1. 1crm da. KU. edu Todd D. Little University of Kansas Director, Quantitative Training Program Director, Center for Research Methods and Data Analysis Director, Undergraduate Social and Behavioral Sciences Methodology Minor Member, Developmental Psychology Training Program crmda. KU.edu Workshop presented 05-24-2012 @ University of Turku, Finland Special Thanks to: Ihno Lee, Chapter co-author in Handbook. Dynamic P-Technique Structural Equation Modeling Dynamic P-Technique Structural Equation Modeling

2. www.crmda.ku.edu2 Cattells Data Box Cattell invented the Box to help us think outside the box Given the three primary dimensions of variables, persons, and occasions, at least 6 different structural relationships can be utilized to address specific research questions

3. www.crmda.ku.edu3 Cattells Data Box Occasions of Measurement Variables (or Tests) Persons (or Entities)

4. www.crmda.ku.edu4 Cattells Data Box R-Technique: Variables by Persons Most common Factor Analysis approach Q-Technique: Persons by Variables Cluster analysis – subgroups of people P-Technique: Variables by Occasions Intra-individual time series analyses O-Technique: Occasions by Variables Time-dependent (historical) clusters S-Technique: People by Occasions People clustering based on growth patterns T-Technique: Occasions by People Time-dependent clusters based on people

5. www.crmda.ku.edu5 Michael Lebos Example Data Lebo asked 5 people to rate their energy for 103 straight days The 5 folks rated their energy on 6 items using a 4 point scale: Active, Lively, Peppy Sluggish, Tired, Weary A priori, we would expect two constructs, positive energy and negative energy

6. www.crmda.ku.edu6 Lag 0 Observational RecordO 1 O 2 O 3 O 4 O n O n O n O n Selected Variables V P-Technique Data Setup

7. www.crmda.ku.edu7 Multivariate Time-series (Multiple Variables x Multiple Occasions for 1 Person)

8. www.crmda.ku.edu8 1 st 15 days for Subject 4, Lag 0 1 111 212 2 333 011 3 111 333 4 333 011 5 233 111 6 333 111 7 344 000 8 222 111 9 222 111 10 333 001 11 434 011 12 101 443 13 343 111 14 334 111 15 110 343 The Obtained Correlations All Days Positive Items Negative Items 1.000 0.849 1.000 0.837 0.864 1.000 -0.568 -0.602 -0.660 1.000 -0.575 -0.650 -0.687 0.746 1.000 -0.579 -0.679 -0.724 0.687 0.786 1.000

9. www.crmda.ku.edu9 Var 1 Var 2 Three Indicators of the Same Construct in a Time Series Var 3 Time

10. www.crmda.ku.edu10 L15.1.s1.Lag0.LS8 PositiveNegative 1.15.99.86.811.27.92 -.19 (-.64) ActiveWearyTiredSluggishPeppyLively.19.56 Model Fit: χ 2 (8, n=101) = 9.36, p =.31, RMSEA =.039 (.000;.128), TLI/NNFI =.994, CFI=.997 X.88.52

11. www.crmda.ku.edu11 L15.1.s2.Lag0.LS8 PositiveNegative 1.041.10.86.921.031.05 -.74 (-.65) ActiveWearyTiredSluggishPeppyLively.931.43 Model Fit: χ 2 (8, n=101) = 8.36, p =.40, RMSEA =.014 (.000;.119), TLI/NNFI =.999, CFI=.999 X 1.09.96

12. www.crmda.ku.edu12 L15.1.s3.Lag0.LS8 PositiveNegative 1.071.11.83.731.171.10 -.21 (-.43) ActiveWearyTiredSluggishPeppyLively.77.32 Model Fit: χ 2 (8, n=101) = 9.70, p =.31, RMSEA =.050 (.000;.134), TLI/NNFI =.992, CFI=.997 X 1.26.28

13. www.crmda.ku.edu13 L15.1.s4.Lag0.LS8 PositiveNegative.911.011.08.951.051.00 -.82 (-.81) ActiveWearyTiredSluggishPeppyLively.971.05 Model Fit: χ 2 (8, n=101) = 14.6, p =.07, RMSEA =.084 (.000;.158), TLI/NNFI =.983, CFI=.991 X 1.861.05

14. www.crmda.ku.edu14 L15.1.s5.Lag0.LS8 PositiveNegative 1.03.961.02.081.671.25 -.59 (-.60) ActiveWearyTiredSluggishPeppyLively 1.19.81 Model Fit: χ 2 (8, n=101) = 5.11, p =.75, RMSEA =.000 (.000;.073), TLI/NNFI = 1.02, CFI=1.0 X 1.151.03

15. www.crmda.ku.edu15 Measurement Invariance by Participant Model χ2 df p RMSEA 90% CI TLI/NNFI CFI Constraint Tenable Null 3351.349 123<.001------ - ------------ Configural47.16140.203.038.000-.0820.993 0. 998--- Invariance Loading166.39256<.001.137.113-.1620.9250.966No Invariance Intercept 373.73872<.001.192.172-.2130.8430.907No Invariance Partial 90.25563<.014.063.025-.0920.9840.982Yes Invariance (L3.alternative null fit.xls) (L15.s1-s5.0.Lag0.null) (L15.s1-s5.1.Lag0.config) (L15.s1-s5.2.Lag0.weak) (L15.s1-s5.3.Lag0.partial) (L15.s1-s5.4.Lag0.strong)

16. www.crmda.ku.edu16 Some Thoughts The partial invariance across persons highlights the ideographic appeal of p- technique Nomothetic comparisons of the constructs is doable, but the composition of the constructs is allowed to vary for some persons (e.g., person 5 did not endorse sluggish). In fact, Nesselroade has an idea that turns the concept of invariance on its head

17. www.crmda.ku.edu17 Dynamic P-Technique Setup

18. www.crmda.ku.edu18 C 12 C 13 CL 21* CL 12* C 1*3* C 2*3* C 1*2* CL 13* CL 23* CL 31* CL 32* AR 11* AR 22* AR 33* C 23 2 1 2 2 2 3 2 1* 2 2* 2 3* Variable 1 Variable 2 Variable 3 Variable 1* Variable 2* Variable 3* Variable 1Variable 2Variable 3Variable 1*Variable 2*Variable 3* Lag 0Lag 1 A Lagged Covariance Matrix AR = Autoregressive Correlation CL = Cross-lagged Correlation C = Within Lag Covariance

19. www.crmda.ku.edu19 1 st 15 days for Subject 4, 3 Lags 1 111 212 333 011 111 333 2 333 011 111 333 333 011 3 111 333 333 011 233 111 4 333 011 233 111 333 111 5 233 111 333 111 344 000 6 333 111 344 000 222 111 7 344 000 222 111 222 111 8 222 111 222 111 333 001 9 222 111 333 001 434 011 10 333 001 434 011 101 443 11 434 011 101 443 343 111 12 101 443 343 111 334 111 13 343 111 334 111 110 343 14 334 111 110 343 444 000 15 110 343 444 000 333 120

20. www.crmda.ku.edu20 L15.4.s4.3lags: Subject 4 Negative Lag 0 Positive 1* Negative Lag 1.84 Positive Lag 1.95 Negative Lag 2.82 Positive Lag 2.95 -.79-.88.65.23.65.23.36 Model Fit: χ 2 (142, n=101) = 154.3, p =.23; RMSEA =.02; TLI/NNFI =.99 (Initial model: L15.3.s4.3lags)

21. www.crmda.ku.edu21 L15.4.s1.3lags: Subject 1 Negative Lag 0 Positive 1* Negative Lag 1.94 Positive Lag 1 1 Negative Lag 2.94 Positive Lag 2 1 -.64-.66.24 Model Fit: χ 2 (144, n=101) = 159.9, p =.17; RMSEA =.05; TLI/NNFI =.99 (Initial model: L15.3.s1.3lags)

22. www.crmda.ku.edu22 L15.4.s5.3lags: Subject 5 Negative Lag 0 Positive 1* Negative Lag 1 1 Positive.94 Negative Lag 2.94 Positive Lag 2.94 -.61-.66.24 Model Fit: χ 2 (143, n=101) = 93.9, p =.99; RMSEA =.00; TLI/NNFI = 1.05.24 (Initial model: L15.3.s5.3lags)

23. www.crmda.ku.edu23 L15.4.s3.3lags: Subject 3 Negative Lag 0 Positive 1* Negative Lag 1.94 Positive Lag 1 1 Negative Lag 2.92 Positive Lag 2.88 -.41-.51.24.37.31 Model Fit: χ 2 (142, n=101) = 139.5, p = 1.0; RMSEA =.0; TLI/NNFI = 1.0 (Initial model: L15.3.s3.3lags)

24. www.crmda.ku.edu24 L15.4.s2.3lags: Subject 2 Negative Lag 0 Positive 1* Negative Lag 1.95 Positive Lag 1.95 Negative Lag 2.91 Positive Lag 2.94 -.63.24 -.17 -.24 Model Fit: χ 2 (142, n=101) = 115.2, p =.95; RMSEA =.0; TLI/NNFI = 1.0 (Initial model: L15.3.s2.3lags)

25. www.crmda.ku.edu25 As Represented in Growth Curve Models How does mood fluctuate during the course of a week? Restructure chained, dynamic p-technique data into latent growth curve models of daily mood fluctuation Examine the average pattern of growth Variability in growth (interindividual variability in intraindividual change)

26. www.crmda.ku.edu26 Weekly Growth Trends Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Carrig, M., Wirth, R.J., & Curran, P.J. (2004)Carrig, M., Wirth, R.J., & Curran, P.J. (2004). A SAS Macro for Estimating and Visualizing Individual Growth Curves. Structural Equation Modeling: An Interdisciplinary Journal, 11, 132-149.

27. www.crmda.ku.edu27 P-technique Data Transformation Traditional P-technique Dynamic P-tech, Arbitrary Dynamic P-tech, Structured Single person - Identical variable relationships (same r at every time point) - Independent observations - With time lags, how do scores at T1 affect those at T2 - Time points are unstructured (Time 1, Time 2) - Time dependency - Time points are non- arbitrary (Mon, Tues, Wed) - Compare equivalent relationships Chained / 2+ people - Stacked subject data, pools intra- individual info - Assume identical relationships - With time lags - Time dependency - Unstructured time points - Time dependency - Structured time points - Compare equivalent relationships across a sample

28. www.crmda.ku.edu28 Data Restructuring Add 7 lags – autoregressive effects of energy/mood within a one-week period Ex: Subj Day Lag0 Lag1 Lag2 Lag3 Lag4 Lag5 Lag6 1 Mo...... 1 1 Tu..... 1 2 1 We.... 1 2 1 1 Th... 1 2 1 0 1 Fr.. 1 2 1 0 1 1 Sa. 1 2 1 0 1 0 1 Su 1 2 1 0 1 0 1 1 Mo 2 1 0 1 0 1 2 1 Tu 1 0 1 0 1 2 2 1 We 0 1 0 1 2 2 1 Impute empty records Create parcels by averaging 3 positive/negative items

29. www.crmda.ku.edu29 Data Restructuring Retain selected rows (with Monday as the beginning of the week) Stack participant data sets Subj Day PA_Mo PA_Tu PA_We PA_Th PA_Fr PA_Sa PA_Su 1 Mo1 1.00 0.67 0.67 1.33 1.00 1.33 0.67 1 Mo2 0.67 0.67 1.00 1.00 1.33 0.67 1.00 1 Mo3 0.33 1.00 1.00 1.67 1.67 0.00 1.00 1........ 1 Mo15 1.00 0.67 0.67 1.33 1.00 1.33 0.67 2 Mo1 1.00 0.33 0.67 0.33 0.67 2.33 0.00 2 Mo2 0.00 0.00 1.00 0.67 1.33 1.33 2.67 2 Mo3 1.33 3.00 1.33 3.00 1.67 0.00 2.67......... 5 Mo15 0.00 1.67 0.00 1.33 0.67 1.00 0.33 Note: meaning assigned to arbitrary time points

30. www.crmda.ku.edu30 Raw Means and Standard Deviations Energy ratings on a 5-point scale: MonTuesWedThursFriSatSun Positive / High Energy 1.23 (1.05) 1.23 (.97) 1.24 (1.10) 1.24 (.97) 1.32 (1.01) 1.18 (.94) 1.29 (1.02) Negative / Low Energy 0.97 (1.14) 0.92 (1.17) 0.90 (1.05) 0.81 (.97) 0.96 (1.17) 0.84 (1.06) 1.05 (1.08) N = 75 [15 weeks x 5 subjects]

31. www.crmda.ku.edu31 Level and Shape model 0* Mon NegIntercept NegSlope 1* 1.35 -.30.01.24 -.04 1* TuesWed Thurs FriSat Sun PosSlope 1.08.13.08.002 1* S4 S3 S2 S1.04 PosIntercept Model fit: χ2 (116) = 126.79, p =.23, RMSEA =.000, CFI =.98, TLI/NNFI =.98.06.12.06-.10 (L15.7lags.LevShape)

32. www.crmda.ku.edu32 Positive Affect model 1* 1* 1.23.07.05.19.09 SundayFriday.01.07.09.002 Model fit: χ2 (25) = 25.96, p =.41, RMSEA =.021, CFI =.99, TLI/NNFI =.99 Mon TuesWed Thurs FriSat Sun 1*.79 (L15.7lags.pos) PosIntercept

33. www.crmda.ku.edu33 Negative Affect model Model fit: χ2 (20) = 18.46, p =.56, RMSEA =.000, CFI = 1.00, TLI/NNFI = 1.01 Mon TuesWed Thurs FriSat Sun.70 1* FridaySunday 2* 3*.40.01.09.12.02.10 -.03.001.003 -.001.84.21.05.13 (L15.7lags.neg) NegInterceptNegSlope

34. www.crmda.ku.edu34 Cost-benefit analysis Extrapolates the average within-person change from pooled time series data But obscures unique information about each individuals variability and growth patterns Does not utilize the strengths of P-technique data Add subject covariates to detect individual differences at the mean level

35. Update Dr. Todd Little is currently at Texas Tech University Director, Institute for Measurement, Methodology, Analysis and Policy (IMMAP) Director, Stats Camp Professor, Educational Psychology and Leadership Email: yhat@ttu.eduyhat@ttu.edu IMMAP (immap.educ.ttu.edu) Stats Camp (Statscamp.org) 35ww w.Q uan t.K U.e du