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Mplus Discussion > Structural Equation Modeling >
 Anthony S. Boyce posted on Wednesday, March 28, 2007 - 3:02 pm
A colleague and I both recently ran the same model on the same data, I used MPlus and he used LISREL. Our models were identical although the chi-square values differed by 2.0 and some of the estimates differed by less than .01. However, the CFI and TLI indices were substantially different (i.e., MPLUS: CFI=.73, TLI=.72; LISREL: CFI=.89, TLI/NNFI=.88). Do you have any idea why the fit indices would be so different?

Thanks very much for any help you can provide.
 Linda K. Muthen posted on Thursday, March 29, 2007 - 8:40 am
I suspect that your model has covariates. In this case, the baseline model differs between LISREL and Mplus. The baseline model in LISREL does not contain covariances among the covariates. In Mplus, it does.
 laura smith posted on Friday, February 01, 2008 - 2:25 pm

i am a beginner to SEM and to Mplus, so thanks in advance for your patience.

my question is: can fit indices be too high? initially, i ran the measurement portion of my model and obtained a nonsignificant chi-square (good) but a CFI of .88, a TLI of .65, and an RMSEA of .25 (not so good).

next, as one of the model modification indices was theoretically consistent with my model, i added it (it was a WITH path). Consequently, the last three fit indices improved dramatically(CFI=1, TLI=1, RMSEA=0).

The model is not just-identified, but it has only one degree of freedom. could that be the "problem" that is creating a near-perfect model fit?

also, as i went on to the structural model, the degree of freedom increased, but the fit indices remained at those high levels.

i would like to be happy about the seemingly excellent fit of this model, but it seems suspicious to me. can you suggest some factors that i should investigate to see whether they are inflating these indices spuriously?

thanks so much! this discussion board is a treasure.
 Linda K. Muthen posted on Friday, February 01, 2008 - 2:52 pm
It sounds like the correlations among your observed variables are low. This makes it difficult to reject the H0 model. And with only one degree of freedom, the model does not place many restrictions on the H1 model. You may also have a small sample size which results in low power.
 laura smith posted on Saturday, February 02, 2008 - 10:22 am
thanks very much for those pointers, linda.

looking into those possibilities, my sample size is 321, which i think is reasonable.

the correlations among the 4 indicators of the proposed latent range from .61 to .34 (with three of them below .40 at .39, .39, and .34).

do those sound low enough to you to suggest that i've found where the problem may lie?

thanks once again...
 Linda K. Muthen posted on Monday, February 04, 2008 - 8:49 am
Your correlations don't sound that low and your sample size is not particularly large. But with one degree of freedom, you don't have many restrictions. If you send two outputs, one without the WITH statement and one where the WITH statement dramatically changes the fit, and your license number to, I can take a look at it.
 Lauree Tilton-Weaver posted on Monday, April 21, 2008 - 10:31 am
If you have a fully saturated model, is it a good idea to add another variable (say a control), so that you have fit indices that are meaningful?
 Linda K. Muthen posted on Monday, April 21, 2008 - 10:48 am
This does not make sense to me.
 Lauree Tilton-Weaver posted on Monday, April 21, 2008 - 12:51 pm
Okay - I'm looking at someone else's model - it's fully saturated (they're looking at mediation)...and saying that the fit indices can't be evaluated, I'm assuming because of the saturation. I just wondered if there wasn't something that could be done to make the fit indices meaningful, rather than just leaving it at that.
 Linda K. Muthen posted on Monday, April 21, 2008 - 4:49 pm
A saturated model has perfect fit. It is only when there are restrictions on the model that fit can be assessed.
 Lauree Tilton-Weaver posted on Tuesday, April 22, 2008 - 6:04 am
That's part of my point/question. If it has perfect fit because it's saturated, does it make sense to just leave it at that? They've tested a mediation model, and have two control variables with the exogenous, outcomes, and mediators all controlled. I can't see where a constraint would make sense. But it seems strange to just say "it's saturated, we can't evaluate model fit."
 Linda K. Muthen posted on Tuesday, April 22, 2008 - 8:29 am
You can't evaluate model fit but you can evaluate whether the indirect effect is significant. Perhaps that is sufficient.
 Rob Nobel posted on Tuesday, November 11, 2008 - 1:23 am

I was wondering: is the term saturated a "discrete" term (is a model only saturated with df=0) or can you also say that a model with for example df=1 is "highly saturated" and thus that fit indices are less informative?
 Linda K. Muthen posted on Wednesday, November 12, 2008 - 8:14 am
In my experience a saturated model is a model with no degrees of freedom. I have never seen a discussion of degrees of saturation.
 Sandra posted on Thursday, March 20, 2014 - 8:51 am

I am conducting a CFA on my own, and I am not sure about my chi-square and RMSEA:

Chi-square test of Model fit: 2777.516 and p <.000
(I have 295 participants in this analysis, can I consider this a large sample size to justify a non-significant result?)

RMSEA estimate= .044
90% C.I. = .041 .047
P-value = .999
(RMSEA is lower than .06 however it is not significant, how should I interpret this result?)

CFI = .86
(not good but near)

SRMR = .058

The modification indices suggest relationships that do not make sense theoretically...

Also how can I know that a variable is problematic for my factor?

Many thanks in advance!
 Linda K. Muthen posted on Thursday, March 20, 2014 - 1:35 pm
With such a small sample, you cannot discount chi-square. I would say the model does not fit.

EFA is a good way to isolate a problematic variable. See the Topic 1 course handout and video on the website for further information.
 tom norton posted on Thursday, April 17, 2014 - 7:04 am

I'm using Anderson & Gerbings 2-step approach to SEM:
1. CFA: using "Latent variable BY indicator" commands
2. SEM: using "Latent variable BY indicator" and "Latent variable ON latend variable" commands

When I run the SEM , I generate the same model fit statistics as I do when running the CFA.

Is there a default in Mplus that generates model fit based on the CFA part ("latent variable BY indicator") part of the syntax

Warm Regards
 Linda K. Muthen posted on Thursday, April 17, 2014 - 9:36 am
The structural part of the model must be just-identified if you get the same fit for both models. The structural part does not contribute to fit. There is no option to generate fit for a subset of the model.
 tom norton posted on Thursday, April 17, 2014 - 5:09 pm
To be clear, wouldn't a just-identified model have a df=0? Both the measurement model and structural model have df=505.
 Bengt O. Muthen posted on Thursday, April 17, 2014 - 8:30 pm
Your model is only just-identified in the structural part, not overall.

I don't know what you mean about generating model fit based on the CFA part - if you have only f BY y statements, that's how you get the CFA fit.
 tom norton posted on Thursday, April 17, 2014 - 8:46 pm
When I run the CFA with just the f B y commands (i.e. the measurement model) I get model fit statistics.

When I run the SEM by adding f ON f commands to the model (i.e. the structural model), the model fit statistics are precisely the same.

I've just tested this with the data provided for ex 5.11 in the user's guide by running the SEM and then removing the f ON f command. The same model fit statistics were produced each time.

Is there something else I should be doing to somehow differentiate the measurement model from the structural models? Or is it the case that I have reduced my df from >0 in the measurement model to = 0 in the structural model by introducing the paths between the latent factors (and thus making my structural model just-identified)?

warm regards
 Linda K. Muthen posted on Friday, April 18, 2014 - 8:58 am
For model fit to change when you add the structural part of the model, the structural part of the model must have degrees of freedom. It cannot be just-identified. Fit cannot be assessed on a just-identified model or part of a model. The change should be to the structural model not the measurement model.
 LIDYANE CAMELO posted on Thursday, January 28, 2016 - 4:47 am
I am creating a latent variable using CFA to use in other analysis (a regression model) and my test model is equal to the saturated model. Can I use the results obtained from a saturated model? If so, since I cannot use the fit indices, is it ok to say in the paper that we did not use fit indices because we use a saturated model?
 Linda K. Muthen posted on Thursday, January 28, 2016 - 12:55 pm
Fit is not available for a saturated model.
 LIDYANE CAMELO posted on Thursday, January 28, 2016 - 1:08 pm
Yes, this I know, but I would like to know if I could use scores from a latent construct that was obtained from a saturated model using CFA. Is there some problem with that?
 Bengt O. Muthen posted on Thursday, January 28, 2016 - 6:21 pm
No problem with that.
 Margarita  posted on Sunday, February 28, 2016 - 7:52 am
Prof. Muthén,

I am testing a moderated mediation model with two mediators and 1 moderator, and I get the following fit indices (my model is the equivalent of no. 59 in PROCESS):

chi-squared = 2133.29
df = 9
p < .001

RMSEA = .81 (.78 - .84)
CFI = .00
TLI = -1.725

These results seem odd to me. I was wondering whether there is something wrong with my model or are such results expected in moderated mediation?

Thank you for your help
 Linda K. Muthen posted on Sunday, February 28, 2016 - 2:41 pm
Please send your output and your license number to
 Nisse posted on Sunday, June 18, 2017 - 5:18 am

The fit indices are similar in the CFA and SEM I run. I came across a paper that mentioned "the better fit indices of SEM indicates the structural model better explains the data". This sounds rational, but makes me worried whether my structural model is no better compared to when all variables are freely related. The structural model is a mediating model, and I've tested the mediation via bootstrapping.

Thank you very much in advance.
 Vaiva Gerasimaviciute posted on Wednesday, May 09, 2018 - 12:16 pm
I am testing reciprocal associations between two dichotomous variables, I also include categorical covariates and use WLSMV estimator. My concern is that final model has CFI=1 and TLI=1 (chi-square test of model fit 11.6, p=0.3112, df=10). Should I be concerned about high CFI and TLI? Thank you, Vaiva
 Bengt O. Muthen posted on Thursday, May 10, 2018 - 2:47 pm
First see the FAQ on our website:

Reciprocal interaction with categorical and continuous DVs inadmissible using ML
 Vaiva Gerasimaviciute posted on Thursday, May 10, 2018 - 2:53 pm
Dear Muthen, I am using WLSMV, not ML. Thank you
 Bengt O. Muthen posted on Thursday, May 10, 2018 - 3:23 pm
Please send your output to Support along with your license number.
 Noémie Bigras posted on Tuesday, March 05, 2019 - 6:40 am

I am running a CFA model (measurement model before I run whole SEM) with three continuous indicators but no fit indices appeared in the output, chi-square, p-value, RMSEA are all zero. Yet, I have good factor loadings for the three indicators, ranging from .73 to .82. I don't understand why there are no fit indices?

Thank you very much,
 Bengt O. Muthen posted on Tuesday, March 05, 2019 - 2:31 pm
This model has no fit stats because it is just-identified, that is, it has as many parameters as there are sample variances and covariances.
 Noémie Bigras posted on Wednesday, March 13, 2019 - 4:50 am
Thank you for your quick answer! Does that mean I can't use it as an independent latent variable in a SEM model and I should rather compute a composite score or use the three separate scales?
 Bengt O. Muthen posted on Wednesday, March 13, 2019 - 4:22 pm
No, it doesn't mean that. It is perfectly fine to use it in a SEM.
 Daniel Lee posted on Tuesday, August 20, 2019 - 5:30 pm
Hi, to follow up on the previous question, I am reviewing a paper where the authors were upfront about their saturated CFA model (hence no model fit). However, the authors also added that the saturated measurement model probably fits the data well because, when the saturated measurement model was included in the structural model,the structural model fit the data well.

So the question I have is, can the authors really make claims about the fit of their three-item latent factor in this case?
 Bengt O. Muthen posted on Friday, August 23, 2019 - 6:11 am
I assume that the structural model has more variables than the 3 indicators and their factor. If so, no further information is gained with respect to the correlations among the 3 indicators - that part is still just-identified - but if adding those other variables gives a well-fitting model then the correlations between those 3 indicators and the other variables are well fitted. So in that sense the 1-factor model for those 3 is good - there are a lot of restrictions on the correlations with other variables that have to be in line with the data.
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