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 = Df = 1 Pr(>Chisq) = e-06 Chisquare (null model) = Df = 6 Goodness-of-fit index = Adjusted goodness-of-fit index = RMSEA index = % CI: ( , ) Bentler-Bonnett NFI = Tucker-Lewis NNFI = Bentler CFI = SRMR = BIC =

Path Model 3 A more complex model that subsumes the previous

Path Model 3 Model Chisquare = Df = 1 Pr(>Chisq) = e-06 Chisquare (null model) = Df = 10 Goodness-of-fit index = Adjusted goodness-of-fit index = RMSEA index = % CI: ( , ) Bentler-Bonnett NFI = Tucker-Lewis NNFI = Bentler CFI = SRMR = BIC = The fit is practically identical, though there is still room for improvement

Path Model 4 Derived from modification indices

Path Model 4 Model Chisquare = Df = 1 Pr(>Chisq) = Chisquare (null model) = Df = 10 Goodness-of-fit index = Adjusted goodness-of-fit index = RMSEA index = 0 90% CI: (NA, ) Bentler-Bonnett NFI = Tucker-Lewis NNFI = Bentler CFI = 1 SRMR = BIC = Excellent fit

Fully Saturated Model

Psychosomatic Model Model Chisquare = Df = 5 Pr(>Chisq) = e-07 Chisquare (null model) = Df = 10 Goodness-of-fit index = Adjusted goodness-of-fit index = RMSEA index = % CI: ( , ) Bentler-Bonnett NFI = Tucker-Lewis NNFI = Bentler CFI = SRMR = BIC =

Conventional Medical Model Model Chisquare = Df = 3 Pr(>Chisq) = Chisquare (null model) = Df = 10 Goodness-of-fit index = Adjusted goodness-of-fit index = RMSEA index = % CI: (NA, ) Bentler-Bonnett NFI = Tucker-Lewis NNFI = Bentler CFI = SRMR = BIC =

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 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