1. Examples

2. Path Model 1 Simple mediation model. Much of the influence of Family Background (SES) is indirect

3. Path Model 2 Additional mediator

4. 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

5. Path Model 3 A more complex model that subsumes the previous

6. 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

7. Path Model 4 Derived from modification indices

8. 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

9. Fully Saturated Model

10. 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

11. 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

12. 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 R 2 and adjusted R 2 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 R 2 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