This book focuses on a span of statistical topics relevant to researchers who seek to conduct person-specific analysis of human data. Our purpose is to provide one consolidated resource that includes techniques from disciplines such as engineering, physics, statistics, and quantitative psychology and outlines their application to data often seen in human research. The book balances mathematical concepts with information needed for using these statistical approaches in applied settings, such as interpretative caveats and issues to consider when selecting an approach.
The statistical topics covered here include foundational material as well as state-of-the-art methods. These analytic approaches can be applied to a range of data types such as psychophysiological, self-report, and passively collected measures such as those obtained from smartphones. We provide examples using varied data sources including functional MRI (fMRI), daily diary, and ecological momentary assessment data.
Features:
- Description of time series, measurement, model building, and network methods for person-specific analysis
- Discussion of the statistical methods in the context of human research
- Empirical and simulated data examples used throughout the book
- R code for analyses and recorded lectures for each chapter available via a link available at www.routledge.com/9781482230598
Across various disciplines of human study, researchers are increasingly seeking to conduct person-specific analysis. This book provides comprehensive information, so no prior knowledge of these methods is required. We aim to reach active researchers who already have some understanding of basic statistical testing. Our book provides a comprehensive resource for those who are just beginning to learn about person-specific analysis as well as those who already conduct such analysis but seek to further deepen their knowledge and learn new tools.
Author(s): Kathleen M. Gates, Sy-Miin Chow, Peter C. M. Molenaar
Series: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences
Publisher: CRC Press/Chapman & Hall
Year: 2023
Language: English
Pages: 259
City: Boca Raton
Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Acknowledgments
About the Authors
Notation Used
List of Abbreviations
1. Introduction
1.1. First Encounter with Intra-Individual Variation
1.1.1. Cattell’s Data Box
1.1.2. IAV in Psychology and Related Sciences
1.1.3. In What Areas Have the Studies of IAV Been Useful?
1.2. Statistical Analysis of IAV: An Overview of the Structure of This Book
1.2.1. Focus on Dynamic Factor Models
1.2.2. Focus on Replicated Multivariate Time Series
1.2.3. Focus on User-Friendly Model Selection and Estimation Approaches
1.2.4. Special Topic: Methods for Dealing with Heterogeneous Replications
1.2.5. Special Topic: Non-Stationary Dynamic Factor Models
1.2.6. Special Topic: Control Theory
1.2.7. Special Topic: Intersection of Network Science and IAV
1.3. Description of Exemplar Data Sets
1.3.1. Big Five Personality Daily Data
1.3.2. Fisher Data
1.3.3. The ADID Study
1.3.4. fMRI Data
1.4. Notation
1.5. Conclusion
References
Appendix:. Heuristic Introduction to Time Series Analysis for Psychologists
2. Ergodic Theory: Mathematical Theorems about the Relation between Analysis of IAV and IEV
2.1. Introduction
2.2. Some History Regarding Generalizability of IEV and IAV Results
2.3. Two Conceptualizations of Time Series
2.4. Some Preliminaries
2.5. When Is a System Ergodic?
2.6. Birkhoff's Theorem of Ergodicity
2.7. Heterogeneity as Cause of Non-Ergodicity
2.8. Example of a Non-Ergodic Process
2.9. Conclusion
References
3. P-Technique
3.1. The P-Technique Factor Model
3.2. The Structural Model of the Covariance Function of y(t) in P-Technique Factor Analysis
3.3. Conducting P-Technique Factor Analysis
3.3.1. Simulated Data
3.3.2. Constraints for Exploratory P-Technique Factor Analysis
3.3.3. Assessing Goodness of Fit
3.3.4. Alternative Indices of Model Fit
3.3.5. An Important Caveat
3.3.5.1. The Recoverability of P-Technique
3.3.5.2. Statistical Theory
3.3.5.3. Concluding Thoughts
3.3.6. Convention
3.3.7. Determining the Number of Factors in P-Technique Factor Analysis
3.3.8. Oblique Rotation to Simple Structure
3.3.9. Testing the Final Oblique P-Technique Two-Factor Model
3.3.10. Empirical Example
3.4. Conclusion
3.4.1. Statistical Background
3.4.2. Application of P-Technique to Empirical Data Sets
References
4. Vector Autoregression (VAR)
4.1. Brief Introduction to the Use of AR and VAR Analysis in the Study of Human Dynamics
4.2. Elementary Linear Models for Univariate Stationary Time
4.3. Stability and Stationarity
4.3.1. Technical Details Regarding Stability
4.3.2. Testing for Stability
4.3.3. Tests for Stationarity
4.4. Detrending Data
4.5. Univariate Order Selection
4.6. General VAR Model
4.7. Multivariate Order Selection
4.8. Testing of Residuals
4.9. Structural Vector Autoregression
4.10. Granger Causality
4.11. Discussion
References
5. Dynamic Factor Analysis
5.1. General Dynamic Factor Models
5.1.1. Process Factor Analysis
5.1.2. Shock Factor Analysis
5.2. Lag Order Selection
5.3. Estimation
5.3.1. SEM Estimation with Maximum Likelihood
5.3.1.1. Application 5.1: Exploratory SFA Estimated on Simulated Data with SEM
5.3.1.2. Application 5.2: PFA Estimated on Simulated Data with SEM
5.3.2. SEM with MIIV-2SLS Estimation
5.3.2.1. Application 5.3: PFA Estimated on Simulated Data with MIIV-2SLS
5.3.2.2. Application 5.4: PFA on fMRI Data
5.3.3. Raw Data Likelihood Approach
5.3.3.1. Application 5.4: PFA Estimated on Simulated Data with the Kalman Filter
5.4. Conclusions
References
6. Model Specification and Selection Procedures
6.1. Data-Driven Methods for Person-Specific Discovery of Relations among Variables
6.2. Filter Methods
6.3. Wrapper Methods
6.3.1. Wald’s Test
6.3.2. Likelihood Ratio Tests
6.3.3. Score Functions
6.3.4. Example: Automated Relation Selection Using Wrapper Methods
6.3.4.1. Model Search Procedure
6.3.4.2. Simulated Data Example
6.3.4.3. Empirical Data Example
6.3.5. Conclusion on Wrapper Approaches
6.4. Embedded Methods: Regularization
6.4.1. Exemplar Approach: Regularization in Graphical VAR
6.5. Problems with Individual-Level Searches
6.6. Data Aggregation Approaches
6.6.1. Exemplar Output of Aggregated Approaches
6.6.2. Issues with Traditional Forms of Aggregation
6.7. Replication Approaches: Group Iterative Multiple Model Estimation (GIMME)
6.7.1. Original GIMME
6.7.2. Hybrid GIMME
6.8. Conclusions
References
7. Models of Intra-Individual Variability with Time-Varying Parameters (TVPs)
7.1. The DFM(p,q,l,m,n) across N ≥ 1 Individuals
7.2. The DFM(p,q,l,m,n) with TVPs as a State-Space Model
7.3. Nonlinear State-Space Model Estimation Methods
7.3.1. Estimation Procedures
7.3.1.1. The Extended Kalman Filter (EKF) and the Extended Kalman Smoother (EKS)
7.3.1.2. Parameter Estimation
7.4. Observability and Controllability Conditions in TVPs
7.5. Possible Functions for Representing Changes in the TVPs
7.6. Illustrative Examples
7.6.1. DFM Model with Time-Varying Set-Point
7.6.2. DFM(p,q,0,1,0) with Time-Varying Set-Point and Cross-Regression Parameters
7.7. Closing Remarks
References
8. Control Theory Optimization of Dynamic Processes
8.1. Control Theory Optimization
8.2. Illustrative Simulation
8.3. Summary
References
9. The Intersection of Network Science and Intensive Longitudinal Analysis
9.1. Terminology
9.2. Network Measures
9.2.1. Summarizing Edge Values: Degree, Density, Weight, and Strength
9.2.2. Centrality Measures
9.2.3. Measures of Segregation and Integration
9.3. Community Detection Algorithms
9.3.1. Walktrap
9.4. Using Community Detection to Subgroup Individuals with Similar Dynamic Processes
9.4.1. Exemplar Method: Subgrouping GIMME
9.4.2. Community Detection Empirical Example: Identifying Subsets of Individuals
9.5. Assessing Robustness of Community Detection Solutions
9.5.1. Obtaining Random Networks
9.5.2. Approach 1: Identifying When Solution Changes
9.5.3. Approach 2: Evaluating Modularity
9.6. Community Detection and P-Technique
9.6.1. Community Detection Example: Identifying Subsets of Variables
9.7. Discussion
References
Index
