Interaction Model and Fit Indices PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Dale Glaser posted on Monday, December 06, 2004 - 12:07 pm
Hi All...I am testing a model where a vignette is rated for frequency (fr1 to fr9) and impact (im1 to im9) for 9 exposures (over time) with 'trauma' being the DV....we are interested in assessing the frequency x impact interaction for each of the 9 data points, thus, I centered the continuous level predictors and created the interaction term: (frim1-frim9) as per the following syntax (using MLMV as an estimator). We were able to attain model convergence but the only index of model fit was the following:

Number of Free Parameters 95

SRMR (Standardized Root Mean Square Residual)
Value 0.024

WRMR (Weighted Root Mean Square Residual)
Value 0.517

The sample size is n = 375. Would anyone be able to shed insight as to why the chi-square and TLI/CFI indices of fit are not reported?

Thank you..........Dale Glaser


MODEL: i s | tr1@0 tr2@1 tr3@2 tr4@3 tr5@4 tr6@5 tr7@6 tr8@7 tr9@8;
tr1 on fr1;
tr2 on fr2;
tr3 on fr3;
tr4 on fr4;
tr5 on fr5;
tr6 on fr6;
tr7 on fr7;
tr8 on fr8;
tr9 on fr9;
tr1 on im1;
tr2 on im2;
tr3 on im3;
tr4 on im4;
tr5 on im5;
tr6 on im6;
tr7 on im7;
tr8 on im8;
tr9 on im9;
tr1 on frim1;
tr2 on frim2;
tr3 on frim3;
tr4 on frim4;
tr5 on frim5;
tr6 on frim6;
tr7 on frim7;
tr8 on frim8;
tr9 on frim9;

output: sampstat standardized residual ;
 bmuthen posted on Monday, December 06, 2004 - 3:00 pm
Please send your full input, output and data to so we can take a clear look at this.
 wendy posted on Saturday, July 29, 2006 - 10:12 pm
Hi, Dr. Muthen:
I am exploring a real dataset on my growth model with interaction between initial status and an exogenous covariate predicting growth rate. However, one question is that I could not find any fit index in M-plus output. There is no error and warning in the output as well. I also fit both unconditional and conditional growth modeling without interaction with one covariate predicting I and S respectively. Results show that covariate significantly impact both initial status and growth rate and all fit indices show favorable result. I just wonder why my growth model with interaction did not show fit index, is it because my total model fit is extremely poor? How could I detect the fitting of the interaction model? Thank you.
 Linda K. Muthen posted on Sunday, July 30, 2006 - 6:16 pm
When means, variances, and covariances are not sufficient statistics for model estimation as with latent variable interactions, chi-square and other related fit statistics are not available.
 wendy posted on Sunday, July 30, 2006 - 8:47 pm
Hi,Dr. Muthen:
I very appreciate your reply. I just wonder how to make means, variances, and covariance be sufficient statistics for model estimation? Does that mean I need to change my model with interaction between latent initial status and the covariate? Why even the model means, variances, and covariance are not sufficient, Mplus still give results? Could I still use the results or whether those estimations are reliable? Thank you
 Linda K. Muthen posted on Monday, July 31, 2006 - 7:52 am
When means, variances, and covariances are not sufficient statistics, then raw data are used and the results are fine. If a model converges but you do not obtain chi-square and related tests statistics in Mplus, this tells you that means, variances, and covariances are not sufficient for model estimation. There is nothing you can do about this except change to a model where they are sufficient. In cases where chi-square and related test statistics are not available, nested models can be tested using the loglikelihoods.
 Luo Wenshu posted on Tuesday, December 16, 2014 - 12:12 am
Dear Dr. Muthen,

As susggested, to compare two models where the model without the latent interaction term is more restricted and nested in the model with the interaction term, we can use loglikelihood ratio test. Do we do this based on the H0 value of loglikelihood between the two models?

In addition, do we need to consider the H0 Scaling Correction Factor for MLR, and how?

Thank you very much
 Linda K. Muthen posted on Tuesday, December 16, 2014 - 9:21 am
Just use the z-score for the interaction term. It is the same as a one degree of freedom difference test.
 Luo Wenshu posted on Tuesday, December 16, 2014 - 5:38 pm
Thank you, Dr. Muthen.
This is the significance test of the interaction term.
How about to compare the fit of the
models with and without latent interaction term?

In addition, is it OK to compare the AIC and BIC of the models with and without latent interaction term?
 Linda K. Muthen posted on Thursday, December 18, 2014 - 9:57 am
A difference test with one degree of freedom is the same as the test of the interaction term.

You can compare AIC and BIC as long as the models have the same set of dependent variables.
 Luo Wenshu posted on Friday, December 19, 2014 - 1:47 am
Thank you Dr. Muthen. This is very clear to me now.
I'd like to confirm with you that if I want to try the loglikelihood ratio test to compare two nested models, should I use the H0 (not H1) value of loglikelihood reported in Mplus outcome?
 Linda K. Muthen posted on Friday, December 19, 2014 - 6:45 am
You should use H0.
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