Introductory And Intermediate Growth Models - Mplus

Chi-Square Difference TestingOf Nested Models• When a model H a imposes restrictions on parameters ofmodel H b , H a is said to be nested within H b• To test if the nested model H a fits significantly worse than H b ,a chi-square test can be obtained as the difference in the chisquarevalues for the two models (testing against anunrestricted model) using as degrees of freedom thedifference in number of parameters for the two models• The chi-square difference is the same as 2 times thedifference in log likelihood values for the two models• The chi-square theory does not hold if H a has restricted any ofthe H b parameters to be on the border of their admissibleparameter space (e.g. variance = 0)59CFA Model ModificationModel modification indices are estimated for all parameters thatare fixed or constrained to be equal.• Modification Indices – expected drop in chi-square if theparameter is estimated• Expected Parameter Change Indices – expected value of theparameter if it is estimated• Standardized Expected Parameter Change Indices –standardized expected value of the parameter if it is estimatedModel Modifications• Residual covariances• Factor cross loadings6030