Intensive Longitudinal Analysis of Human Processes: Systems Approaches to Human Process Analysis

260 Pages·2023·15.606 MB·English

by  Kathleen M. Gates, Sy-Miin Chow, Peter C. M. Molenaar

Intensive Longitudinal
Analysis of Human Processes
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 that
outlines their application to data often seen in human research. The book bal-
ances mathematical concepts with information needed for using these statis-
tical 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 collect-
ed 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 net-
work 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 seek-
ing 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 sta-
tistical 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 knowl-
edge and learn new tools.
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Intensive Longitudinal Analysis of Human Processes
Kathleen M. Gates, Sy-Miin Chow, and Peter C. M. Molenaar
For more information about this series, please visit: https://www.routledge.
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book-series/CHSTSOBESCI
Intensive Longitudinal
Analysis of Human
Processes
Kathleen M. Gates
Department of Psychology, University of North Carolina
Sy-Miin Chow
Pennsylvania State University
Peter C. M. Molenaar
Pennsylvania State University
First edition published 2023
by CRC Press
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Library of Congress Cataloging-in-Publication Data
Names: Gates, Kathleen M., author. | Chow, Sy-Miin, author. | Molenaar, Peter
C. M., author.
Title: Intensive longitudinal analysis of human processes / Kathleen Gates,
Sy-Miin Chow, Peter C.M. Molenaar.
Description: First edition. | Boca Raton : Chapman & Hall/CRC Press, 2023.
| Series: Chapman & Hall/CRC statistics in the social and behavioral
sciences | Includes bibliographical references and index.
Identifiers: LCCN 2022022626 (print) | LCCN 2022022627 (ebook) | ISBN
9781482230598 (hardback) | ISBN 9781032354958 (paperback) | ISBN
9780429172649 (ebook)
Subjects: LCSH: Psychometrics. | Psychology--Statistical methods. | Human
behavior--Mathematical models.
Classification: LCC BF39 .G38 2023 (print) | LCC BF39 (ebook) | DDC
150.1/5195--dc23/eng/20220914
LC record available at https://lccn.loc.gov/2022022626
LC ebook record available at https://lccn.loc.gov/2022022627
ISBN: 9781482230598 (hbk)
ISBN: 9781032354958 (pbk)
ISBN: 9780429172649 (ebk)
DOI: 10.1201/9780429172649
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by KnowledgeWorks Global Ltd.
Access the support material: www.routledge.com/9781482230598
Contents
Preface ......................................................................................................................xi
Acknowledgments ..............................................................................................xiii
About the Authors ................................................................................................xv
Notation Used .....................................................................................................xvii
List of Abbreviations ..........................................................................................xix
1 Introduction .....................................................................................................1
1.1 First Encounter with Intra-Individual Variation ..............................1
1.1.1 Cattell’s Data Box .....................................................................2
1.1.2 IAV in Psychology and Related Sciences ..............................4
1.1.3 In What Areas Have the Studies of IAV
Been Useful? .............................................................................6
1.2 Statistical Analysis of IAV: An Overview of the Structure
of This Book .........................................................................................10
1.2.1 Focus on Dynamic Factor Models .......................................11
1.2.2 Focus on Replicated Multivariate Time Series ..................12
1.2.3 Focus on User-Friendly Model Selection and
Estimation Approaches .........................................................13
1.2.4 Special Topic: Methods for Dealing with
Heterogeneous Replications .................................................14
1.2.5 Special Topic: Non-Stationary Dynamic Factor Models .........14
1.2.6 Special Topic: Control Theory ..............................................15
1.2.7 Special Topic: Intersection of Network
Science and IAV ......................................................................15
1.3 Description of Exemplar Data Sets ...................................................16
1.3.1 Big Five Personality Daily Data ...........................................16
1.3.2 Fisher Data ..............................................................................16
1.3.3 The ADID Study .....................................................................17
1.3.4 fMRI Data ................................................................................17
1.4 Notation ................................................................................................18
1.5 Conclusion ............................................................................................18
References .......................................................................................................18
Appendix: Heuristic Introduction to Time Series Analysis for
Psychologists ..................................................................................................22
2 Ergodic Theory: Mathematical Theorems about the Relation
between Analysis of IAV and IEV ............................................................27
2.1 Introduction .........................................................................................27
2.2 Some History Regarding Generalizability of IEV
and IAV Results ...................................................................................28
v
vi Contents
2.3 Two Conceptualizations of Time Series ...........................................31
2.4 Some Preliminaries .............................................................................32
2.5 When Is a System Ergodic? ...............................................................36
2.6 Birkhoff’s Theorem of Ergodicity .....................................................37
2.7 Heterogeneity as Cause of Non-Ergodicity .....................................39
2.8 Example of a Non-Ergodic Process ..................................................41
2.9 Conclusion ............................................................................................44
References .......................................................................................................45
3 P-Technique ....................................................................................................49
3.1 The P-Technique Factor Model ..........................................................50
3.2 The Structural Model of the Covariance Function
of y(t) in P-Technique Factor Analysis ..............................................52
3.3 Conducting P-Technique Factor Analysis .......................................54
3.3.1 Simulated Data .......................................................................54
3.3.2 Constraints for Exploratory P-Technique
Factor Analysis .......................................................................55
3.3.3 Assessing Goodness of Fit ....................................................57
3.3.4 Alternative Indices of Model Fit ..........................................58
3.3.5 An Important Caveat .............................................................59
3.3.5.1 The Recoverability of P-Technique ......................60
3.3.5.2 Statistical Theory ....................................................60
3.3.5.3 Concluding Thoughts ............................................60
3.3.6 Convention ..............................................................................61
3.3.7 Determining the Number of Factors in P-Technique
Factor Analysis .......................................................................61
3.3.8 Oblique Rotation to Simple Structure .................................63
3.3.9 Testing the Final Oblique P-Technique Two-Factor
Model .......................................................................................64
3.3.10 Empirical Example .................................................................65
3.4 Conclusion ............................................................................................68
3.4.1 Statistical Background...........................................................68
3.4.2 Application of P-Technique to Empirical
Data Sets ..................................................................................69
References .......................................................................................................69
4 Vector Autoregression (VAR) .....................................................................73
4.1 Brief Introduction to the Use of AR and VAR
Analysis in the Study of Human Dynamics ...................................73
4.2 Elementary Linear Models for Univariate
Stationary Time ...................................................................................74
4.3 Stability and Stationarity ...................................................................78
4.3.1 Technical Details Regarding Stability ................................80
4.3.2 Testing for Stability ................................................................81
4.3.3 Tests for Stationarity ..............................................................81
Contents vii
4.4 Detrending Data ..................................................................................85
4.5 Univariate Order Selection ................................................................88
4.6 General VAR Model ............................................................................90
4.7 Multivariate Order Selection .............................................................93
4.8 Testing of Residuals ............................................................................95
4.9 Structural Vector Autoregression .....................................................96
4.10 Granger Causality ...............................................................................98
4.11 Discussion ............................................................................................99
References .....................................................................................................100
5 Dynamic Factor Analysis ..........................................................................103
5.1 General Dynamic Factor Models ....................................................104
5.1.1 Process Factor Analysis .......................................................105
5.1.2 Shock Factor Analysis .........................................................108
5.2 Lag Order Selection ..........................................................................109
5.3 Estimation ..........................................................................................109
5.3.1 SEM Estimation with Maximum Likelihood ..................110
5.3.1.1 Application 5.1: Exploratory SFA
Estimated on Simulated Data with SEM...........113
5.3.1.2 Application 5.2: PFA Estimated on
Simulated Data with SEM ...................................116
5.3.2 SEM with MIIV-2SLS Estimation .......................................118
5.3.2.1 Application 5.3: PFA Estimated on
Simulated Data with MIIV-2SLS ........................120
5.3.2.2 Application 5.4: PFA on fMRI Data ....................121
5.3.3 Raw Data Likelihood Approach ........................................121
5.3.3.1 Application 5.4: PFA Estimated on
Simulated Data with the Kalman Filter ............127
5.4 Conclusions ........................................................................................128
References .....................................................................................................128
6 Model Specification and Selection Procedures ....................................131
6.1 Data-Driven Methods for Person-Specific Discovery
of Relations among Variables ..........................................................132
6.2 Filter Methods....................................................................................133
6.3 Wrapper Methods .............................................................................134
6.3.1 Wald’s Test .............................................................................135
6.3.2 Likelihood Ratio Tests .........................................................135
6.3.3 Score Functions ....................................................................136
6.3.4 Example: Automated Relation Selection
Using Wrapper Methods.....................................................137
6.3.4.1 Model Search Procedure .....................................137
6.3.4.2 Simulated Data Example .....................................139
6.3.4.3 Empirical Data Example ......................................141
6.3.5 Conclusion on Wrapper Approaches ................................142
viii Contents
6.4 Embedded Methods: Regularization .............................................142
6.4.1 Exemplar Approach: Regularization
in Graphical VAR .................................................................144
6.5 Problems with Individual-Level Searches .....................................146
6.6 Data Aggregation Approaches ........................................................147
6.6.1 Exemplar Output of Aggregated
Approaches ...........................................................................147
6.6.2 Issues with Traditional Forms of
Aggregation ..........................................................................148
6.7 Replication Approaches: Group Iterative Multiple
Model Estimation (GIMME) ...........................................................150
6.7.1 Original GIMME ..................................................................151
6.7.2 Hybrid GIMME ....................................................................154
6.8 Conclusions ........................................................................................156
References .....................................................................................................157
7 Models of Intra-Individual Variability with Time-Varying
Parameters (TVPs) ......................................................................................161
7.1 The DFM(p,q,l,m,n) across N ≥ 1 Individuals .................................163
7.2 The DFM(p,q,l,m,n) with TVPs as a State-Space Model ................163
7.3 Nonlinear State-Space Model Estimation Methods .....................167
7.3.1 Estimation Procedures ........................................................168
7.3.1.1 The Extended Kalman Filter (EKF) and
the Extended Kalman Smoother (EKS) .............169
7.3.1.2 Parameter Estimation ..........................................171
7.4 Observability and Controllability Conditions
in TVPs ...............................................................................................173
7.5 Possible Functions for Representing Changes
in the TVPs .........................................................................................174
7.6 Illustrative Examples ........................................................................177
7.6.1 DFM Model with Time-Varying Set-Point .......................177
7.6.2 DFM(p,q,0,1,0) with Time-Varying Set-Point and
Cross-Regression Parameters .............................................183
7.7 Closing Remarks ...............................................................................188
References .....................................................................................................188
8 Control Theory Optimization of Dynamic Processes ........................193
8.1 Control Theory Optimization .........................................................194
8.2 Illustrative Simulation ......................................................................198
8.3 Summary ............................................................................................206
References .....................................................................................................206
9 The Intersection of Network Science and Intensive
Longitudinal Analysis ...............................................................................209
9.1 Terminology .......................................................................................209
Contents ix
9.2 Network Measures ............................................................................213
9.2.1 Summarizing Edge Values: Degree, Density, Weight,
and Strength .........................................................................213
9.2.2 Centrality Measures ............................................................215
9.2.3 Measures of Segregation and Integration ........................216
9.3 Community Detection Algorithms ................................................217
9.3.1 Walktrap ................................................................................219
9.4 Using Community Detection to Subgroup Individuals with
Similar Dynamic Processes .............................................................221
9.4.1 Exemplar Method: Subgrouping GIMME ........................222
9.4.2 Community Detection Empirical Example:
Identifying Subsets of Individuals ....................................224
9.5 Assessing Robustness of Community Detection Solutions ........225
9.5.1 Obtaining Random Networks ...........................................225
9.5.2 Approach 1: Identifying When Solution Changes ..........226
9.5.3 Approach 2: Evaluating Modularity .................................230
9.6 Community Detection and P-Technique .......................................230
9.6.1 Community Detection Example: Identifying Subsets
of Variables ............................................................................232
9.7 Discussion ..........................................................................................234
References .....................................................................................................234
Index .....................................................................................................................237