12_IntraVarDynamics_041410

12_IntraVarDynamics_041410 - HDFS 597K April 13, 2010...

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1 INTRAINDIVIDUAL DYNAMICS: Extensions for Intraindividual Variabilit HDFS 597K April 13, 2010 Extensions for Intraindividual Variability J. Pol ock, Summertime: Number 9A, 1948 Modeling Process (Browne & Nesselroade, 2005) • The way we are today reflects, in part, what happened to us today • But also – the way we are today reflects, in part, what happened to us yesterday • sense of “history” or “memory” – P-technique • Modeling pure state constructs – Dynamic Factor Analysis • Modeling processes that occur over time Dynamic Factor Analysis (Molenaar, 1985) • Group of models combining P-technique factor analysis and time-series methods (Browne & Nesselroade, 2005) – P-Technique Factor Analysis: (Cattel et al., 1947) Identify latent variables that explain patterns in the relationships • Identify latent variables that explain patterns in the relationships among variables that are defined across occasions for a single person – Multivariate Time-Series: • Represent the between-occasion covariation (or between- occasion structure) [ ] 11 2 2 ... tt s t s t Z BB B e ζη η −− + + + + + F1 t M 2t M 3t M 1t U 3t U 2t U 1t F1 t-1 M 2t-1 M 3t-1 M 1t-1 U 2t-1 U 3t-1 U 1t-1 P-technique Model F2 t M 6t M 5t M 4t U 6t U 5t U 4t F2 t-1 M 4t-1 M 5t-1 M 6t-1 U 6t-1 U 5t-1 U 4t-1 Time t t-1 F1 t M 2t M 3t M 1t U 3t U 2t U 1t F1 t-1 M 2t-1 M 3t-1 M 1t-1 U 2t-1 U 3t-1 U 1t-1 Dynamic Factor Model (Molenaar, 1985) F2 t M 6t M 5t M 4t U 6t U 5t U 4t F2 t-1 M 4t-1 M 5t-1 M 6t-1 U 6t-1 U 5t-1 U 4t-1 Time t t-1 F1 t+1 F1 t M 2t+1 M 3t+1 M 1t+1 M 2t M 3t M 1t U 2t+1 U 3t+1 U 1t+1 U 3t U 2t U 1t F1 t-1 M 2t-1 M 3t-1 M 1t-1 U 2t-1 U 3t-1 U 1t-1 F1 t-2 F1 t-3 Dynamic Factor Model (Molenaar, 1985) F2 t F2 t+1 M 4t+1 M 5t+1 M 6t+1 M 6t M 5t M 4t U 6t+1 U 5t+1 U 4t+1 U 6t U 5t U 4t F2 t-1 M 4t-1 M 5t-1 M 6t-1 U 6t-1 U 5t-1 U 4t-1 F2 t-2 F2 t-3 Time t+1 t t-1 t-2 t-3
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2 E t L t P t A t U 3t U 2t U 1t E t-1 L t-1 P t-1 A t-1 U 2t-1 U 3t-1 U 1t-1 Dynamic Factor Analysis Lebo#1 CFA Model Fit: χ 2 = 50, df = 32, RMSEA = .069 1.0 -.65 .31 .44 .47 .18 .05 .14 F t W 6t T t S t U 6t U 5t U 4t F t-1 S t-1 T t-1 W t-1 U 6t-1 U 5t-1 U 4t-1 Time t t-1 • Additional Assumptions: – Equally spaced observations – Stochasticity .58 .82 .51 1.0 .26 .28 .21 F1 t+1 F1 t M 2 M 3 M 1 M 2 M 3 M 1 U 2 U 3 U 1 U 3 U 2 U 1 F1 t-1 M 2 M 3 M 1 U 2 U 3 U 1 F1 t-2 F1 t-3 Dynamic Factor Model (McArdle, 1982) F2 t F2 t+1 M 4 M 5 M 6 M 6 M 5 M 4 U 6 U 5 U 4 U 6 U 5 U 4 F2 t-1 M 4 M 5 M 6 U 6 U 5 U 4 F2 t-2 F2 t-3 Time t+1 t t-1 t-2 t-3 State Space Model F1 t+1 F1 t M 2 M 3 M 1 M 2 M 3 M 1 U 2 U 3 U 1 U 3 U 2 U 1 F1 t-1 M 2 M 3 M 1 U 2 U 3 U 1 F1 t-2 F1 t-3 Dynamic Factor Model (DAFS Specification) F2 t F2 t+1 M 4 M 5 M 6 M 6 M 5 M 4 U 6 U 5 U 4 U 6 U 5 U 4 F2 t-1 M 4 M 5 M 6 U 6 U 5 U 4 F2 t-2 F2 t-3 Time t+1 t t-1 t-2 t-3 “Dynamic Interactions” in Ecological Context Bronfenbrenner (1979) G. Uecker, Aschekreis , 1987 (1917-2005) Development in Ecological Context
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12_IntraVarDynamics_041410 - HDFS 597K April 13, 2010...

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