1 crmda.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
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1crmda.KU.edu
Todd D. LittleUniversity of Kansas
Director, Quantitative Training ProgramDirector, Center for Research Methods and Data Analysis
Director, Undergraduate Social and Behavioral Sciences Methodology MinorMember, Developmental Psychology Training Program
crmda.KU.eduWorkshop presented 05-24-2012 @
University of Turku, Finland
Special Thanks to: Ihno Lee, Chapter co-author in Handbook.
Dynamic P-Technique Structural Equation Modeling
www.crmda.ku.edu 2
Cattell’s 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
www.crmda.ku.edu 3
Cattell’s Data Box
Occasions of Measurement
Variables
(or T
ests)
Per
son
s (o
r E
nti
ties
)
www.crmda.ku.edu 4
Cattell’s 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
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Michael Lebo’s 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
• 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’
Model Fit: χ2(142, n=101) = 154.3, p = .23; RMSEA = .02; TLI/NNFI = .99
(Initial model: L15.3.s4.3lags)
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L15.4.s1.3lags: Subject 1
NegativeLag 0
PositiveLag 0
1*
1*
NegativeLag 1
.94
PositiveLag 1
1
NegativeLag 2
.94
PositiveLag 2
1
-.64 -.66 -.66
.24 .24
Model Fit: χ2(144, n=101) = 159.9, p = .17; RMSEA = .05; TLI/NNFI = .99
(Initial model: L15.3.s1.3lags)
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L15.4.s5.3lags: Subject 5
NegativeLag 0
PositiveLag 0
1*
1*
NegativeLag 1
1
PositiveLag 1
.94
NegativeLag 2
.94
PositiveLag 2
.94
-.61 -.66 -.66
.24 .24
Model Fit: χ2(143, n=101) = 93.9, p = .99; RMSEA = .00; TLI/NNFI = 1.05
.24
(Initial model: L15.3.s5.3lags)
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L15.4.s3.3lags: Subject 3
NegativeLag 0
PositiveLag 0
1*
1*
NegativeLag 1
.94
PositiveLag 1
1
NegativeLag 2
.92
PositiveLag 2
.88
-.41 -.51 -.51
.24 .24
.37
.31 .31
Model Fit: χ2(142, n=101) = 139.5, p = 1.0; RMSEA = .0; TLI/NNFI = 1.0
(Initial model: L15.3.s3.3lags)
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L15.4.s2.3lags: Subject 2
NegativeLag 0
PositiveLag 0
1*
1*
NegativeLag 1
.95
PositiveLag 1
.95
NegativeLag 2
.91
PositiveLag 2
.94
-.63 -.63 -.63
.24 .24
-.17
-.24 -.24
Model Fit: χ2(142, n=101) = 115.2, p = .95; RMSEA = .0; TLI/NNFI = 1.0
(Initial model: L15.3.s2.3lags)
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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)
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Weekly Growth TrendsWeek 1 Week 2 Week 3
Week 4 Week 5 Week 6
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.