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Dear Linda and Bengt, I ran two group model SEM with latent interactions (an interaction between one latent factor and one manifest variables) and wanted to test whether there are gender differences in the structural relations among the variables. Thus I compared two models  with and without equality constraints on the regression weights and the covariance. The log likelihood is 4304.84 for the invariance model and 4297.17 for the "freed" model. Thus the 2 loglikelihood diff is 15.34 which is significant according to the chisquare distribution. Then which model is the better fitting model? Does this mean the model with smaller absolute LL (4297.17) is better than the other one? or the one with smaller value (4304) is better than the other one? Thank you for helping with clarifying my confusion. 


The model with the fewest restrictions will have the higher loglikelihood as you see. When the difference in the loglikelihoods is signficant, it means that placing the constraints on the model significantly worsens model fit. 

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