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 minyuedong posted on Wednesday, December 07, 2005 - 2:14 am
I am doing a two-level SEM by using MLR estimator.
For the chi-square difference anlysis, I refer to the 4-steps suggested by Bentler as shown in the web. I got higher DFs (+7) and higher adjusted chi-square values (+29.04)when compare model 2 (with restrictions) to model 1, so my question is: in order to check if the chi-square difference is significant, shall I refer to the chi-square distribution or something else?

Thanks in advance
 Linda K. Muthen posted on Wednesday, December 07, 2005 - 6:04 am
You should refer to the chi-square distribution.
 Leif Edvard Aaroe posted on Wednesday, January 18, 2006 - 12:14 am
I have carried out a series of SEM analyses with one dependent variable (latent) and a number of predictors (a combination of latent variables and observed). I am using the complex and cluster options. The output provides the MLR estimator.

Can I use the Satorra-Bentler 4-step procedure (steps 3 and 4) for testing differences between models in this case?

I use the "model constraint" option and compare models by constraining parameters (one by one) to be equal to zero, comparing with the unconstrained model. Does this sound right?

Is it possible to get negative Chi-square values?
 Linda K. Muthen posted on Wednesday, January 18, 2006 - 9:28 am
Yes, you can use the Satorra-Bentler 4-steps.

You can use MODEL CONSTRAINT for fixing parameters to zero but it might be easier to just do theses simple constraints in the model command using @0.

Negative chi-square values are possible and have been discussed by Bentler in the literature.
 Leif Edvard Aarų posted on Tuesday, February 07, 2006 - 11:10 pm
Dear Linda,

I have read carefully all the dialogues on the Satorra-Bentler test for differences between nested models. There is however, one point that is still unclear to me.

The T0 and T1 values that I use when I apply the formula, are these the chi-square values that I obtain when running the analysis with the MLR estimiation procedure, or do I have to multiply the chi square values with their respective scaling correction factors first?

Best regards

 Linda K. Muthen posted on Wednesday, February 08, 2006 - 9:08 am
Those are ML and yes you need to multiply MLR by the scaling correction factor to obtain ML.
 Sophie Potter posted on Tuesday, October 23, 2018 - 1:01 am

I ran a Chi-Square Difference Testing Using the Loglikelihood on two models, one where the residual variances for my latent growth model was set as invariant (nested model) and one where they are set at varying (comparison model).

Nested Model:
Loglikelihood value: -26148.950
No. of parameters: 55
Scaling Correction Factor: 1.1884

Comparison model:
Loglikelihood value: -26130.583
No. of parameters: 61
Scaling Correction Factor: 1.3295

Test Scaling Correction Difference (CD):2.6229
Chi-Square Difference (TRd): 14.0050
Number of Parameters Difference: 6

I was wondering how to interpret this these results (i.e., how do i tell which model is the best to use)?

Any help is appreciated,
 Tihomir Asparouhov posted on Tuesday, October 23, 2018 - 2:39 pm
Since the p-value is 0.03 (<0.05) you would typically reject the nested model. You can get the p-value using a chi-square online calculator or the CHIDIST(14,6) function in excel.
 Sophie Potter posted on Wednesday, October 24, 2018 - 4:38 am
AH thank you Tohomir!
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