation
334(1)
13.3.2 Descriptive Statistics
335(1)
13.3.3 Model Development
335(2)
13.3.4 Granger Causality Analyses
337(4)
13.4 Discussion
341(10)
References
343(8)
14 On the Causal Relation of Academic Achievement and Intrinsic Motivation: An Application of Direction Dependence Analysis Using SPSS Custom Dialogs
351(28)
Xintong Li
Wolfgang Wiedemann
14.1 Direction of Dependence in Linear Regression
352(7)
14.1.1 Distributional Properties of x and y
353(1)
14.1.2 Distributional Properties of ex and ey
354(1)
14.1.3 Independence of Error Terms with Predictor Variable
355(1)
14.1.4 DDA in Confounded Models
356(1)
14.1.5 DDA in Multiple Linear Regression Models
356(3)
14.2 The Causal Relation of Intrinsic Motivation and Academic Achievement
359(4)
14.2.1 High School Longitudinal Study 2009
360(3)
14.3 Direction Dependence Analysis Using SPSS
363(8)
14.3.1 Variable Distributions and Assumption Checks
363(3)
14.3.2 Residual Distributions
366(2)
14.3.3 Independence Properties
368(1)
14.3.4 Summary of DDA Results
369(2)
14.4 Conclusions
371(8)
14.4.1 Extensions and Future Work
372(1)
References
372(7)
Author Index 379(16)
Subject Index 395
WOLFGANG WIEDERMANN is Associate Professor at the University of Missouri-Columbia. He received his Ph.D. in Quantitative Psychology from the University of Klagenfurt, Austria. His primary research interests include the development of methods for causal inference, methods to determine the causal direction of dependence in observational data, and methods for person-oriented research settings. He has edited books on advances in statistical methods for causal inference (with von Eye, Wiley) and new developments in statistical methods for dependent data analysis in the social and behavioral sciences (with Stemmler and von Eye).

DAEYOUNG KIM is Associate Professor of Mathematics and Statistics at the University of Massachusetts, Amherst. He received his Ph.D. from the Pennsylvania State University in Statistics. His original research interests were in likelihood inference in finite mixture modelling including empirical identifiability and multimodality, development of geometric and computational methods to delineate multidimensional inference functions, and likelihood inference in incompletely observed categorical data, followed by a focus on the analysis of asymmetric association in multivariate data using (sub)copula regression.

ENGIN A. SUNGUR has a B.A. in City and Regional Planning (Middle East Technical University, METU, Turkey), M.S. in Applied Statistics, METU, M.S. in Statistics (Carnegie-Mellon University, CMU) and Ph.D. in Statistics (CMU). He taught at Carnegie-Mellon University, University of Pittsburg, Middle East Technical University, and University of Iowa. Currently, he is a Morse-Alumni distinguished professor of statistics at University of Minnesota Morris. He is teaching statistics for more than 38 years, 29 years of which is at the University of Minnesota Morris. His research areas are dependence modeling with emphasis on directional dependence, modern multivariate statistics, extreme value theory, and statistical education.

ALEXANDER VON EYE is Professor Emeritus of Psychology at Michigan State University (MSU). He received his Ph.D. in Psychology from the University of Trier, Germany. He received his accreditation as Professional Statistician from the American Statistical Association (PSTATTM). His research focuses (1) on the development and testing of statistical methods for the analysis of categorical and longitudinal data, and for the analysis of direction dependence hypotheses. In addition (2), he is member of a research team at MSU (with Bogat, Levendosky, and Lonstein) that investigates the effects of violence on women and their newborn children. His third area of interest (3) concerns theoretical developments and applied analysis of person-orientation in empirical research.