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Mplus Discussion > Structural Equation Modeling >
 ruben milla posted on Wednesday, March 26, 2008 - 10:53 am
Dear all,
i am running a SEM analysis which includes 1 latent continuous
variable and 12 dependent variables (3 of them categorical). I am
using MLR as estimator.

When i run the script, i obtain parameter estimates, with their
corresponding estandar errors. But i dont get chi-square, CFI or TLI
to be able to assess overall model fit.
I only get loglikelihood and information criteria values as output
under the "tests of model fit" subheading. I am not comparing
alternative models, but just trying to assess the overall fit of my
data to 1 model.

how can i get chi-square, CFI and TLI?

thanks in advance,
Ruben Milla
 Linda K. Muthen posted on Wednesday, March 26, 2008 - 11:37 am
You will not obtain these fit statistics because numerical integration is required for your analysis. You could use the default estimator WLSMV.
 ruben milla posted on Thursday, March 27, 2008 - 4:44 am
thanks a lot,
but we have a modest sample size (190), and, as i understand, WLS-related estimators require larger sample sizes than ML (is this correct?).
Thus, i run my model using WLSMV, and get the "NO CONVERGENCE. NUMBER OF ITERATIONS EXCEEDED." output.
Also, i need an estimator robust to multivariate non-normality
any alternative suggestion? would simplification of the model increase the likelihood of it to converge using WLSMV?

thanks in advance,
 Linda K. Muthen posted on Thursday, March 27, 2008 - 9:32 am
I don't know of any definitive study that has shown sample size needs to be larger for weighted least squares relative to maximum likelihood.

I'm not sure why maximum likelihood would converge and weighted least squares not. Please send your input, data, the two outputs, and your license number to
 Henrika McCoy posted on Friday, July 11, 2008 - 9:38 am
I would also like to be able to get chi-square, CFI and TLI. Would you say that WLSMV is appropriate to use versus ML for a small sample size of 90?
 Linda K. Muthen posted on Friday, July 11, 2008 - 9:59 am
Only a simulation study can answer that question. It depends not only on sample size but the number of parameters you are estimating.
 Henrika McCoy posted on Friday, July 11, 2008 - 10:02 am
I have 21 free parameters with 1 IV, 4 MVs and 1 DV.
 Linda K. Muthen posted on Friday, July 11, 2008 - 10:18 am
That's a large model for 90 observations.
 Henrika McCoy posted on Friday, July 11, 2008 - 10:24 am
Yes I know, it's primary data for my dissertation so the small sample size could not be avoided. Is there a way to get the model fit statistics that I would like with this model?
 Linda K. Muthen posted on Friday, July 11, 2008 - 10:37 am
If you want standard fit statistics, use WLSMV. It doesn't sound like you have any choice.
 Henrika McCoy posted on Friday, July 11, 2008 - 10:45 am
Okay thank you!
 Juan Madiedo posted on Monday, November 18, 2013 - 8:16 am

I'm using MLR to run a mediation model with a continuos IV, one categorical and one continuous mediator and a continuous outcome.
Since Mplus does not provide the standard GOF indices, due the use of numerical integration, I was wondering how would you go about reporting overall model fit. I've been asked to report on that, but I'm not really sure how to proceed or whether that is absolutely necesary. (I'm using MLR because of non-normality issues)

 Bengt O. Muthen posted on Monday, November 18, 2013 - 8:25 am
You can use "neighboring models", that is, models that are less restrictive than the one you are considering. And then do a likelihood ratio chi-square test of your model against that model.
 Hyunzee Jung posted on Friday, February 07, 2014 - 9:02 am

My outcome is three-category "nominal" variable, and with MLR default estimator I get relative fit statistics of AIC and BIC in addition to Log Likelihood values. I hoped to obtain absolute fit statistics as well, so tried WLSMV, but found out WLSMV cannot be used for nominal outcome.

My question is: Is there a way to obtain absolute fit statistics such as RMSEA and CFI from a path model with final outcome being nominal variable (three categories)? FYI, measurement model is also included for an exogenous latent variable.

Thank you so much.
 Linda K. Muthen posted on Friday, February 07, 2014 - 9:07 am
With a nominal variable, means, variances, and covariances are not sufficient statistics for model estimation. Chi-square and related fit statistics are not available in this case.
 Hyunzee Jung posted on Saturday, February 08, 2014 - 12:20 am
Thanks so much for prompt confirming, Linda. As a follow-up on my previous question, here is my next question. I plan to do multi-group SEM, for which comparison of models is necessary among models of different degrees of restriction. I wonder what your recommendations would be with respect to comparing models that provide only relative fit statistics.

(1) Bengt seems to have suggested right above doing a likelihood ratio chi-square test of a study model against a less restrictive model. Is this a chi-square difference test using H0 log likelihood values?

(2) Would it also be a possibility to simply compare relative fit stats although what is meaningful increase or decrease has not yet been established?

I am interested to learn about your suggestions on measures for model comparison.

 Linda K. Muthen posted on Sunday, February 09, 2014 - 9:21 am
1. Yes for nested models this is a chi-square difference test.

2. You can compare non-nested models that have the same set of dependent variables using BIC.
 Sangshin Park posted on Sunday, March 25, 2018 - 4:33 pm

I am performing a survival analysis with an outcome - "time to events." Isn't there any method to obtain absolute fit statistics such as CFI and RMSEA? Now I can obtain only relative fit statistics.

Thanks you in advance.
 Tihomir Asparouhov posted on Monday, March 26, 2018 - 9:32 am
Both CFI and RMSEA are not absolute fit statistics. They are based on comparing the estimated model to the baseline model. BIC is one possible option that might work for you. You can also construct a custom test statistic using model test, for example, testing the hypothesis that all predictors have zero coefficients. Another possible direction is to use survival curves.
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