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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(>Chisq) = 7.5654e-06 Chisquare (null model) = 1082.2 Df = 6

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path model 1
Path Model 1
  • Simple mediation model. Much of the influence of Family Background (SES) is indirect
path model 2
Path Model 2
  • Additional mediator
path model 24
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
Path Model 3
  • A more complex model that subsumes the previous
path model 36
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
Path Model 4
  • Derived from modification indices
path model 48
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
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
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
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