Message/Author 

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? 


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 


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. 


I am testing a series of measurement invariance models using multigroup CFA. I have four latents variables, and orderedcategorical 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, 


See pages 398401 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. 


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 GOFindicators) including for the factor loadings. I am especially doubtfull if I can correlate the error terms this way... Variable: Names are et1et6 ethno1ethno6; Usevariables are et1et6 ethno1ethno6; 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; 


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 secondorder model. First, I run a multiplegroup CFA with ordered categorical data using Mplus 5.2 and trying to test a model. The code I am using is: TITLE: multiplegroup CFA cfa for 4 factor DATA: file is "C:\r_4mp.txt"; format is 22f1.0; VARIABLE: names are s1s22; usevariables are s1s20; grouping is s21 (0=female 1=male); categorical are all; MODEL: r1 by s1s5; r2 by s6s10; r3 by s11s15; r4 by s16s20; The model fit is acceptable( CFI: 0.961, TLI:0.974, RMSEA: 0.026ï¼ŒWRMR Value: 1.692). When I try to do this for the secondorder model by adding to the last code: Genfact by r1r4; 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 0.456D16. Is there any people having this problem? 


You need to fix the intercepts of the firstorder 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 firstorder 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 firstorder factors to zero, and it work well now. Thank you! 


The firstorder factors have intercepts estimated not means because they are dependent variables regressed on the secondorder 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. 399400, measurement invariance for continuous outcomes, steps 24 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. 


See the Topic 2 course handout on the website under multiple group analysis for the measurement invariance models we suggest for categorical outcomes. 


Dear Dr. Muthen, I want to test Measurement Invariance in a 1 Factor Model with multiplegroups 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 chisquare 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 


It sounds like you are using a version of Mplus before Version 6. The degrees of freedom and chisquare in these earlier versions were adjusted to obtain a correct pvalue. Only the pvalue should be interpreted. You will obtain the degrees of freedom you expect using WLS or WLSM. 


Hello  I fit a multigroup configural invariance model, with one latent construct with three manifest indicators (and #groups=2). My question is about the Chisq statistic. When I fit the same model within one sample only, it is just identified and has a chisq of zero (number of free parameters=9 and df=0). When I fit it to both groups via a configural invariance model, the chisq is nonzero. Isn't the configural model also just identified and shouldn't I thus be getting a zero chisq value? In the configural invariance model, Mplus says that the number of free parameters is 16 and df=2. Thank you for your help! 


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; [F1F2@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! 


You should not mention the first factor loading in the groupspecific MODEL commands. When you do, they are no longer fixed at one but free causing the nonidentification 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 216 for Item 1 in AG1 and 1029 in AG5. Could this be the problem? 


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! 


If you want to set the metric fixing a factor loading, you should choose one that is estimated close to plus one. 


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 ] 


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 = y1y11 gender; usevariables = y1y11 gender; grouping = gender (0=male 1=female); Model: PC by y1y7; AFF by y8y11; [PC@0 AFF@0]; MODEL female: [y1y7]; [y8y11]; Intercept invariance model: PC by y1y7; AFF by y8y11; Does this input look correct? Also, how would I set up the model to examine configural invariance? 


Please see the Topic 1 course handout under Multiple Group. You will find the inputs for testing measurement invariance. 


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! 


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. 


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: f1f2 by y1y10 (*1); [f1f2@0]; Model G2: f1f2 by y1y10 (*1); [y1y10]; My syntax is similar and I don't understand why it does not work: grouping is time (0=time0 1=time1); ... MODEL: F1F2 by phq1phq9 (*1); [F1F2@0]; MODEL time0: F1F2 by phq1phq9 (*1); [phq1phq9]; MODEL time1: F1F2 by phq1phq9 (*1); [phq1phq9]; 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! 


Maybe your outcomes are categorical and so require thresholds ($1 etc) instead of intercepts. 


Hello Dr. Muthen, What is appropriate syntax for running a configural invariance test for this secondorder 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 


I think you are probably forgetting to fix the factor means of the firstorder 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 multigroup 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 


The chisquares for males and females separately will be the sum of the multiple group chisquare 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 chisquare for configural invariance? 


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 


This summation will not work for WLSMV. 

Maria posted on Thursday, January 31, 2013  10:22 am



Thank you! 


Dear Linda/Bengt, Reading your slides, a doubt about Multiplegroup Factor Analysis appeared: in the slide (82/196) from UCONN's conference about HolzingerSwineford's Model fit information (invariance testing) configural and metric model had pvalue<0.00001. However, metric against configural pvalue =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 


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 chisquare distribution in that case. The intended use of chisquare 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. 


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 variablesboth 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! 


The firstorder 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. 


You should fit the model at each time point separately as a first step. If you do not have the same wellfitting 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 secondorder factor model. Everything works perfectly well until I constrain the intercepts of the firstorder 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 firstorder 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 


Please send the output and your license number to support@statmodel.com. 


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 


You are most likely mentioning the first factor indicator in the groupspecific 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. 


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 multigroup comparison for boys and girls, using a measurement model that already has a number of acrosstime 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 multigroup/long'l, so all of it has to be done "by hand" with explicit equalities." So therefore the multigroup 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 


That could be the case. 


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 


Yes. You are in full control of the equalities you want to apply. 


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 onefactor 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! 


Perhaps you have correlations between residuals for the same item at different time points. Not including them can inflate the factor correlation across time. 


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 onefactor model with only 5 indicators and 2 time points... I really cannot figure out what's going on. 


Maybe there isn't that much change between time 1 and time 2. 

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