How to interpret Multiple Group CFA o... PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Tony Jung posted on Wednesday, August 16, 2006 - 9:48 pm
I'm using version 4.0. I'm running a multiple group CFA to test for factorial invariance across 4 groups. Single latent with 3 indicators. The indicator variables are 5-point Likert type. Using MLR and GENERAL MISSING H1, my output is as follows:


Chi-Square Test of Model Fit Value = 151.312*
Degrees of Freedom = 12
P-Value = 0.0000
Scaling Correction Factor for MLR = 1.164

Chi-Square Contributions From Each Group

GROUP 1 32.944
GROUP 2 38.613
GROUP 3 6.830
GROUP 4 72.926

What I don't understand is how to apply the steps for "Chi-Square Difference Testing Using the Satorra-Bentler Scaled Chi-Square" as outlined on your website.

Do I simply take the difference in chi-square contribution values and divide by the scaling correction factor? For example, Group 1 (32.944) minus Group 2 (38.613) divided by 1.164? How would I test for difference between, say Model 1, and the OVERALL model?

My second question is, should I be using WLSMV instead of MLR since the variables are skewed and non-normal?
 Linda K. Muthen posted on Thursday, August 17, 2006 - 7:06 am
If your variables are ordered polytomous with floor or ceiling effects, you should treat them as categorical. You can use either the weighted least squares estimator or maximum likelihood. The key is that you would be using the CATEGORICAL option of the VARIABLE command. This can be used with either estimator.

In Chapter 13 at the end of the disucssion of multiple group analysis, you will find a discussion of testing for measurement invariance. Here you will find the models to compare. The chi-square for the full model should be used.
 Scott R. Colwell posted on Sunday, February 17, 2008 - 10:08 am
Why is it that if you run a CFA without considering grouping then you a much lower Chi-Square value than if you consider groups in the CFA through the "grouping is.." option.

Should the chi-square value stay the same?

 Linda K. Muthen posted on Sunday, February 17, 2008 - 11:35 am
It could be that the model fits differently in the general population that in the separate groups. It could also be that you have not relaxed the default equality constraints in Mplus and that these constraints are affecting the fit. See the following paper for further information:

Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557-585.
 Fatma Ayyad posted on Monday, August 09, 2010 - 10:23 pm
Dear Dr. Muthen:

I'm using version 6.0. I'm running a multiple group CFA to test for factorial invariance across 4 groups. 3 continiuos latent variable, and 40 indicators. The indicator variables are 5-point Likert type. I am using WLSMV estimator and type=general.

My question: why in the output I can not read the Chi square model fit. RMSE, CFI and TLI?


I also tried two factor solution and one factor solution and I was not able to read the model fit.

Thank you,
 Linda K. Muthen posted on Tuesday, August 10, 2010 - 6:12 am
Please send the full output and your license number to
 Keivn Linares posted on Thursday, November 04, 2010 - 12:39 am
Hello Drs. Muthen,

Is there a difference approach to study measurement invariance and investigate variance and structural mean invariance of categorical items using the BAYES estimator in version 6.1? I tried executing a multiple groups analysis and I received the following message:

*** ERROR in ANALYSIS command
ESTIMATOR=BAYES is not currently available for multiple group analysis.
Try using the KNOWNCLASS option for TYPE=MIXTURE.

this was my syntax:
FBITER = 20000;
STVAL = ml;

F1 BY m18* m3 m7 m12 m19 m20;
F2 BY m5* m8 m10 m11 m14 m15 m16;
F3 BY m1* m4 m9 m13 m17;

Model Female:
F1 BY m3* m7 m12 m19 m20;
F2 BY m8* m10 m11 m14 m15 m16;
F3 BY m4* m9 m13 m17;
 Linda K. Muthen posted on Thursday, November 04, 2010 - 6:05 am
Multiple group analysis must be done via TYPE=MIXTURE using the KNOWNCLASS option. The GROUPING option is not available yet with Bayesian analysis. When class membership is known, it is the same as multiple group analysis.
 janni niclasen posted on Friday, April 27, 2012 - 4:26 am
I am running CFA, categorical data, WLS estimator, (N=71000 in total but eight subsamples varying in size from 1200-28000). I am comparing identical models between the groups. I have two questions:

question 1. when I compare two groups using the 'grouping is' command i get the following output:

Chi-Square Contributions From Each Group
DRENG 1671.136
PIGE 1471.437

What do I do next. I assume that I cannot just say that the model works better for girls (I suppose I need some sort of statistical difference)? Will I have to carry out some sort of significance test og what do I report in my article?

question 2: I want to compare the models among all eight groups. Is there a way to do that and how do I interpret these output? And is it problematic that my groups vary in size from 1200-28000?

 Linda K. Muthen posted on Friday, April 27, 2012 - 9:01 am
The chi-square contributions for each group are descriptive and are not meant to be used to make decisions about which group fits best. A first step in multiple group analysis is to run the analysis for each group separately. If the same model does not fit well in each group, it does not make sense to do a multiple group analysis. See the Topic 2 course handout under multiple group analysis to see the steps we recommend for testing for measurement invariance for categorical outcomes.
 janni niclasen posted on Monday, April 30, 2012 - 1:43 am
I have already specified well working models for each group and also identified one overall well-working model for all groups (i.e. I have done what is recommended in topic 2). The model that I wnat to compare between groups is the model that I have identified to be a well working model for all sub-samples. so my questions:

1. Can I conclude that the model is better for group PIGE in the output above?

2. is it problematic that my groups vary in size from 1200-28000 - when I compare the sub-samples with each other?
 Linda K. Muthen posted on Monday, April 30, 2012 - 8:38 am
1. No. These are for descriptive purposes only. Use the fit from the individual group analyses.

2. The larger groups will dominate to some extent. You can take random samples from the larger groups to bring them in line with the other groups.
 Yen posted on Friday, September 28, 2012 - 6:15 pm
I used MLR as the estimator for Multiple group CFA analysis. When I gradually imposed equality constraint to the model, the CFI values increase instead of decrease.
How can this be interpreted? Is there any reference that discuss about this?

Thank you.
 Linda K. Muthen posted on Sunday, September 30, 2012 - 10:36 am
Please send the two outputs and your license number to
 luk bruyneel posted on Thursday, July 27, 2017 - 8:24 am
For identification purposes, in the below model I fixed factor variance and latent mean to be 1 and 0. My findings for scalar invariance are however better than those for configural invariance. Is something wrong with the model specification or can it indeed be that scalar invariance produces better model fit?

a1 a2 a3 a4 a6 a7 a12 a13 a14 a15 a16 a17 a9 a10 a28
a21 a22 a25 a26 a18 a19 a20 a30 a31 a23 a24 a27 a29
a32 a35;


GROUPING = type (1 2 3 4 5 6 9);

one by a1 a2 a3 a4;
two by a6 a7;
three by a12 a13 a14 a15 a16 a17;
four by a9 a10 a28;
five by a21 a22 a25 a26;
six by a18 a19 a20;
seven by a30 a31;
eight by a23 a24 a27 a29;
nine by a32 a35;


iteration = 1000;
model = configural scalar;
 Linda K. Muthen posted on Thursday, July 27, 2017 - 9:54 am
When you set the metric of the factor in the factor variance, you need to free the first factor loading which is fixed at one as the default to set the metric of the factor, for example,

one by a1* a2 a3 a4;
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