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Examples

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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Examples

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  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 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

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