Transcript Introductions - David A. Kenny

Example Models for
Multi-wave Data
David A. Kenny
December 15, 2013
Example Data
Dumenci, L., & Windle, M. (1996).
Multivariate Behavioral Research, 31, 313-330.
Depression with four indicators (CESD)
PA: Positive Affect (lack thereof)
DA: Depressive Affect
SO: Somatic Symptoms
IN: Interpersonal Issues
Four times separated by 6 months
433 adolescent females
Age 16.2 at wave 1
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Models
• Models
– Trait
– Autoregressive
– STARTS
– Trait-State-Occasion (TSO)
– Latent Growth Curve
• Types
– Univariate (except TSO) -- DA
– Latent Variable
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Latent Variable
Measurement Models
• Unconstrained
– c2(74) = 107.71, p = .006
– RMSEA = 0.032; TLI = .986
• Equal Loadings
– c2(83) = 123.66, p = .003
– RMSEA = 0.034; TLI = .986
• The equal loading model has reasonable
fit.
• All latent variable models (except growth
curve) are compared to this model.
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Trait Model:
Univariate
• Test of Equal Loadings: No
• Model Fit: RMSEA = 0.071; TLI = .974
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Trait Model:
Latent Variables
• Model with just the trait factor
does not fit as well as the
saturated model: c2(74) = 1xx.81
• More Trait than State Variance
• Trait Variance: 12.64
• State Variance 10.39
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Autoregressive
Model: Univariate
• Fixed error variances equal.
• Good fitting model: c2(2) = 4.98, p =
.083
Reliabilities
Stabilities
1: .657
1  2: .802
2: .650
2  3: .847
3: .597
3  4: .738
4: .568
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Autoregressive Model:
Latent Variables
• Not a very good fitting model compared to
the CFA
– c2(3) = 60.08, p < .001
• Overall Fit: c2(xx) = 1.81, p < .0xx,
RMSEA = 0.0xx; TLI = .9xx
• Stabilities
1  2: .xxx
2  3: .xxx
3  4: .xxx
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Growth Curve Model:
Univariate
• Unlike other models it fits the
means.
• Fit: c2(74) = 1xx.81, p < .0xx,
RMSEA = 0.0xx; TLI = .9xx
Intercept
Mean
Slope
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Growth Curve Model:
Latent Variables
Fit: c2(74) = 1xx.81, p < .0xx, RMSEA =
0.0xx; TLI = .9xx
Intercept
Slope
Mean
Variance
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Trait State Occasion
Model
• Standard TSO does not have
correlated errors, but they are
added.
• Fit: c2(74) = 1xx.81, p < .0xx,
RMSEA = 0.0xx; TLI = .9xx
– Variances
– Trait
– State
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STARTS Univariate
• Difficulty in finding trait factor. None
of the models converged.
• Trait factor as Seasonality: Loadings in
the Fall are 1 and in the Spring are -1
• Models converged.
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Univariate STARTS
Results
• Fit: c2(74) = 1xx.81, p < .0xx, RMSEA =
0.0xx; TLI = .9xx
• Variances
– Seasonality
– ART
– State
• AR coefficient:
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Latent Variable
STARTS
• Fit: c2(74) = 1xx.81, p < .0xx, RMSEA
= 0.0xx; TLI = .9xx
• Variances
– Seasonality
– ART
– State
• AR coefficient:
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•
•
•
•
Summary of Fit:
Univariate
Trait
Autoregressive
Growth Curve
STARTS
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Summary of Fit:
Latent Variables
No Model
Trait
Autoregressive
Growth Curve
TSO
STARTS
RMSEA
0.034
TLI
.986
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