2
Example DataDumenci, 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
3
Models• Models
– Trait– Autoregressive– STARTS– Trait-State-Occasion (TSO)– Latent Growth Curve
• Types– Univariate (except TSO) -- DA– Latent Variable
4
Latent Variable Measurement Models
• Unconstrained– 2(74) = 107.71, p = .006– RMSEA = 0.032; TLI = .986
• Equal Loadings– 2(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.
6
Trait Model: Latent Variables
• Model with just the trait factor does not fit as well as the saturated model: 2(74) = 1xx.81
• More Trait than State Variance• Trait Variance: 12.64• State Variance 10.39
7
Autoregressive Model: Univariate
• Fixed error variances equal.• Good fitting model: 2(2) = 4.98, p = .083Reliabilities Stabilities
1: .657 1 2: .802 2: .650 2 3: .8473: .597 3 4: .7384: .568
8
Autoregressive Model: Latent Variables
• Not a very good fitting model compared to the CFA– 2(3) = 60.08, p < .001• Overall Fit: 2(xx) = 1.81, p < .0xx, RMSEA = 0.0xx; TLI
= .9xx• Stabilities
1 2: .xxx 2 3: .xxx3 4: .xxx
9
Growth Curve Model: Univariate
• Unlike other models it fits the means.• Fit: 2(74) = 1xx.81, p < .0xx, RMSEA = 0.0xx; TLI
= .9xx
Intercept SlopeMeanVariance
10
Growth Curve Model: Latent
VariablesFit: 2(74) = 1xx.81, p < .0xx, RMSEA = 0.0xx; TLI = .9xx
Intercept SlopeMeanVariance
11
Trait State Occasion Model
• Standard TSO does not have correlated errors, but they are added.
• Fit: 2(74) = 1xx.81, p < .0xx, RMSEA = 0.0xx; TLI = .9xx– Variances– Trait– State
13
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.
14
Univariate STARTS Results
• Fit: 2(74) = 1xx.81, p < .0xx, RMSEA = 0.0xx; TLI = .9xx
• Variances– Seasonality – ART– State
• AR coefficient:
15
Latent Variable STARTS
• Fit: 2(74) = 1xx.81, p < .0xx, RMSEA = 0.0xx; TLI = .9xx
• Variances– Seasonality – ART– State
• AR coefficient: