Description
Taylor and Francis Ltd Analysis of Intra-Individual Variation 1st Edition 2022 Hardbound by Gates, Kathleen M.
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 provided as an online supplementRecorded lectures accompany each chapter 1. Introduction 1.1 First encounter with intra-individual variation. 1.2 Statistical Analysis of IAV: An overview of the structure of this book. 1.3 Description of exemplar data sets.1.4 Notation. 1.5 Conclusions. 2. Ergodic Theory: Mathematical theorems about the relation between 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 Birkhoff's theorem of ergodicity. 2.6 When is a system ergodic? 2.7 Heterogeneity as cause of non-ergodicity. 2.8 Example of a non-ergodic process. 2.9 Conclusions. 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. 3.4 Conclusions. 4. Vector Autoregression (VAR). 4.1 Brief introduction on 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. 4.4 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. 5. Dynamic Factor Analysis. 5.1 General dynamic factor models. 5.2 Lag order selection. 5.3 Estimation. 5.4 Conclusions. 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. 6.4 Embedded methods: Regularization. 6.5 Problems with individual-level searches. 6.6 Data aggregation approaches. 6.7 Group Iterative Multiple Model Estimation (GIMME) Approaches. 6.8 Conclusions. 7. Models of Intraindividual Variability with Time-Varying Parameters (TVPs). 7.1 The DFM(p,q,l,m,m) across N individuals. 7.2 The DFM(p,q,l,m,m) with TVPs as a state-space model. 7.3 Nonlinear state-space model estimation methods. 7.4 Observability and controllability conditions in TVPs. 7.5 Possible functions for representing changes in the TVPs. 7.6 Illustrative examples. 7.7 Closing remarks. 8. Control Theory Optimization of Dynamic Processes. 8.1 Control theory optimization. 8.2 Illustrative simulation. 8.3 Summary. 9. The Intersection of Network Science and IAV. 9.1 Terminology. 9.2 Network measures. 9.3 Community detection algorithms. 9.4 Using community detection to subgroup individuals with similar dynamic processes. 9.5 Assessing robustness of community detection solutions. 9.6 Community detection and P-technique. 9.7 Discussion.