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.
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