Introduction to Dynamic Structural Equation Modeling for Intensive Longitudinal Data

Dynamic Structural Equation Modeling (DSEM) is a powerful analytical tool used to analyze intensive longitudinal data, combining multilevel modeling, time series modeling, structural equation modeling, and time-varying effects modeling. By modeling correlations and changes over time at both individual and group levels, DSEM provides a comprehensive understanding of the dynamics within the data. Through examples like interpersonal neurobiology and research on empathy in the medical field, DSEM allows for nuanced insights into complex relationships and processes.

• DSEM
• Longitudinal Data
• Structural Equation Modeling
• Multilevel Modeling
• Time Series

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1. A GENTLE INTRODUCTION TO DYNAMIC STRUCTURAL EQUATION MODELING (DSEM) FOR INTENSIVE LONGITUDINAL DATA ANGELA B. BRADFORD SCHOOL OF FAMILY LIFE

2. DSEM USED TO ANALYZE INTENSIVE LONGITUDINAL DATA (ILD) COMBINES MULTILEVEL MODELING, TIME SERIES MODELING, STRUCTURAL EQUATION MODELING, AND TIME VARYING EFFECTS MODELING GOAL IS TO PARSE OUT AND MODEL THESE TYPES OF CORRELATIONS, GIVING A FULLER PICTURE OF THE DYNAMICS OF ILD UNLIKE CROSS-CLASSIFIED MODELING (I.E., LONG FORMAT GROWTH MODEL), IT ALLOWS YOU TO REGRESS A VARIABLE ON: OTHER VARIABLES AT THE SAME TIMEPOINT ITSELF AT A PREVIOUS TIMEPOINT OTHER VARIABLES AT PREVIOUS TIMEPOINT Asparouhov, T., Hamaker, E.L. & Muth n, B. (2017). Dynamic structural equation models. Technical Report. Version 3. Submitted for publication. Retrieved from https://www.statmodel.com/TimeSeries.shtml.

3. DSEM (CONT.) MODELS INTRA-INDIVIDUAL CHANGES OVER TIME ON LEVEL 1 AND ALLOWS THE PARAMETERS OF THESE CHANGES TO VARY ACROSS INDIVIDUALS ON LEVEL 2 USING RANDOM EFFECTS SAMPLES WITH MANY SUBJECTS (E.G., 200) AND FEW TIME POINTS (E.G., 20-50) PERFORM BETTER THAN THOSE WITH FEW SUBJECTS AND MANY TIME POINTS (IN TERMS OF BIASED SE AND POWER)

4. LAG CREATE A LAG VARIABLE Observation Variable (T) Lagged Variable (T-1) 1 2.68 2 2.90 2.68 3 3.12 2.90 4 3.11 3.12 5 3.67 3.11 6 3.84 3.67 CORRELATION BETWEEN THESE IS THE AUTOCORRELATION (REGRESS T ON T-1)

5. BETWEEN VS. WITHIN BETWEEN PART: INDIVIDUALS MEAN OVER TIME ON A VARIABLE (I.E., BASELINE); IN OTHER WORDS, THE OVER-TIME MEAN FOR EACH PERSON WITHIN PART: AN ESTIMATE OF INDIVIDUALS SCORE OVER TIME; WITHIN-PERSON CENTERED OR CLUSTER-MEAN CENTERED SCORE (DEVIATION FROM THE MEAN OVER TIME)

6. WITHIN- AND BETWEEN- PERSON PARTS WITHIN-PERSON/CLUSTER PART: MODELED WITH FIRST-ORDER AUTOREGRESSIVE MODEL T REGRESSED ON T-1 PHI IS THE ESTIMATED PARAMETER, RANGING BETWEEN 0 AND 1, AND IS CALLED INERTIA. THE CLOSER PHI IS TO 1, THE LONGER IT TAKES TO RECOVER FROM A CHANGE FROM THE INDIVIDUAL S MEAN. BETWEEN-PERSON/CLUSTER PART: AVERAGE ACROSS ALL INDIVIDUALS YOU HAVE THE MEAN AND THE PHI, MODELED AS A RANDOM EFFECTS

7. EXAMPLE INTERPERSONAL NEUROBIOLOGY SUGGESTS THAT ONE S PHYSIOLOGY CATCHES THERAPISTS SHOULD HAVE THE MOST REGULATORY INFLUENCE IN THE ROOM, THEREBY HELPING CLIENTS REGULATE RESEARCH ON EMPATHY IN THE MEDICAL PROFESSION SUGGEST THAT THE MOST EMPATHETIC PHYSICIANS HAVE PHYSIOLOGY THAT SYNCHRONIZES WITH THEIR CLIENTS SO, DOES THERAPIST AND CLIENT LAGGED PHYSIOLOGY PREDICT THERAPIST AND CLIENT PHYSIOLOGY?

8. T T physio (t-1) physio (t) W W physio (t) physio (t-1) H H physio (t) physio (t-1)

9. MPLUS INPUT (FOR MULTIVARIATE MODEL) CLUSTER = subjecID; Analysis: TYPE=TWOLEVEL RANDOM; ESTIMATOR=BAYES; biterations = (5000); bseed = 250; chain = 4; thin = 10; process=4; Model: %WITHIN% acTRSA|THRV7_23 ON pTHRV7_23; acTPEP|TIMP6_23 ON pTIMP6_23; acTSCL|TEDA4_23 ON pTEDA4_23; These are the autocorrelations of t regressed on t-1.

10. cHRSA_th|HHRV7_23 ON pTHRV7_23; cHPEP_th|HIMP6_23 ON pTIMP6_23; cHSCL_th|HEDA4_23 ON pTEDA4_23; pHHRV7_23 WITH pWHRV7_23 pTHRV7_23; pWHRV7_23 WITH pTHRV7_23; pHIMP6_23 WITH pWIMP6_23 pTIMP6_23; pWIMP6_23 WITH pTIMP6_23; pHEDA4_23 WITH pWEDA4_23 pTEDA4_23; pWEDA4_23 WITH pTEDA4_23; %BETWEEN% acTRSA WITH THRV7_23; acTPEP WITH TIMP6_23; acTSCL WITH TEDA4_23; These are the cross-lagged effects. These are correlations of variables at time t-1. These are the random slopes modeled above with the | symbol, correlated with the random mean at time t. OUTPUT: STANDARDIZED(cluster); RESIDUAL(cluster); TECH8; PLOT: type is plot2; type is plot3;

11. INTRACLASS CORRELATION (TYPE= TWOLEVEL BASIC), CALCULATED AS: BETWEEN VARIANCE/(BETWEEN+WITHIN VARIANCE) HOW MUCH VARIABILITY IS BETWEEN CLUSTERS (IN MEANS) VS. WITHIN Variable Correlation Variable Correlation Variable Correlation THRV7_23 0.27 TEDA4_23 0.07 TIMP6_23 0.29 WHRV7_23 0.51 WEDA4_23 0.02 WIMP6_23 0.38 HHRV7_23 0.56 HEDA4_23 0.05 HIMP6_23 0.46

12. CONVERGENCE AND MODEL FIT POTENTIAL SCALE REDUCTION (PSR) AS CLOSE TO 1.00 AS POSSIBLE NORMAL POSTERIOR PARAMETER DISTRIBUTION TRACE PLOTS SHOW CONVERGENCE MODEL FIT IS ASSESSED WITH DIC (AND RELATIVE FIT WITH DIC). LOWER IS BETTER. UNSTABLE/DIFFICULT TO COMPUTE IF LATENT VARIABLES ARE TREATED AS PARAMETERS COMPARING SAMPLE STATISTICS TO MODEL-ESTIMATED QUANTITIES

13. PARAMETER TRACE PLOTS SHOULD LOOK LIKE THIS:

14. MINE LOOK LIKE THIS

15. POSTERIOR PARAMETER DISTRIBUTIONS SHOULD LOOK LIKE THIS:

16. MINE LOOK LIKE THIS

17. SO I SHOULD BE RUNNING MORE ITERATIONS UNTIL I HAVE BETTER EVIDENCE OF CONVERGENCE. NOTE: MY PSR IS 1.002, WHICH IS GOOD, BUT MPLUS ALWAYS GIVE THIS WARNING: TECH8 TELLS YOU WHAT THE PSR IS AT EACH 100 ITERATIONS

18. RESULTS MODEL RESULTS Within Level PHHRV7_2 WITH PWHRV7_23 0.394 0.050 0.000 0.297 0.494 * PTHRV7_23 -0.257 0.034 0.000 -0.326 -0.193 * Posterior One-Tailed 95% C.I. Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance

19. Means PTEDA4_23 10.115 0.175 0.000 9.771 10.464 * PWEDA4_23 12.342 0.213 0.000 11.921 12.746 * PHEDA4_23 12.123 0.285 0.000 11.581 12.685 * PTHRV7_23 5.884 0.026 0.000 5.833 5.935 * PWHRV7_23 6.409 0.037 0.000 6.334 6.481 * PHHRV7_23 5.870 0.040 0.000 5.791 5.950 * PTIMP6_23 93.115 0.631 0.000 91.894 94.346 * PWIMP6_23 93.498 0.501 0.000 92.501 94.471 * PHIMP6_23 93.361 0.734 0.000 91.947 94.804 * Between Level ACTRSA WITH THRV7_23 -0.138 0.118 0.002 -0.465 -0.019 * ACTPEP WITH TIMP6_23 -4.656 5.695 0.010 -21.318 -0.331 * ACTSCL WITH TEDA4_23 -0.460 0.355 0.003 -1.447 -0.099 *

20. Means ACTRSA 0.110 0.053 0.019 0.006 0.215 * ACTPEP 0.346 0.103 0.001 0.161 0.571 * ACTSCL 0.695 0.058 0.000 0.580 0.809 * ACWRSA 0.214 0.055 0.000 0.104 0.323 * ACHRSA 0.192 0.047 0.000 0.095 0.283 * ACWPEP 0.274 0.109 0.001 0.095 0.525 * ACHPEP 0.245 0.114 0.006 0.056 0.506 * ACWSCL 0.751 0.047 0.000 0.656 0.841 * ACHSCL 0.719 0.054 0.000 0.605 0.817 * CTRSA_W 0.024 0.031 0.208 -0.035 0.087 CTPEP_W 0.005 0.047 0.457 -0.086 0.098 CTSCL_W 0.031 0.025 0.100 -0.018 0.082 CTRSA_H 0.008 0.030 0.394 -0.050 0.068 CTPEP_H 0.035 0.049 0.225 -0.053 0.141 CTSCL_H 0.047 0.035 0.070 -0.017 0.122

21. STANDARDIZED RESULTS CAN REQUEST STANDARDIZED RESULTS MPLUS USES WITHIN-PERSON STANDARDIZATION (AS YOU WOULD IF IT WERE TIME-SERIES ANALYSIS) ADD THIS LINE TO THE INPUT: OUTPUT: STANDARDIZED(CLUSTER); RESIDUAL(CLUSTER); STANDARDIZES BY CLUSTER AND THEN GIVES AVERAGE OF THOSE STANDARDIZED PARAMETERS R-SQUARE TELLS YOU AVERAGE ACROSS CLUSTERS ALSO GIVES WITHIN-CLUSTER RESULTS

22. THANK YOU!