Dynamic Structural Equation Modeling of Intensive Longitudinal Data Using Mplus Version 8

Transcription

1 Dynamic Structural Equation Modeling of Intensive Longitudinal Data Using Mplus Version 8 (Part 1) Ellen L. Hamaker Utrecht University e.l.hamaker@uu.nl Tihomir Asparouhov & Bengt Muthén Muthén & Muthén PSMG, March 14, / 58

2 variables Cattell s data box 2 / 58

3 variables Cross-sectional research: N is large, T=1 3 / 58

4 variables Cattell s data box 4 / 58

5 Panel research: N is large, T is small 5 / 58

6 variables Cattell s data box 6 / 58

7 variables Time series data: N=1 and T is large 7 / 58

8 Time series analysis: Looking at the movie 8 / 58

9 Pioneers of idiographic research in psychology 9 / 58

10 Idiographic (N=1) research in psychology N=1 research has included: Cattell s P-technique: factor analysis of N=1 data Dynamic factor analysis: considering lagged relationships Measurement burst design: multiple waves of intensive measurements Intervention research: ABAB design etc. Critique of this kind of research: within-person fluctuations are just noise results are not generalizable no one has these data 10 / 58

11 New technology Smart phones Secure continuous remote alcohol monitor (SCRAM) Smart glasses Activity trackers Smart watches 11 / 58

12 Intensive longitudinal data Different forms of intensive longitudinal data: daily diary (DD); self-report end-of-day experience sampling method (ESM); self-report of subjective experience ecological momentary assessment (EMA); healthcare related self-report ambulatory assessment (AA); physiological measurements event-based measurements; self-report after a particular event observational measurements; expert rater For more info on methodology, check out: Seminar of Tamlin Conner and Joshua Smyth on YouTube ( Society for Ambulatory Assessment ( Life Data ( Quantified Self ( 12 / 58

13 Characteristics of these kind of data Data structure: one or more measurements per day typically for multiple days sometimes multiple waves (i.e., Nesselroade s measurement-burst design) Advantages of ESM, EMA and AA no recall bias high ecological validity physiological measures over a large time span monitoring of symptoms and behavior, with new possibilities for feedback and intervention (e-health and m-health) window into the dynamics of processes 13 / 58

14 A paradigm shift Taken from Hamaker and Wichers (2017) 14 / 58

15 Outline Modeling the dynamics of ILD Separating between-person and within-person variance Application 1: Daily negative affect and depressive symptomatology Application 2: Intervention study with ESM Conclusion 15 / 58

16 What is time series analysis? Time series analysis is a class of techniques that is used in econometrics, seismology, meteorology, control engineering, and signal processing. Main characteristics: N=1 technique T is large (say >50) concerned with trends, cycles and autocorrelation structure (i.e., serial dependency) goal: forecasting ( prediction) 16 / 58

17 Lags Y y 1 y 2 y 3 y 4 y 5 y 6 y 7 y 8... y T Y at lag 1 y 1 y 2 y 3 y 4 y 5 y 6 y 7... y T 1 y T Y at lag 2 y 1 y 2 y 3 y 4 y 5 y 6... y T 2 y T 1 y T 17 / 58

18 Partial autocorrelation function (PACF) Partial autocorrelation at lag k: The correlation between y t and y t k after removing the effect of the intermediate observations (i.e., y t 1 to y t k+1 ). Y Y at lag 1 Y at lag 2 y 1 y 2 y 3 y 4 y 5... y T y 1 y 2 y 3 y 4... y T 1 y T y 1 y 2 y 3... y T 2 y T 1 y T 18 / 58

19 Sequence, ACF and PACF White Noise process Series WN Series WN WN ACF Partial ACF Time Lag Lag First order AR process Series AR1 Series AR1 AR ACF Partial ACF Time Lag Lag Second order AR process Series AR2 Series AR2 AR ACF Partial ACF Time Lag Lag 19 / 58

20 Outline Modeling the dynamics of ILD Separating between-person and within-person variance Application 1: Daily negative affect and depressive symptomatology Application 2: Intervention study with ESM Conclusion 20 / 58

21 A fundamental problem in a nutshell Cross-sectional relationship Within-person relationship Between-person relationship P e r c e n t a g e o f t y p o s P e r c e n t a g e o f t y p o s P e r c e n t a g e o f t y p o s Number of words per minute Number of words per minute Number of words per minute Taken from Hamaker (2012). 21 / 58

22 Three perspectives on data Cross-sectional Within Between rho=.4 rho=.4 rho=.4 rho=.4 rho=.4 rho=.4 y x rho=.4 y y y x x rho=.4 rho=.8 rho=0 y y y y y y x x x rho=.4 rho=.8 rho=0 y y y x x x x x x x Taken from Hamaker (2012). 22 / 58

23 Number of typos Negative affect Current negative affect Between-person differences in within-person slopes β B β B =1 β B Typing speed Negative event Preceding negative affect Taken from Hamaker and Grasman (2014). In conclusion: To study within-person processes we need (intensive) longitudinal data to decompose observed variance into within and between to consider individual differences in within-person dynamics 23 / 58

24 Outline Modeling the dynamics of ILD Separating between-person and within-person variance Application 1: Daily negative affect and depressive symptomatology Application 2: Intervention study with ESM Conclusion 24 / 58

25 Data: Daily measurements of negative affect (NA) Data come from the COGITO study of the MPI in Berlin (based on Hamaker et al., in preparation). Here we consider the younger sample: aged individuals 100 daily measurements of negative affect (NA) Decomposition into a between part and a within part NA it = µ i + NA it where Between part: µ i is the individual s mean (i.e., baseline, trait, equilibrium) Within-part: NA it is the within-person centered (cluster-mean centered) score 25 / 58

26 Between versus within Here, the intraclass correlation is: σ 2 between σ 2 between + σ2 within =.64 meaning there is about twice as much variability between people as there is within people in these data. 26 / 58

27 person2 phi= ACF Partial ACF person person1 phi= ACF Partial ACF person Univariate multilevel AR(1) model Autoregressive part: NA it = φ i NA i,t 1 + ζ it where φ i is the autoregressive parameter (i.e., inertia, carry-over) ζ it is the innovation (residual, disturbance, dynamic error) (with ζ it N (0, σ 2 ζ)) Sequence ACF PACF State-space Time Lag Lag person1.lag1 Sequence ACF PACF State-space Time Lag Lag person2.lag1 27 / 58

28 Univariate multilevel AR(1) model Within level: AR(1) with random φ i NA it = φ i NA i,t 1 + ζ it ζ it N (0, σ 2 ) Parameters estimated at this level: residual variance σ 2 Between level: fixed and random effects [ ] µ i = γ µ + u 0i u0i MN φ i = γ φ + u 1i u 1i [[ ] [ ]] 0 ψ11, 0 ψ 21 ψ 22 Parameters estimated at this level: fixed effects (means): γ µ and γ φ random effects (variances): ψ 11 and ψ 22 relation between random effects (covariance): ψ / 58

29 Univariate multilevel AR(1) model 29 / 58

30 Mplus input 30 / 58

31 Mplus results: Trace plots 31 / 58

32 Mplus results: Parameter estimates 32 / 58

33 Dynamic multilevel mediation model Within level: AR(1) with random φ i NA it = φ i NA i,t 1 + ζ it ζ it N (0, σ 2 ) Between level: Mediation model µ i = γ µ + γ 01 CESDpre i + u 0i φ i = γ φ + γ 11 CESDpre i + u 1i CESDpost i = γ 20 + γ 21 CESDpre i + γ 22 µ i + γ 23 φ i + u 2i 33 / 58

34 Mplus input mediation model 34 / 58

35 Mplus output mediation model 35 / 58

36 Mplus output mediation model (continued) 36 / 58

37 Mediation model: Standardized results 37 / 58

38 Random variance (cf. Jongerling et al., 2015) Within level: AR(1) with random φ i NA it = φ i NA i,t 1 + ζ it ζ it N (0, σ 2 ) Where ζ is the innovation, consisting of: external influences reactivity to external influences Reasons to assume individual differences for σ 2 : individuals may differ with respect to the variability in exposure to external factors individuals may differ with respect to their reactivity to external influences (see reward experience and stress sensitivity research) Hence, we allow for a random innovation variance using a log normal distribution. 38 / 58

39 Random innovation variance Within level: AR(1) with random φ i NA it = φ i NA i,t 1 + ζ it ζ it N (0, σi 2 ) Between level: fixed and random effects µ i = γ µ + u 0i φ i = γ φ + u 1i log(σ 2 i ) = γ log(σ 2 ) + u 2i u 0i 0 ψ 11 u 1i MN 0, ψ 21 ψ 22 u 2i 0 ψ 31 ψ 32 ψ / 58

40 Mplus results 40 / 58

41 Mplus results (cf. Schuurman et al., 2016) 41 / 58

42 Mediation model with random innovation variance 42 / 58

43 Mediation model with random innovation variance 43 / 58

44 Mediation model with random innovation variance 44 / 58

45 Mediation model with random innovation variance 45 / 58

46 Bivariate model: Multilevel vector AR(1) model Decomposition, Within, Between 46 / 58

47 Bivariate model: Mplus code 47 / 58

48 Mplus results: Fixed, random, and standardized 48 / 58

49 Outline Modeling the dynamics of ILD Separating between-person and within-person variance Application 1: Daily negative affect and depressive symptomatology Application 2: Intervention study Conclusion 49 / 58

50 Intervention study with ESM When ESM is used in a randomized controlled trial, we can investigate whether treatment affects: means dynamics (e.g., autoregression) variability Here we use data from individuals with a history of depression and current residual depressive symptoms (Geschwind et al., 2011). Each ESM period consisted of 6 days, 10 beeps per day. Here we analyze 117 participants, where 56 received a mindfulness training between the two phases, and 61 served as controls. 50 / 58

51 Treatment effect on the within-person mean Decomposition into a between part and a within part Pre-treatment phase: y 1it = µ 1i + y1it Post-treatment phase: y 2it = µ 2i + y2it Between level µ 1i = α 1 + β 1 Group i + u 1i µ 2i = α 2 + µ 1i + β 2 Group i + u 2i β 1 are initial differences between the groups α 2 is the effect of time β 2 is the effect of treatment 51 / 58

52 Mplus results 52 / 58

53 Treatment effect on autoregression Within level Pre-treatment phase: y1it = φ 1iy1it + ζ it Post-treatment phase: y2it = φ 2iy2it + ζ it Between level: Pre-treatment phase µ 1i = α 1 + β 1 Group i + u 1i φ 1i = γ 1 + δ 1 Group i + v 1i We expect β 1 and δ 1 to be zero. Between level: Post-treatment phase µ 2i = α 2 + µ 1i + β 2 Group i + u 2i φ 2i = γ 2 + φ 1i + δ 2 Group i + v 2i α 2 and γ 2 represent the effects of time β 2 and δ 2 represent the effects of treatment 53 / 58

54 Mplus results 54 / 58

55 Mplus results (with fixed change in φ) 55 / 58

56 Outline Modeling the dynamics of ILD Separating between-person and within-person variance Application 1: Daily negative affect and depressive symptomatology Application 2: Intervention study with ESM Conclusion 56 / 58

57 Conclusion DSEM in Mplus version 8 offers many new modeling opportunities for analyzing ILD There are many additional options not covered here We are working on regime-switching extensions We (the research community) need to gain new knowledge about these models 57 / 58

58 References Asparouhov, Hamaker & Muthén (2017). Dynamic latent class analysis. Structural Equation Modeling: A Multidisciplinary Journal, 24, Asparouhov, Hamaker & Muthén (in preparation). Dynamic structural equation models. Hamaker (2012). Why researchers should think within-person : A paradigmatic rationale. In M. R. Mehl & T. S. Conner (Eds.). Handbook of Research Methods for Studying Daily Life, New York, NY: Guilford Publications. Hamaker, Asparouhov, Brose, Schmiedek & Muthén (in preparation). At the frontiers of modeling intensive longitudinal data: Dynamic structural equation models for the affective measurements from the COGITO study. Multivariate Behavioral Research. Hamaker & Grasman (2015). To center or not to center? Investigating inertia with a multilevel autoregressive model. Frontiers in Psychology, 5, Hamaker & Wichers (2017). No time like the present: Discovering the hidden dynamics in intensive longitudinal data. Current Directions in Psychological Science, 26, Jongerling, Laurenceau & Hamaker (2015). A multilevel AR(1) model: Allowing for inter-individual differences in trait-scores, inertia, and innovation variance. Multivariate Behavioral Research, 50, Schuurman, Ferrer, de Boer-Sonnenschein & Hamaker (2016). How to compare cross-lagged associations in a multilevel autoregressive model. Psychological Methods, 21, / 58