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Examples. Path Model 1. Simple mediation model. Much of the influence of Family Background (SES) is indirect. Path Model 2. Additional mediator. Path Model 2. Model Chisquare = 20.045 Df = 1 Pr(&gt;Chisq) = 7.5654e-06 Chisquare (null model) = 1082.2 Df = 6

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Examples

Path Model 1
• Simple mediation model. Much of the influence of Family Background (SES) is indirect
Path Model 2
Path Model 2
• Model Chisquare = 20.045 Df = 1 Pr(>Chisq) = 7.5654e-06
• Chisquare (null model) = 1082.2 Df = 6
• Goodness-of-fit index = 0.99017
• Adjusted goodness-of-fit index = 0.90165
• RMSEA index = 0.13807 90% CI: (0.08961, 0.19369)
• Bentler-Bonnett NFI = 0.98148
• Tucker-Lewis NNFI = 0.89382
• Bentler CFI = 0.9823
• SRMR = 0.048226
• BIC = 13.137
Path Model 3
• A more complex model that subsumes the previous
Path Model 3
• Model Chisquare = 20.045 Df = 1 Pr(>Chisq) = 7.5654e-06
• Chisquare (null model) = 1665.3 Df = 10
• Goodness-of-fit index = 0.99212
• Adjusted goodness-of-fit index = 0.88175
• RMSEA index = 0.13807 90% CI: (0.08961, 0.19369)
• Bentler-Bonnett NFI = 0.98796
• Tucker-Lewis NNFI = 0.88495
• Bentler CFI = 0.9885
• SRMR = 0.043171
• BIC = 13.137
• The fit is practically identical, though there is still room for improvement
Path Model 4
• Derived from modification indices
Path Model 4
• Model Chisquare = 0.36468 Df = 1 Pr(>Chisq) = 0.54592
• Chisquare (null model) = 1665.3 Df = 10
• Goodness-of-fit index = 0.99985
• Adjusted goodness-of-fit index = 0.99781
• RMSEA index = 0 90% CI: (NA, 0.070447)
• Bentler-Bonnett NFI = 0.99978
• Tucker-Lewis NNFI = 1.0038
• Bentler CFI = 1
• SRMR = 0.0027810
• BIC = -6.5431
• Excellent fit
Psychosomatic Model
• Model Chisquare = 40.402 Df = 5 Pr(>Chisq) = 1.2389e-07
• Chisquare (null model) = 415.42 Df = 10
• Goodness-of-fit index = 0.96818
• Adjusted goodness-of-fit index = 0.90453
• RMSEA index = 0.123 90% CI: (0.089527, 0.15949)
• Bentler-Bonnett NFI = 0.90274
• Tucker-Lewis NNFI = 0.82536
• Bentler CFI = 0.91268
• SRMR = 0.065222
• BIC = 9.6491
Conventional Medical Model
• Model Chisquare = 3.2384 Df = 3 Pr(>Chisq) = 0.3563
• Chisquare (null model) = 415.42 Df = 10
• Goodness-of-fit index = 0.99725
• Adjusted goodness-of-fit index = 0.98624
• RMSEA index = 0.013032 90% CI: (NA, 0.080146)
• Bentler-Bonnett NFI = 0.9922
• Tucker-Lewis NNFI = 0.99804
• Bentler CFI = 0.99941
• SRMR = 0.016005
• BIC = -15.213
Fit Index Reference
• Chi square is actually a test of badness of fit, and is not very useful as a result of having to accept a null hypothesis and its sensitivity to sample size
• Compares current model to just-identified one with perfect fit, so no difference is ‘good’
• May easily flag for significance with large N
• Goodness of Fit Index (GFI) and Adjusted GFI
• Kind of like our R2 and adjusted R2 for the structural model world, but a bit different interpretation
• It is the percent of observed covariances explained by the covariances implied by the model
• R2 in multiple regression deals with error variance whereas GFI deals with error in reproducing the variance-covariance matrix
• Rule of thumb: .9 for GFI, .8 for adjusted, which takes into account the number of parameters being estimated; However technically the values of either can fall outside the 0-1 range
• Root mean square residual
• As the name implies, a kind of average residual between the fitted and original covariance matrix
• Standardized (regarding the correlation matrix) it ranges from 0-1
• 0 perfect fit
• Bentler’s Normed Fit Index, CFI (NFI adjusted for sample size), and Non-Normed FI (Tucker-Lewis Index, adjusts for complexity) test the model against an independence model
• Independence model chi-square is given in the output
• E.g. 80% would suggest the current model fits the data 80% better
• Others Akaike Information Criterion, Bayesian Information Criterion
• Good for model comparison, smaller better