Configural invariance with M Plus PreviousNext
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 Anonymous posted on Wednesday, January 28, 2004 - 8:51 am
When investigating configural invariance in a multigroup model should one free the intercepts to test the hypothesis that the smae pattern of zero and nonzero factor loadings is found in both groups?
 Linda K. Muthen posted on Wednesday, January 28, 2004 - 9:10 am
Yes, free the intercepts if you want to test only the invariance of the factor loadings.
 Tim Jackson posted on Monday, November 17, 2008 - 6:08 am
Hi there,
I am trying to test for configural invariance in a 5 factor model, across two time points. In other words, I want to test whether the 5 factor structure is tenable across the two time points.

In order to test configural invariance I have done the following when writing the syntax:
1) specified the factor structure for each time point (i.e., indicators loading on their intended latent factors, and letting the latent factors within a given time point covary with each other). Note that I did not specify that latent factors should correlate with other latent factors at a different time point,
2) fixed the means of each of the latent factors to zero,
3) freed the intercepts of each of the items at each of the time points,
4) allowed like items to correlate with each other across time points (e.g., item1_t1 with item1_t2); this was done to deal with correlated residuals across time.

My question is simply 'have I done this correctly?' I have in my possession some Mplus syntax examples in which configural invariance of a SINGLE construct is tested across groups, or across time points... but I do not have examples of tests of configural invariance in Mplus using a MULTIDIMENSIONAL structure across time points. I just want to take care that I am conducting this test correctly before trying to interpret any output.

Thank you very much for any input you might be able to provide,
Tim
 Linda K. Muthen posted on Monday, November 17, 2008 - 8:41 am
I would not take the approach you describe. See instead the Topic 4 course handout for multiple indicator growth. The first steps in this analysis test for measurement invariance across time. With more than one factor, take the same approach. Allow the factors to correlate.
 Metin Ozdemir posted on Wednesday, February 24, 2010 - 8:38 am
I am testing a series of measurement invariance models using multigroup CFA. I have four latents variables, and ordered-categorical indicators. Therefore, I am using WLSMV estimator.

How should I test the configural invariance given that the MPlus default fixes factor loadings to be equal across groups? Do I free the thresholds following your suggestion above?

Using the following syntax, I freed the thresholds, nothing has changed? The thresholds are still equal across groups so as the loadings.

[TA2N$1* TA2N$2* TA2N$3* TA11R$1* TA11R$2* TA11R$3* .....]

Any suggestion is very much appreciated.

Thanks,
 Linda K. Muthen posted on Wednesday, February 24, 2010 - 9:22 am
See pages 398-401 in the user's guide. See also the Topic 1 course handout on measurement invariance for general principles related to continuous outcomes and the Topic 2 course handout for an application to categorical outcomes.
 Yves Dejaeghere posted on Wednesday, July 07, 2010 - 7:44 am
Hello,

I have a battery of six items/statements measuring ethnocentrism with four scoring possibilities.
I have used it on the same population of adolescents in 2006 and 2008. Because the indicator is categorical I am not 100% if the syntax below is correct to conclude longitudinal invariance (it gives good GOF-indicators) including for the factor loadings. I am especially doubtfull if I can correlate the error terms this way...


Variable: Names are et1-et6 ethno1-ethno6;
Usevariables are et1-et6 ethno1-ethno6;
categorical ARE ALL;
Missing are ALL(99);

analysis:
estimator = WLSMV
type = meanstructure;
Model: RACE1 by et1 et2 (2)
et3 (3)
et4 (4)
et5 (5)
et6 (6);
RACE2 by ethno1 ethno2 (2)
ethno3 (3)
ethno4 (4)
ethno5 (5)
ethno6 (6);
et1 with ethno1;
et2 with ethno2;
et3 with ethno3;
et4 with ethno4;
et5 with ethno5;
et6 with ethno6;
 Linda K. Muthen posted on Wednesday, July 07, 2010 - 3:39 pm
See the discussion of testing for measurement invariance with categorical outcomes and the end of the multiple group discussion in Chapter 14 of the Version 6 user's guide, Chapter 13 of earlier user's guides. You would use the same models across time rather than across groups. See also the multiple indicator growth example in the Topic 4 course handout. You can correlate the error terms if you use the weighted least squares estimator but it is more difficult with maximum likelihood estimation because each residual covariance is one dimension of integration.
 Xiaoying Xu posted on Thursday, December 02, 2010 - 11:09 am
Hi, I have problem to run the factorial invariance for a second-order model.
First, I run a multiple-group CFA with ordered categorical data using Mplus 5.2 and trying to test a model. The code I am using is:
TITLE: multiple-group CFA cfa for 4 factor
DATA: file is "C:\r_4mp.txt";
format is 22f1.0;
VARIABLE: names are s1-s22;
usevariables are s1-s20;
grouping is s21 (0=female 1=male);
categorical are all;
MODEL:
r1 by s1-s5;
r2 by s6-s10;
r3 by s11-s15;
r4 by s16-s20;
The model fit is acceptable( CFI: 0.961,
TLI:0.974, RMSEA: 0.026,WRMR Value: 1.692).
When I try to do this for the second-order model by adding to the last code:
Genfact by r1-r4;
It didnot give a estimate of CFI and massage shows:
THE MODEL ESTIMATION TERMINATED NORMALLY

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.
PROBLEM INVOLVING PARAMETER 49.

THE CONDITION NUMBER IS -0.456D-16.

Is there any people having this problem?
 Linda K. Muthen posted on Thursday, December 02, 2010 - 12:56 pm
You need to fix the intercepts of the first-order factors to zero in all groups for the model to be identified.
 Xiaoying Xu posted on Saturday, December 04, 2010 - 9:09 pm
Hi, Linda,
you mentioned "fix the intercepts of the first-order factors to zero" (in the user's book, it is called the factor mean, instead of intercepts), but they are same thing, right? Could you let me know if I understand wrong?

I tried to fix the intercepts of the first-order factors to zero, and it work well now. Thank you!
 Linda K. Muthen posted on Sunday, December 05, 2010 - 6:12 am
The first-order factors have intercepts estimated not means because they are dependent variables regressed on the second-order factor. The Mplus language is the same for means and intercepts.
 Xiaoying Xu posted on Sunday, December 05, 2010 - 9:09 pm
On the user's book, p. 399-400, measurement invariance for continuous outcomes, steps 2-4 add one more constraint each time. So the procedure is, Step 1 we need to run the baseline model without any constraint first, secondly we add constrains for equal loading, thirdly we add equal intercept. For categorical variables, there are only two models, first is baseline model without any constraint, and second is the threshold and loadings constrained to be equal.

My question is, is the threshold a concept for categorical data which is very similar counterpart to the intercept/mean for continuous data? I am wondering if I can add one constraint each time. For example, I add constraint for factor loading in step 2, and add thresholds constraints for step 3. How do you think about that?

If the threshold and loadings constraints could not be treated separately, then should I fix the first item loading but free the first item threshold? For model identification purpose, I need to fix the first item loading at 1. Shall I also fix the fir item threshold at some value accordingly?

Please correct me if I understand anything wrong. I really appreciate your help about this and any suggested reading about factorial invariance procedure for categorical data.
 Linda K. Muthen posted on Monday, December 06, 2010 - 6:29 am
See the Topic 2 course handout on the website under multiple group analysis for the measurement invariance models we suggest for categorical outcomes.
 Sabine Spindler posted on Wednesday, April 06, 2011 - 10:33 am
Dear Dr. Muthen,

I want to test Measurement Invariance in a 1 Factor Model with multiple-groups comparisons for ordered categorical data. I use the WLSMV estimator.

Before starting nested comparisons, in order to rule out model misspecification, i fit the model separately for each group.
However, when I do this, I get different chi-square df for every group (67 vs. 61). Why is that normal because WLSMV adjusts for deviations from normality which may be different between groups or do I need to be worried?

Thank you very much,
all the best,
Sabine
 Linda K. Muthen posted on Wednesday, April 06, 2011 - 11:41 am
It sounds like you are using a version of Mplus before Version 6. The degrees of freedom and chi-square in these earlier versions were adjusted to obtain a correct p-value. Only the p-value should be interpreted. You will obtain the degrees of freedom you expect using WLS or WLSM.
 christina weiland posted on Friday, November 04, 2011 - 9:23 am
Hello -

I fit a multi-group configural invariance model, with one latent construct with three manifest indicators (and #groups=2). My question is about the Chi-sq statistic. When I fit the same model within one sample only, it is just identified and has a chi-sq of zero (number of free parameters=9 and df=0). When I fit it to both groups via a configural invariance model, the chi-sq is non-zero. Isn't the configural model also just identified and shouldn't I thus be getting a zero chi-sq value? In the configural invariance model, Mplus says that the number of free parameters is 16 and df=2.

Thank you for your help!
 Linda K. Muthen posted on Friday, November 04, 2011 - 11:06 am
The default in Mplus is to hold intercepts and factor loadings equal across groups. You need to relax these constraints. See the Topic 1 course handout under multiple group analysis for an example input.
 steve posted on Saturday, November 05, 2011 - 10:45 am
Dear Linda and Bength,

Im trying to do an invariance multigroup model over five groups starting with configural invariance. The model includes two latent factors measured by two items each. Unfortunately I did the math wrong and the model is not identified (don't rightly know why) - is there any workaround to fix this?

MODEL: F1 BY Y1 Y2;
F2 BY Y4 Y5;
[F1-F2@0];

MODEL AG2: F1 BY Y1 Y2;
F2 BY Y4 Y5;
[Y1 Y2 Y4 Y5];

MODEL AG3: F1 BY Y1 Y2;
F2 BY Y4 Y5;
[Y1 Y2 Y4 Y5];

MODEL AG4: F1 BY Y1 Y2;
F2 BY Y4 Y5;
[Y1 Y2 Y4 Y5];

MODEL AG5: F1 BY Y1 Y2;
F2 BY Y4 Y5;
[Y1 Y2 Y4 Y5];

Thank you!
 Linda K. Muthen posted on Saturday, November 05, 2011 - 12:18 pm
You should not mention the first factor loading in the group-specific MODEL commands. When you do, they are no longer fixed at one but free causing the non-identification message.
 steve posted on Monday, November 07, 2011 - 3:03 am
Thank you! This solved the identification issue. However, the model wont converge. I guess the problem is that the indicators are sum scores of the respective rounds of cognitive tests resulting in different metrics, i.e. range 2-16 for Item 1 in AG1 and 10-29 in AG5. Could this be the problem?
 Linda K. Muthen posted on Monday, November 07, 2011 - 8:13 am
Try freeing the first factor loadings and fixing the factor variances to one. It may be that the first factor indicator is not close to one causing problems when it is fixed at one. If this does not help, please send your output and license number to support@statmodel.com.
 steve posted on Monday, November 07, 2011 - 9:08 am
Thats it! Thank you so much! :-)
 Linda K. Muthen posted on Monday, November 07, 2011 - 1:37 pm
If you want to set the metric fixing a factor loading, you should choose one that is estimated close to plus one.
 Bethany Backes posted on Thursday, December 15, 2011 - 9:15 am
Hi-
I am running a multi group model with categorical data. Below is my syntax and the error message I am receiving in the output. Is there a different way I should be writing the final line under Model males for categorical data? When I remove it, it runs without error. Thanks! ~Bethany

Model: Legal by Pol, OthCJ, GovtVic;
Health by Med, Emo, Phys, PrivVic;

[Legal@0, Health@0];

Model females:

Model males: Legal by OthCJ, GovtVic;
Health by Emo, Phys, PrivVic;

[Med Emo Phys Pol OthCJ GovtVic PrivVic];

Output: modindices;


Error Message: The following MODEL statements are ignored:
* Statements in Group MALES:
[ POL ]
[ EMO ]
[ PHYS ]
[ OTHCJ ]
[ GOVTVIC ]
[ PRIVVIC ]
 Linda K. Muthen posted on Thursday, December 15, 2011 - 11:15 am
Categorical variables have thresholds not means. Thresholds are referred to as

[pol$1];

if the variable is binary.
 Eric Deemer posted on Wednesday, April 18, 2012 - 12:47 pm
Hi all,
I fitted a multigroup CFA model to test for factorial and intercept invariance but I'm not sure if my input is correct:

Factorial invariance model:
Variable: names = y1-y11 gender;
usevariables = y1-y11 gender;
grouping = gender (0=male 1=female);

Model: PC by y1-y7;
AFF by y8-y11;
[PC@0 AFF@0];
MODEL female: [y1-y7];
[y8-y11];


Intercept invariance model:
PC by y1-y7;
AFF by y8-y11;

Does this input look correct? Also, how would I set up the model to examine configural invariance?
 Linda K. Muthen posted on Wednesday, April 18, 2012 - 3:08 pm
Please see the Topic 1 course handout under Multiple Group. You will find the inputs for testing measurement invariance.
 Kelly DeMartini posted on Thursday, May 10, 2012 - 1:53 pm
Hi all,

I am running a multigroup (gender) CFA model (2 latent factors, 10 items) to test for configural invariance. Below is my syntax and error message:


GROUPING is sex (0 = female 1 = male);
ANALYSIS: ESTIMATOR = MLR;
MODEL:
direct by apf4 apf5 apf2 apf1 apf6 apf7;
indirect by apf11 apf12 apf16 apf14;
MODEL female:
direct by apf5 apf2 apf1 apf6 apf7;
indirect by apf12 apf16 apf14;
[direct@0 indirect@0];
[apf1 apf2 apf4 apf5 apf6 apf7 apf11 apf12 apf14 apf16];
OUTPUT: sampstat modindices (10.00) tech1 stand residual;

“Model terminated normally. The standard errors of the model parameter estimates could not be computed. Model may not be identified. Check your model. Problem involving parameter 60.”

Parameter 60 is an alpha error. When I remove items apf4 and 11 (the ones fixed at 1.0) from the brackets, it runs, but I need to test a model with all model parameters free except for the first factor metrics (set to 1.0) and means (set to 0). Is there a different way I should be running this?

Thank you!
 Linda K. Muthen posted on Thursday, May 10, 2012 - 3:44 pm
Move

[direct@0 indirect@0];

from MODEL female to MODEL.
 Stata posted on Thursday, June 07, 2012 - 12:09 pm
I have a factor with only one indicator (composite score). Should I set error value for that indicator?

Thanks.
 Linda K. Muthen posted on Thursday, June 07, 2012 - 2:24 pm
A factor with one indicator and a residual variance of zero is identical to the factor so you should simply use the observed variable. If you want to correct for reliability, see the Topic 1 course handout under measurement error. I personally don't think this is a good idea because it is highly likely that the estimate of reliability is not accurate bringing more problems to that variable.
 EFried posted on Tuesday, June 19, 2012 - 3:25 pm
Regarding Bengt's 5.1 ESEM measurement invariance webtutorial. Syntax for the least strict model:

Grouping is group (1=g1, 2=g2);
Model: f1-f2 by y1-y10 (*1);
[f1-f2@0];
Model G2:
f1-f2 by y1-y10 (*1);
[y1-y10];

My syntax is similar and I don't understand why it does not work:

grouping is time (0=time0 1=time1);
...
MODEL:
F1-F2 by phq1-phq9 (*1);
[F1-F2@0];
MODEL time0:
F1-F2 by phq1-phq9 (*1);
[phq1-phq9];
MODEL time1:
F1-F2 by phq1-phq9 (*1);
[phq1-phq9];

that should free thresholds and loadings, but I receive the error:

*** ERROR
The following MODEL statements are ignored:
* Statements in Group TIME0:
[ PHQ1 ]
[ PHQ2 ]
[ PHQ3 ]
... (all the way to time1 phq9)

Thank you!
 Bengt O. Muthen posted on Tuesday, June 19, 2012 - 3:59 pm
Maybe your outcomes are categorical and so require thresholds ($1 etc) instead of intercepts.
 Morayo Ayodele posted on Thursday, July 05, 2012 - 8:30 pm
Hello Dr. Muthen,

What is appropriate syntax for running a configural invariance test for this second-order model between males and females? All the syntax i attempted to modify were unsuccessful.

Model:
F1 by one two three four;
F2 by five six seven eight;
Lead by F1@1 F2@1;
Output: Standardized mod;

Thank you
 Linda K. Muthen posted on Friday, July 06, 2012 - 11:04 am
I think you are probably forgetting to fix the factor means of the first-order factors to zero in all groups. Without this, the model is not identified. If this is not the problem, please send the output and your license number to support@statmodel.com.
 Maria posted on Thursday, January 31, 2013 - 4:04 am
HI Linda,

I would like to test for measurement invariance across gender. After doing some reading it appears I should

1. test for configural invariance by running a CFA on the measurement model for males and females separately

2. test for metric invariance (I have ordinal/categorical data) using multi-group CFA.

Some articles suggest that the chi square obtained in step 2 should be the sum of the chi squares obtained for males and females separately.

Is this the case?

Thanks
 Linda K. Muthen posted on Thursday, January 31, 2013 - 5:54 am
The chi-squares for males and females separately will be the sum of the multiple group chi-square for configural invariance. not for metric invariance.
 Maria posted on Thursday, January 31, 2013 - 6:35 am
Thanks - could it ever be that that the sum is not exactly equal to the chi-square for configural invariance?
 Linda K. Muthen posted on Thursday, January 31, 2013 - 7:31 am
It depends on which estimator you use. For maximum likelihood, it should be the same. If you have a specific question, send the outputs and your license number to support@statmodel.com.
 Maria posted on Thursday, January 31, 2013 - 7:47 am
thanks - I am using the WLSMV estimator
 Linda K. Muthen posted on Thursday, January 31, 2013 - 9:44 am
This summation will not work for WLSMV.
 Maria posted on Thursday, January 31, 2013 - 10:22 am
Thank you!
 Hugo Cogo-Moreira posted on Saturday, June 08, 2013 - 6:45 am
Dear Linda/Bengt,
Reading your slides, a doubt about Multiple-group Factor Analysis appeared: in the slide (82/196) from UCONN's conference about Holzinger-Swineford's Model fit information (invariance testing) configural and metric model had p-value<0.00001.
However, metric against configural p-value =0.2755.
Issue: 1) Why, in the separately form, configural model is rejected while against the metric model it is not? Partial invariance involing configural model?
Thanks in advance
 Bengt O. Muthen posted on Saturday, June 08, 2013 - 10:09 am
The test says that it is the Metric model that is not rejected as compared to the Configural model. In this case where the Configural model doesn't fit, it is unclear how useful this information is. One can perhaps say that the Metric model doesn't fit much worse than the Configural. But the test itself is called into question when the more relaxed model, the Configural model, does not fit. The test may not have a chi-square distribution in that case. The intended use of chi-square difference testing is that the more relaxed model fits and you are interested in seeing if a more restricted model doesn't fit significantly worse.
 Hadar Baharav posted on Monday, October 21, 2013 - 3:27 pm
Dear Mplus team,

I am trying to examine 2nd order factor invariance across two groups. Fairly early in the process, at the configural invariance stage, I run into a problem.

I fail to freely estimate the intercepts of the observed variables--both groups share the same indicator intercepts in the output I get.
Also, I believe all factor means (1st order latent factor means and 2nd order latent factor mean) should equal zero in both groups, but the output I obtain provides an estimate for the 1st order means of the second group (while all other latent means are zero).

This is the syntax I am using:

Model:
ICE by BYT13 BYT14 BYT15 BYT16;
CA by BYTE21CR BYTE21AR BYTE21BR BYTE21DR;
AP by BYS89V BYS89J BYS89O BYS89S;
CAC by BYTXMIRR BYTXRIRR;
CR by ICE CA AP CAC;
[BYT13 - BYTXRIRR];
[ICE CA AP CAC CR@0];

Model Hispanic:
ICE by BYT14 BYT15 BYT16;
CA by BYTE21AR BYTE21BR BYTE21DR;
AP by BYS89J BYS89O BYS89S;
CAC by BYTXRIRR;

Thanks!
 Linda K. Muthen posted on Monday, October 21, 2013 - 4:57 pm
The first-order means in the second group must be fixed to zero. This is not the default in Mplus.
 RuoShui posted on Monday, October 28, 2013 - 3:06 pm
Hello Linda,

I am testing measurement invariance over four time points. The model has poor CFI and TLI (around .68). But after I adopted the modification indices by correlating error variance among items, the model fit improved to adequate. I am wondering whether modification indices can be adopted? Does it defeat the purpose of testing measurement invariance?

Thank you.
 Linda K. Muthen posted on Monday, October 28, 2013 - 4:43 pm
You should fit the model at each time point separately as a first step. If you do not have the same well-fitting model at each time point, you should not test for measurement invariance. When you combine them, it may be that correlating residuals across time is necessary.
 Anna Koch posted on Tuesday, July 29, 2014 - 2:19 am
Dear Linda or Bengt,

I am testing measurement invariance for a second-order factor model. Everything works perfectly well until I constrain the intercepts of the first-order latent factors to be equal (testing for strong factorial invariance). According to the output Mplus neither constrains the intercepts to be equal nor gives an error message. I just keep getting the exact same results as when testing for strong factorial without constraining the intercepts of the first-order latent factors. It seems like Mplus ignores the additional syntax paths...I double checked the syntax. Do you have an idea what might went wrong?

Thank you very much!

Best regards
Anna
 Linda K. Muthen posted on Tuesday, July 29, 2014 - 5:58 am
Please send the output and your license number to support@statmodel.com.
 Simone Croft posted on Wednesday, March 04, 2015 - 4:53 am
Hello,

I'm having some difficulty replicating manually the results provided by mplus for measurement invariance across group using the MODEL = Config, metric, scalar command.

Initially I achieved measurement invariance over time for my scales of interest. I now want to make appropriate constraints across gender.

The results suggest that the scales have configural and metric invariance across groups, but not scalar. To work out where the noninvariance is, I have tried to program mplus manually to do run the same models. However, when I try to replicate the results I cannot get the model to converge. The error messages suggests the model may not be identified, but if I'm just copying the model directly, but including 'MODEL FEMALE' and 'MODEL MALE' subcommands, I don't understand why the model will not converge. I've tried several things to fix the problem but cannot seem to replicate the findings. Can you provide any insights as to why this might be?

Thanks in advance,
Simone
 Linda K. Muthen posted on Wednesday, March 04, 2015 - 5:57 am
You are most likely mentioning the first factor indicator in the group-specific MODEL commands. When you do this, the first factor loading is no longer fixed to one. The inputs for testing for measurement invariance for continuous indicators are shown in the Topic 1 course handout on the website under multiple group analysis. The inputs for categorical outcomes is shown in the Topic 2 course handout.
 Simone Croft posted on Thursday, March 05, 2015 - 7:13 am
I've just seen a response from Bengt in response to someone else's question that I think is relevant. I am trying to do a multi-group comparison for boys and girls, using a measurement model that already has a number of across-time constraints. Bengt's reply was:

"Using

Model = configural metric scalar;

will ignore any parameter equality settings.

We don't yet have that kind of convenience feature for longitudinal or combined multi-group/long'l, so all of it has to be done "by hand" with explicit equalities."

So therefore the multi-group fit indices I was getting did not also have the across time constraints (which my manually coded model had), which presumably explains why they did not match up?

Simone
 Bengt O. Muthen posted on Thursday, March 05, 2015 - 9:25 am
That could be the case.
 Simone Croft posted on Friday, March 06, 2015 - 7:34 am
Hello,

on the same note as my message above, I would like to constrain some of my parameters across time, and I also want to test for invariance across group simultaneously. Once parameters are constrained to be the same over time, is it possible to also get different estimates for the parameters across groups, while maintaining the across time constraints?

Simone
 Bengt O. Muthen posted on Friday, March 06, 2015 - 8:03 am
Yes. You are in full control of the equalities you want to apply.
 Ann-Renee Blais posted on Wednesday, June 03, 2015 - 3:16 pm
Hello,

I've been struggling with a configural invariance model (2 time points).

My 5 indicators are binary (so I'm using WLSMV), and my no. of obs. is 284 at Time 1 and 238 at Time 2.

The one-factor CFA models look good at both time points (X2>.05 both times, CFI=.95 & .99, and WRMR=.79 & .72).

However, when I attempt to assess configural invariance, I get an error message ("...a correlation greater or equal to one between 2 latent variables,..."), and my factor correlation is indeed greater than 1.

What might be the cause of that? I'm at loss. Everything else looks fine (that I can tell). Any help/advice would be appreciated!

Thanks!
 Bengt O. Muthen posted on Wednesday, June 03, 2015 - 4:59 pm
Perhaps you have correlations between residuals for the same item at different time points. Not including them can inflate the factor correlation across time.
 Ann-Renee Blais posted on Wednesday, June 03, 2015 - 6:06 pm
Dr. Muthen,

Thank you for the prompt response. I checked my model again, and I had included the correlations between the residuals for the same item across time points. There were no errors there.

This is a very simple one-factor model with only 5 indicators and 2 time points... I really cannot figure out what's going on.
 Bengt O. Muthen posted on Thursday, June 04, 2015 - 8:44 am
Maybe there isn't that much change between time 1 and time 2.
 Tahir Wani posted on Tuesday, August 04, 2015 - 5:48 am
I am trying to do an invariance measurement for the model. I have MPlus 6 installed.
Syntax used:

Grouping is Gender (1=Male 2=Female)


Analysis:
Type=general;
Estimator=MLR;
MODEL IS CONFIGURAL METRIC SCALAR;

Model:


But it shows the following error:
*** ERROR in ANALYSIS command
Unrecognized setting for MODEL option:
CONFIGURAL.

Any thoughts why is it happening.
 Linda K. Muthen posted on Tuesday, August 04, 2015 - 6:15 am
These options are not available in Version 6. They were introduced in Version 7.1.
 Rasha Qudisat posted on Wednesday, October 14, 2015 - 7:00 pm
Dr. Muthen,
I am trying to test the measurement invariance between two groups for one factor mode, using the code: MODEL IS CONFIGURAL SCALAR;

The result is:
Invariance Testing

Configural p-value 0.0000
Scalar -value 0.0000
Scalar against Configural p-value 0.0203

I checked the models for the two groups (i.e. male and female, where the male is the reference group) and the two models have close degree of fit (CFI, TLI, and RMSEA) are excellent, and the item loading are also good.
If the two groups fit the model, I do not understand why the configural model is significant!
Do you have any suggestions for making the configural invariance better between the two groups?
 Linda K. Muthen posted on Thursday, October 15, 2015 - 9:59 am
The testing using the CONFIGURAL option is done using chi-square. Your comparison should be to chi-square not CFI etc.
 Matthew Courtney posted on Tuesday, January 26, 2016 - 6:09 pm
Dear professors Muthen,

I'm trying to perform longitudinal invariance tests with correlated residuals.

I have the following standard code running well:

Variable:
Names are StudentID Programme Cond_C Gender_C Maori_C Pac_C Asian_C Incomp_C Time PREs1a PREs2 PREs3 PREs4a PREs5a PREs6a PREs7 PREs8 POSTs1a POSTs2 POSTs3 POSTs4a POSTs5a POSTs6a POSTs7 POSTs8 OYPPs1b OYPPs2 OYPPs3 OYPPs4b OYPPs5b OYPPs6b OYPPs7 OYPPs8;

usevariables = Time OYPPs1b OYPPs2 OYPPs3 OYPPs4b OYPPs5b OYPPs6b OYPPs7 OYPPs8;

grouping = Time (0 = TimeZero 1 = TimeOne);

categorical = OYPPs1b OYPPs2 OYPPs3 OYPPs4b OYPPs5b OYPPs6b OYPPs7 OYPPs8;

Analysis:
estimator = wlsmv;
model = configural metric scalar;

Model:
Social by OYPPs1b OYPPs2 OYPPs3 OYPPs4b OYPPs5b OYPPs6b OYPPs7 OYPPs8;

Output:
standardized tech1;

Is it possible to extend this code to correlate residuals? Or will I have to first re-arrange my data so that the MODEL command specifies two separate factors representing the two time points?
 Bengt O. Muthen posted on Tuesday, January 26, 2016 - 6:43 pm
Do you have 2 different samples of subjects at the 2 time points? Otherwise, multiple-group analysis is not right. Since you say you want to correlate residuals I assume you don't have different samples. You can correlate them if you have the same sample measured twice, so longitudinal data. The principles of configural, metric, scalar are the same for longitudinal data, but you have to do them manually yourself.
 Matthew Courtney posted on Friday, January 29, 2016 - 12:21 am
Thanks for your help :-)
 Anders Hofverberg posted on Monday, February 29, 2016 - 1:26 am
Hello,

I am new to CFA and Mplus, but try to investigate configural invariance between two groups in a three factor model. Based on Wang 2012, I use this input:

VARIABLE: NAMES ARE SEX SWE_GER GRADE
AG_1 AG_2 AG_3 AG_4 AG_5 AG_6 AG_7 AG_8 AG_9 AG_10 AG_11 AG_12 AG_13 AG_14 FILTER_01;

USEOBSERVATIONS IS (FILTER_01 EQ 1);

USEVARIABLES ARE
SWE_GER AG_1 AG_2 AG_4 AG_5 AG_6 AG_7 AG_8 AG_9 AG_10 AG_11 AG_12 AG_13 AG_14;

MISSING ARE ALL (99);

GROUPING=SWE_GER (1=SWEDEN 2=GERMANY);

MODEL: Mastery BY AG_6 AG_7 AG_8 AG_9 AG_10;
PAp BY AG_1 AG_2 AG_4 AG_5;
PAv BY AG_11 AG_12 AG_13 AG_14;
Mastery@0; PAp@0; PAv@0;

MODEL SWEDEN: Mastery BY AG_6@1 AG_7 AG_8 AG_9 AG_10;
PAp BY AG_1@1 AG_2 AG_4 AG_5;
PAv BY AG_11@1 AG_12 AG_13 AG_14;
[AG_1-AG_14*];

ANALYSIS: TYPE IS GENERAL;

I get the the following error message:
THE MODEL ESTIMATION TERMINATED NORMALLY

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.
PROBLEM INVOLVING PARAMETER 76.

TECH1 shows that parameter 76 is an alpha error for Mastery. What am I missing?
 Linda K. Muthen posted on Monday, February 29, 2016 - 4:42 pm
Why do you fix the factor variances to zero:

Mastery@0; PAp@0; PAv@0;

I think you want to fix the means to zero:

[mastery-pav@0];
 Anders Hofverberg posted on Monday, February 29, 2016 - 11:09 pm
Yes, exactly, I missed the brackets. Thank you. However, I discovered the CONFIGURAL METRIC SCALAR commands and was able to test invariance through them. They are nice additions to the program.

Also thank you for a quick answer! The response times on this forum are impressive.
 Eileen Moon posted on Thursday, September 15, 2016 - 4:43 am
Hello,

I'm currently investigating factorial/measurement invariance between two groups in 5 factors, using MLR and Mplus7.

My problem is with the comparison of the first models that, in my opinion, are not nested and so cannot be compared.

I used "ex 5.27: MULTIPLE-GROUP EFA WITH CONTINUOUS FACTOR INDICATORS" (User Guide, 2010, p. 93ff) for orientation.

I am aware that I have to fix some parameters, e.g. latent factor means@0 across groups, to identify the "configural invariance" model 1 that per se does not entail any constraints. But in the example, this is still done for the following model 2 "equality of factor loadings".

This confuses me and opens up the following problems:

1) I could not find any ESEM literature saying that the factor means still have to be constrained when factor loadings are constrained (model 2), for purposes of model identification. Why does Mplus ask for it?

2) Model 2 cannot be compared with model 3 (factor loadings AND intercepts constrained, but latent factor means free), as they are not nested models.

3) What if I do not want to constrain factor means across groups for my configural invariance model (model 1), as I cannot assume that this actually holds true and it therefore might manipulate my invariance model and model comparisons?
 Bengt O. Muthen posted on Thursday, September 15, 2016 - 10:47 am
1) The equality of factor loadings in model 2 does not make factor means identifiable. This is because the factor indicator intercepts are not equal so a change in factor means can be absorbed in the intercepts - hence you have indeterminacies and an unidentified model. This is true also for CFA.

2) Model 3 is nested within model 2. It is true that model 3 frees up factor means but it also restricts indicator intercepts to be equal.

3) The configural model doesn't really say that the factor means are equal (despite them being fixed at zero) - rather, it says that the configural model does not make any statement about means.
 Filipa Alexandra da Costa Rico Cala posted on Thursday, September 29, 2016 - 12:04 pm
Hello,

I am trying to perform a multi-group CFA in order to test the configural invariance between two independent samples with regard to an instrument. However, when I computed the Sintax in Mplus, the model fit was not estimated and I received the following warning:
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.
PROBLEM INVOLVING THE FOLLOWING PARAMETER:
Parameter 37, Group PT: { DSM9REC }
Could you please explain to me what is this and how I can solve this problem? many thanks in advance for all your help
 Linda K. Muthen posted on Thursday, September 29, 2016 - 1:53 pm
Please send the output and your license number to support@statmodel.com.
 Yilma Woldgabreal posted on Saturday, February 11, 2017 - 8:03 pm
Dear all
I have data across two waves and trying to test the configural, metric and scalar models. I have a second order factor with four first order factors. Can the first order factors (composite scores) be used to test ME/I? My input for the configural (unconstrained model), for example, looks like as follows and not sure whether this can be done with sub-scales as indicators. Your help is much appreciated.

Usevariables Are
TotS1Frq TotS1Dur TotS1Int TotS1Thr
TotS2Frq TotS2Dur TotS2Int TotS2Thr;
ANALYSIS:
ESTIMATOR = ML;

! Measurement Model without !constraints (CFA 1)

MODEL:
Time1 by S1Frq S1Dur S1Int S1Thr;

Time2 by S2Frq S2Dur S2Int S2Thr;

S1Frq with S2Frq;
S1Frq with S2Dur;
S1Frq with S2Int;
S1Frq with S2Thr;

S1Dur with S2Dur;
S1DUr with S2Int;
S1Dur with S2Thr;

S1Int with S2Int;
S1Int with S2Thr;

S1Thr with S2Thr;
 Bengt O. Muthen posted on Sunday, February 12, 2017 - 11:18 am
Yes, first-order factors can be tested for measurement invariance (but your model does not show a second-order factor model).

SEMNET is a better outlet for these general analysis strategy questions.
 John D Peipert posted on Thursday, March 09, 2017 - 10:44 pm
Dear Professors,

When testing measurement invariance with a categorical CFA model using the WLSMV estimator and the "MODEL IS CONFIGURAL METRIC SCALAR;" command, is the DIFFTEST for model comparison automatically applied and shown in the "Invariance Testing" portion of the output?

Thanks in advance for the clarification.
 Linda K. Muthen posted on Friday, March 10, 2017 - 10:00 am
Yes.
 John D Peipert posted on Friday, March 10, 2017 - 7:42 pm
Thank you very much for the quick reply!

I have two more questions regarding the use of the "MODEL IS CONFIGURAL METRIC SCALAR;" command.

1) The standard output is restricted for this option. In examining measurement invariance in a 2 group CFA model, if I want to get standardized loadings and other parameters for each of the groups, can I just estimate the model in each group separately?

2) Is there a way to get the modification indices with the "MODEL IS CONFIGURAL METRIC SCALAR;" command?

Again, thanks in advance for the help.
 Bengt O. Muthen posted on Saturday, March 11, 2017 - 8:01 am
1) Only if you are considering the configural model.

2) If it isn't produced when requested, it isn't available.
 Orpha de Lenne  posted on Friday, September 08, 2017 - 5:43 am
Dear Dr. Muthen,

I would like to test measurement invariance for a second-order CFA model. To test the configural model, I relaxed the defaults regarding factor means, factor loadings and intercepts. Should I also relax these defaults for the first-order factors?

Thank you in advance for your help.
 Bengt O. Muthen posted on Saturday, September 09, 2017 - 3:39 pm
Yes.
 Samuel Abplanalp posted on Monday, April 08, 2019 - 7:54 am
Hello,

I am testing gender configural invarinace on a two-factor ESEM model. When I run the model separately for males and females and add the chi-square values, they are not equaling the configural invariance model chi-square value. Is there a reason this could be happening?

Thanks for your help.
 Bengt O. Muthen posted on Monday, April 08, 2019 - 9:27 am
Send your two outputs to Support along with your license number.
 Samuel Abplanalp posted on Tuesday, April 09, 2019 - 9:00 am
In reference to my last message, here is my syntax:

Male model:


USEOBS gender EQ 1;
!GROUPING IS gender (1 = male 2 = female);

usevar = SEAS_3 SEAS_6
!SEAS_8
SEAS_9 SEAS_10 SEAS_12
SEAS_13 SEAS_15 SEAS_16 SEAS_17
SEAS_19 SEAS_22 SEAS_23;


Missing are all (-99);

ANALYSIS: ROTATION = GEOMIN;
MODEL: f1 f2 BY SEAS_3 SEAS_6
!SEAS_8
SEAS_9 SEAS_10 SEAS_12 SEAS_13 SEAS_15
SEAS_16 SEAS_17 SEAS_19 SEAS_22 SEAS_23 (*1);
SEAS_9 WITH SEAS_19;

OUTPUT: stdyx; MODINDICES(ALL);

Configural invariance model:


!USEOBS gender EQ 2;
GROUPING IS gender (1 = male 2 = female);

usevar = SEAS_3 SEAS_6
!SEAS_8
SEAS_9 SEAS_10 SEAS_12
SEAS_13 SEAS_15 SEAS_16 SEAS_17
SEAS_19 SEAS_22 SEAS_23;

Missing are all (-99);

ANALYSIS: ROTATION = GEOMIN;


MODEL: f1 f2 BY SEAS_3 SEAS_6
!SEAS_8
SEAS_9 SEAS_10 SEAS_12 SEAS_13 SEAS_15
SEAS_16 SEAS_17 SEAS_19 SEAS_22 SEAS_23 (*1);
SEAS_9 WITH SEAS_19;

MODEL MALE: f1 f2 BY SEAS_3 SEAS_6
!SEAS_8
SEAS_9 SEAS_10
SEAS_12 SEAS_13 SEAS_15 SEAS_16 SEAS_17 SEAS_19
SEAS_22 SEAS_23 (*1);
SEAS_9 WITH SEAS_19;

OUTPUT: stdyx; MODINDICES(ALL);
 Bengt O. Muthen posted on Tuesday, April 09, 2019 - 5:40 pm
We need to see your full output - send to Support along with your license number.
 Dan Waschbusch posted on Wednesday, July 15, 2020 - 3:55 pm
Hello,
In a recent manuscript we used MPLUS to test measurement invariance across groups (e.g., boys vs. girls). The journal editor is requesting that we report effect sizes. Here is the exact feedback: "In my reading of the work, I would ask that you provide some summary effect size measure of non-invariance for your work. It appears that your work was done in Mplus and the dmacs package in R would work well with the configural invariance models to provide effect size estimates of non-invariance."

Any advice on how to compute the requested effect sizes within MPLUS, or resources I could look into for figuring out how to do so?

Thanks much.
 Bengt O. Muthen posted on Wednesday, July 15, 2020 - 4:50 pm
I don't know what non-invariance effect size is referred to. Try asking on SEMNET.
 dwasch posted on Thursday, July 16, 2020 - 8:54 am
Thank you for your reply. Following up in case it's helpful to other users.

Here are two papers I found on the topic:

Nye, C. D., & Drasgow, F. (2011). Effect size indices for analyses of measurement equivalence: Understanding the practical importance of differences between groups. Journal of Applied Psychology, 96(5), 966-980. https://doi.org/10.1037/a0022955

Gunn, H. J., Grimm, K. J., & Edwards, M. C. (2020). Evaluation of six effect size measures of measurement non-invariance for continuous outcomes. Structural Equation Modeling: A Multidisciplinary Journal, 27(4), 503-514.

Also, apparently the dmacs package in R interfaces with MPLUS output.

Thanks again.
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