Dependent Data in Social Sciences Research: Forms, Issues, and Methods of Analysis

Preface
Acknowledgments
In Memoriam John J. McArdle, Jr. (1951–2022)
	References
Contents
About the Editors
Part I Growth Curve Modeling, Continuous Time Modeling and Dynamic Modeling
	1 Continuous Time Modeling in the Social Sciences: History and Philosophical Background
		1.1 Introduction
		1.2 Social Science Methodology After World War II
		1.3 Karl Jöreskog and the State Space Model Entering the Social Science Scene
		1.4 Stochastic Linear Time-Invariant Continuous-Time State Space Model in Social Science
		1.5 Some Philosophical Issues in Structural Equation and State Space Modeling
		1.6 Indirect Parameter Estimation Procedure Criticized and Replaced
		1.7 Some Recent Developments
			Toward a Flexible Direct SEM Procedure
			Hierarchical Bayesian Analysis
			Time-Varying Parameters
			Mediation Analysis
		1.8 Does Continuous Time Modeling Make Sense?
		1.9 Conclusion
		References
	2 Time in Latent Growth Curve Models
		2.1 Time in Social Science Research
			A Brief Introduction to Time as a Variable
		2.2 Outline of the Latent Growth Curve Model
			Overall Model
			The Basis Vector
			Effects of Intercept Location and Scaling of Growth Factor Basis
		2.3 Sampling-Time Variation (STV)
			Introduction to STV
				Sources of STV
				Effects and Importance of Time Binning with STV
			Handling STV in LGCMs
				Explicit Approaches
				Coding Examples for SEMs
				When You Must Use Time-Binned Data
		2.4 Conclusion
		References
	3 Score-Guided Recursive Partitioning of Continuous-Time Structural Equation Models
		3.1 Introduction
		3.2 Continuous-Time Models
		3.3 SEM Trees
			Recursive Partitioning
			The Score-Guided SEM Tree Algorithm
				Step 1: Template Model
				Step 2: Model Estimation
				Step 3: Covariate Testing
				Step 4: Covariate Selection
		3.4 Demonstration of Score-Guided CTSEM Trees
			SHARE Subsample
			CT Model
			CTSEM Trees
		3.5 Discussion
		References
	4 Studying the Interaction Between Harsh Parenting and the Child's Social Behavior Problems over Time Using Continuous Time Modeling
		4.1 Introduction
		4.2 Discrete Versus Continuous Time Modeling
			The Discrete Time Framework
			The Continuous Time Framework
		4.3 Method
			Sample and Participation Rates
			Measures
			Statistical Analyses
			Results
				Bivariate Correlations
				Continuous Time Model with Two Variables
				Continuous Time Model with Two Time-Independent Variables
				Continuous Time Model with Two Time-Independent Variables and One Additional Time-Independent Variable
		4.4 Discussion
		References
	5 A Variational Approach to Continuous Time Dynamic Models
		5.1 Introduction
		5.2 Machine Learning-Type Approach to Continuous Time Modeling
			Empirical Example
			Results
			Discussion
		Appendix
			ctsem Settings
			Reformulation of the Variational Stochastic Approach
		References
	6 Finite Mixture Models for an Underlying Beta Distribution with an Application to COVID-19 Data
		6.1 Introduction
		6.2 The Generalized Finite Mixture Model for an Underlying Beta Distribution
			Finite Mixture Models
			The Beta Distribution
			Finite Mixture Models for the Beta Distribution
		6.3 The R Package trajeR
		6.4 An Example with Simulated Data
		6.5 An Application to COVID-19 Data
			Data
			Model Selection
			Description of the Groups
			Predictors of Trajectory Group Membership
			Stringency as Time-Dependent Covariate
		6.6 Conclusion
		Appendix
		References
Part II Network Analysis and Causal Structure Learning
	7 What the Fuzz!? Leveraging Ambiguity in Dynamic Network Models
		7.1 Simulated Illustration
		7.2 Discussion
		References
	8 Causal Discovery with Hidden Variables Based on Non-Gaussianity and Nonlinearity
		8.1 Introduction
		8.2 Non-Gaussian and Nonlinear Models for Causal Discovery
		8.3 Causal Models with Unobserved Variables
		8.4 Causal Discovery for Observed Variables and Latent Factors
			Linear Mixed Causal Model
			LiNGAM for Latent Factors
		8.5 Conclusions
		References
	9 Direction of Dependence in Non-linear Models via Linearization
		9.1 Introduction
		9.2 Linearizable Regression Functions
		9.3 Distinguishing Cause and Effect in Linearized Models
			Higher Moments of Observed Variables
			Higher Moments of Residuals
			Independence Properties
			A Unified Framework
		9.4 Monte Carlo Simulation
		9.5 Results
			Type I Errors
			Statistical Power
		9.6 Real-World Data Example
		9.7 Discussion
		References
	10 Exploration of Dependence Structures in Longitudinal Categorical Data with Ordinal Responses
		10.1 Introduction
		10.2 Review on the Scaled Checkerboard Copula Regression Association Measure
			Checkerboard Copula
			Scaled Checkerboard Copula Regression Association Measure
			Statistical Inference
		10.3 Utility of SCCRAM for Ordinal Longitudinal Data
			Aspects of Ordinal Longitudinal Categorical Data
			Application of the SCCRAM to Ordinal Longitudinal Categorical Data
				Trend Data
				Panel Data
		10.4 Case Studies
			Abuse of Social Security Concern and Crime Concern in the Netherlands
			Marijuana and Alcohol Use in Adolescence
		10.5 Conclusion
		References
	11 Bayesian Network for Discovering the Potential Causal Structure in Observational Data
		11.1 Example: Effects of Social Adversity on Posttraumatic Stress and Mood Symptoms
			Method
				Participants
				Measures
				Analysis Strategies
			Results
				Causal Structure
				Parameter Learning and Model Validation
				Inferences
		11.2 Discussion
			Limitations
		Appendix A: Negative Social Events Scale
			Direction
		References
Part III Multilevel Analysis
	12 Missing Data in the Analysis of Multilevel and Dependent Data
		12.1 Missing Data in the Analysis of Multilevel and Dependent Data
		12.2 Multilevel Data
			Analysis of Multilevel Data
		12.3 Missing Data
			Missing Data Mechanisms
			Missing Data Patterns
		12.4 Multiple Imputation
			Specification of the Imputation Model
				Joint Modeling
				Sequential Modeling
				Fully Conditional Specification
			Challenge 1: Multilevel Structure
				Between- and Within-Group Effects
				Heterogeneous and Nonlinear Effects
			Challenge 2: Substantive Analysis Model
				SMC-JM, SMC-SM, and SMC-FCS
			Challenge 3: Auxiliary Variables
		12.5 Model-Based Methods
			Maximum-Likelihood Estimation
			Bayesian Estimation
			Model Specification
		12.6 Comparison of Imputation-Based and Model-Based Methods
		12.7 Example Analyses
			Example 1 (Homogeneous Case)
			Treatment of Missing Data
			Results
			Example 2 (Heterogeneous Case)
			Treatment of Missing Data
			Results
		12.8 Software
		12.9 Discussion
		Appendix
		Computer Code for Example 12.7
			JM
			FCS
			SMC-SM
			BE
		References
	13 Bootstrap Methods for Robust Multilevel Analysis
		13.1 An Overview of Bootstrap Methods
			Model Equation and Assumptions
			Basics of Bootstrap Methods
		13.2 Bootstrapping for Multilevel Models
			Types of Bootstrapping
			Parametric Bootstrap
			Residual Bootstrap
			Wild Bootstrap
			Cases Bootstrap
		13.3 Confidence Intervals
			Bootstrap Normal CI
			Basic/Hall's Percentile
			Studentized/Bootstrap-t CI
			Percentile CI
			Bias-Corrected and Bias-Corrected and Accelerated CI
			Comparing Different Bootstrap Confidence Intervals
		13.4 Illustration
			Parametric Bootstrap
			Residual Bootstrap
			Wild Bootstrap
			Cases Bootstrap
			Comparison
			Bootstrap CI with Transformation
			Software for Multilevel Bootstrap
		13.5 Summary
		References
	14 Investigating the Use of Robust Standard Errors to Account for Two-Way Clustering in Cross-Classified Data Structures
		14.1 Background on Cross-Classified Random Effects Models
			Cross-Classified Data Structures
		14.2 Ordinary Least Squares Regression with Cluster Robust Standard Errors (OLS-CRSE)
		14.3 CR2 Correction for a Small Number of Cluster
		14.4 The Current Study
		14.5 Methods
			Data Generating Process (DGP)
			Analytic Strategy
		14.6 Results
			Scenario 1: Complete Cross-Classification
			Scenario 2: Partial Cross-Classification
			Applied Example
		14.7 Discussion
		References
	15 Self-Normalized, Score-Based Tests of Parameter Heterogeneity in Mixed Models
		15.1 Score-Based Tests
		15.2 Self-Normalization
		15.3 Simulation
			Method
			Results
		15.4 Application
			Method
			Results
		15.5 General Discussion
			Extensions of Self-Normalization
			Weighted Statistics
			Computation
			Summary
		15.6 Computational Details
		References
	16 Statistical Power in Cross-Sectional Multilevel Experiments in Education
		16.1 Multilevel Randomized Designs
			The Sampling Design
			Clustering
			Types of Experimental Designs
		16.2 Cluster Randomized Designs
			Two Levels
			Illustrative Example
			Three Levels
			Illustrative Example
		16.3 Block Randomized Designs
			Two Levels
			Illustrative Example
			Three Levels
				Treatment at the Second Level
				Illustrative Example
				Treatment at the First Level
				Illustrative Example
		16.4 Unbalanced Designs
			Illustrative Example
		16.5 Optimal Sampling of Units in Balanced Designs
			Cluster Randomized Designs
			Illustrative Example
			Block Randomized Designs
				Treatment at the Second Level
				Illustrative Example
				Treatment at the First Level
				Illustrative Example
		16.6 The Impact of Sample Sizes on Power in Balanced Designs
		16.7 Discussion
		References
Part IV Longitudinal and Cross-Sectional Dependent Categorical Data Analysis and Discrete Sequence Analysis
	17 Exploring Temporal Pattern of Intergenerational Educational Mobility in Germany: An Application of Configural Frequency Analysis Using Weighted Prediction
		17.1 Introduction
			Educational Mobility
			Educational Expansion in Germany
			The German General Social Survey
		17.2 Methodological Considerations
			Sample, Data, and Weighting
			Variables for Pattern of Educational Attainment and Covariates
			Configuration Frequency Analysis and the Prediction Model
			Introducing Survey Weighting into CFA
		17.3 Summary of Research Questions and Methodological Procedures
		17.4 Results
		17.5 Discussion
			Effects of Weighted and Unweighted Analysis with Different CFA Models
			Educational Mobility in Germany
				Gender Differences in Educational Mobility
				Differences Between East and West Germany
		References
	18 Configural Frequency Analysis Under Multinormality
		18.1 The Four Steps of CFA
		18.2 Base Models of CFA
		18.3 Identification
		18.4 Data Example
		18.5 Discussion
		References
	19 Configural Frequency Analysis Under Multinormality in Incomplete Tables
		19.1 Estimating Probabilities Under the Assumption of Multinormality
		19.2 CFA Base Models that Consider Multinormality
		19.3 Data Example
		19.4 Discussion
		References
	20 Higher-Order Configural Frequency Analysis of Groups of Variables: Dependencies in Test Data
		20.1 Base Models for Two Groups of Variables
		20.2 Interpretation of Types and Antitypes in Higher-Order CFA of Groups of Variables
		20.3 Data Example
		20.4 Discussion
		References
	21 Visualization of Dependence in Multidimensional Contingency Tables with an Ordinal Dependent Variable via Copula Regression
		21.1 Introduction
		21.2 Review on the Copula Regressions for Multidimensional Contingency Tables
			Subcopula and Checkerboard Copula for Ordinal Contingency Tables
			Subcopula Regression and Checkerboard Copula Regression
		21.3 Statistical Inference
			Estimation
			Evaluation of the Prediction by the Estimated Copula Regression
		21.4 Case Studies
			Ice Cream Study
			Back Pain Data
			Three Mile Island (TMI) Accident Data
		21.5 Conclusion
		References
	22 Mental Health Symptom Profiles Over Time: A Three-Step Latent Transition Cognitive Diagnosis Modeling Analysis with Covariates
		22.1 Introduction
		22.2 Cognitive Diagnosis Modeling
			Model Formulation
			Three-Step Latent Transition CDM with Covariates
			Technical Details
		22.3 Methods
			Sample
			Measures
				Alcohol-Related Problems
				Psychological Symptoms
			Data Analysis
		22.4 Results
			Model Fit, Classification Without Correction, and CEP Matrix (Steps 1 and 2)
			Latent Logistic Regression (Step 3)
		22.5 Discussion
		Appendix
		References
Part V Longitudinal Modeling and Estimation of Missing Data
	23 Multiple Imputation of Longitudinal Data: A Comparison of Robust Imputation Methods Regarding Sample Size Requirements, with an Application to Corporal Punishment Data
		23.1 Introduction
		23.2 Theoretical Background
			Missing Values and Multiple Imputation
			Robust Imputation by Predictive Mean Matching
			Quantile Regression-Based Multiple Imputation
			Random Forest-Based Multiple Imputation
		23.3 Monte Carlo Simulation
			Evaluation Criteria
			Sample and Measures
			Procedure
			Results
		23.4 Application: Development of Corporal Punishment by Fathers over Time
			A Parallel Latent Growth Curve Model of Corporal Punishment and Children's Social Behaviour Problems
			A Cross-Lagged Panel Model of Corporal Punishment and Children's Social Behaviour Problems
		23.5 Discussion
			Predictive Mean Matching
			Random Forest-Based Multiple Imputation
			Quantile Regression-Based Multiple Imputation
		References
	24 Multiple Imputation of Incomplete Panel Data Based on a Piecewise Growth Curve Model: An Evaluation and Application to Juvenile Delinquency Data
		24.1 Introduction and Overview
		24.2 Theoretical Background
			Growth Modeling in a Nutshell
			Piecewise Growth Models
			Missing Data and Multiple Imputation
				Assumptions
		24.3 Multiple Imputation by a Piecewise Growth Model in mice
			Imputation by a Piecewise Growth Curve Model
		24.4 Monte Carlo Simulation
			Overview, Rationale and Aims of the Simulation
			Hypotheses
			Evaluation Criteria
			Results and Discussion
		24.5 Application
			Sample and Data
			Data Imputation and Analysis
			Results and Discussion
		24.6 Summary and Conclusions
			Implications for Applied Researchers
		References
	25 Impact of Inconsistent Imputation Models in Mediation Analysis with Clustered Data
		25.1 Introduction
		25.2 Methods
			Notation
			1-1-1 Multilevel Mediation Analysis Model
			Multiple Imputation
		25.3 Analytic Comparison of JM Versus FCS Imputation
			Population joint distribution
			Implied Conditional Distributions Under JM
			Individual Distributions Under FCS
			Bias Under JM and FCS
				Mediation Effect Estimate Under JM and FCS
		25.4 Simulation Study
			Data Generation
			Estimation and Evaluation Criteria
			Summary of the Results
		25.5 Discussion
		Appendix
			Derivation for -122, Yij, Mij|Xij, αY, αM
			Derivation of MLE Estimator for , , , and
			Derivation of f(Y|M, X) and E(Y|M, X) for FCS
			Derivation of f(M|Y, X) for FCS
			Derivation of f(M|X) and E(M|X) for FCS
			Derivation of f(Y,M|X) for JM
			Derivation of f(Y|X), E(Y|X), and f(M|X) for JM
			Derivation of f(Y|M,X) and E(Y|M,X) for JM
		References
	26 Ecological Momentary Assessment (EMA) Designs with Planned Missingness
		26.1 Ecological Momentary Assessment (EMA) Designs with Planned Missingness
			Planned Missingness Designs in the Literature
			Deterministic vs. Stochastic Change Models
			Current Investigation
		26.2 Method
			Simulation Design Characteristics
			Data Analysis and Outcome Measures
		26.3 Results
			LCM and MLM Results
				``Idealized'' Parameter Condition with Small Residual Variance and Large Explained Variance
				Empirically Based Parameter Condition with Large Residual Variance and Small Explained Variance
			AR(1) and MA(1) Results
			Fitting Misspecified Models
		26.4 Discussion
			Recommendations for Applied Researchers
			Limitations and Future Directions
		Appendix: Sample AR(1) and MA(1) Mplus Code
		References
Part VI Item-Response-Modeling for Dependent Data
	27 Variants of Estimating an IRT-Based Actor-Partner Interdependence Model (APIM) with R
		27.1 Introduction
			Self-Esteem and Relationship Satisfaction
			Variants of Modeling an APIM
			IRT Models
			IRT-Based APIM Using R
			Research Questions
		27.2 Methods
			Sample
			Measures
			Analytic Strategy
		27.3 Results
			Fit of IRT-Based Measurement Models
			Item Fit of IRT-Based Measurement Models
			The APIMs
		27.4 Discussion
		Scales
			The Rosenberg Self-Esteem Scale (RSES)
			The Relationship Assessment Scale (RAS)
		References
	28 Assessing Individual Change: A Comparison of Reliable Change Indices Based on Classical Test Theory and Various Item Response Theory Models
		28.1 General Introduction and Overview
		28.2 Assessment of Individual Change
			The Classical Reliable Change Index (RCI)
			IRT-Based Modeling of Individual Change
			Studies Comparing Classical and IRT-Based RCI
			Summary and Limitations of Present Studies
		28.3 Extending IRT-Based Approaches
			Candidate IRT Models
			Uni- Versus Multidimensional Calibration
			Research Questions
		28.4 Methods
			Sample
			Instrument
			Analytic Plan
		28.5 Results
			Fit of the IRT-Based Models
			Visual Inspection of Pre- and Post-Measures with the RCI
			Classifications of Change Based on Different RCIs
		28.6 Discussion
			Classical RCI Versus IRT-Based RCI
			Other Approaches for Evaluating Change
			Limitations
			Outlook
		References
Part VII Other Methods for the Analysis of Dependent Data
	29 Assessing Unobserved Within-Group Individual Differences
		29.1 Easily Observed, Often Difficult to Conceptualize
		29.2 Central Concerns in Mixture Model Approaches
			Are There Subpopulations and If So How Many?
			What Is the Shape of Each of the Subpopulations?
			How Are Subpopulations Functionally Related to One Another?
		29.3 Two Mixture Model Approaches
			The Height ``Lost Label'' Problem: A Standard Normal Mixture Solution
			The Cut-Point Model for Repeated Measures Settings
		29.4 Discussion
		References