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Juliette posted on Tuesday, November 20, 2012  3:24 pm



Hi, I am running a multilevel CFA with ordinal indicators using WLSMV/WLSM. I would like to perform a multigroup analysis to test the invariance of item loadings and thresholds across 6 groups. However, when I try to run it I get an error message saying "TYPE = TWOLEVEL with estimators ULSMV, WLS, WLSM, and WLSMV is not currently available for multiple group analysis". I am using Mplus version 7. Is there some other way to perform this analysis? Do you have any suggestions? Thank you so much! 


You can do this with ML or Bayes where the groups are handled using KNOWNCLASS. 


Hello, I want to model a multigroup multilevel CFA to test the factorial invariance of my survey instrument. I have nurse workforce data (hypothesis is there are five factors) from nurses (n=33000) within nursing units (n=2000, randomly selected) within hospitals (n=500, randomly selected) within countries (n=12). 1. Is my sample large enough to do this kind of analysis? (cf. Hox et al. How few countries will do? Comparative survey analysis from a Bayesian perspective). 2. Why multigroup (country) multilevel (hospital) and not threelevel? 3. I looked at example 9.11, yet my data are categorical. I know it has to do with KNOWNCLASS and MIXTURE but I can't find out the full syntax. Could you please aid me with a syntax that would work? 5. In a book chapter of the recent book by Van de Vijver 'Multilevel analysis of individuals and cultures' there is a chapter on 'Latent Variable Structural Equation Modeling in CrossCultural Research: Multigroup and Multilevel Approaches' by Selig et al. They included a predictor (one of Hofstede's dimensions of national culture) in their model. How can I do this? Please help me, I'm a complete newbie to Mplus! All the best, Luk 


1  2. Typically, you want more than 12 units on the highest level to do 3level analysis. With Bayes, however, good performance can be obtained even for such a low number. See for instance my paper: Muthén, B. (2010). Bayesian analysis in Mplus: A brief introduction. Technical Report. Version 3. which is on our web site under Papers, Bayesian Analysis. Another aspect is the usual fixed vs random model consideration  what your inference concerns.  Do you want to think of the countries as a random sample from a population of countries (random mode  3level analysis) so that you draw inference to this population or do you want the inference to be to only these 12 countries (fixed mode  multiplegroup analysis). Adding another wrinkle to this is the new development where even for the fixed mode case, you may want to take a Bayes random measurement parameter approach for the 12 countries  see General random effect latent variable modeling: Random subjects, items, contexts, and parameters. which is under Technical Appendices for Version 7. We are currently writing on a more applied paper on this. 3. Start by looking at UG ex 7.21. Then look at the output including Tech1 to see that you get what you want. 5. Our UG has many examples of predictors (covariates) of factors  also for multilevel models. 

luk bruyneel posted on Wednesday, November 28, 2012  12:16 pm



Thank you for your excellent reply. I should have started by doing a standard CFA in each country. As it turns out, my 5factor solution doesn't work out in any of the countries. Standard EFA models in each country seperately point to a 6 to 7factor solution. I came across the relatively new method of ESEM. This seems like a good approach for my problem would you agree? I ran three models: 1. No measurement invariance 2. introduce factor loading matrix invariance 3. introduce intercept variance I haven't modeled factor covariance matrix invariance and factor mean invariance yet. These are the results: 1. Number of Free Parameters=2079, H0 Value= 809768.148, H0 Scaling Correction Factor= 1.1879, ChiSquare Test of Model Fit Value= 7699.150*, Degrees of Freedom=1827, PValue=0.0000, RMSEA (Root Mean Square Error Of Approximation) Estimate=0.031, CFI=0.975, TLI=0.953, SRMR (Standardized Root Mean Square Residual)= 0.015 

luk bruyneel posted on Wednesday, November 28, 2012  12:19 pm



... 2. Number of Free Parameters=903, H0 Value= 814654.626, H0 Scaling Correction Factor= 1.1333, ChiSquare Test of Model Fit Value= 15914.658*, Degrees of Freedom=3003, PValue=0.0000, RMSEA (Root Mean Square Error Of Approximation) Estimate=0.036, CFI=0.944, TLI=0.937, SRMR (Standardized Root Mean Square Residual)= 0.044 3. Number of Free Parameters=735, H0 Value= 824405.147, H0 Scaling Correction Factor=1.1689, ChiSquare Test of Model Fit Value=33432.099*, Degrees of Freedom=3171, PValue=0.0000, RMSEA (Root Mean Square Error Of Approximation) Estimate=0.054, CFI=0.870, TLI=0.860, SRMR (Standardized Root Mean Square Residual)= 0.062 Some questions: 1. Is chisq per definition significant because of large sample size? (n=33000) 2. RMSEA and SRMS increased a bit and TLI and CFI decreased a bit every time I added a country to the model. Is this per definition what you would expect? I’ve seen a comment from Linda stating that many groups in multiple group analysis is not easy. 3. What do you make of these findings? Just before I added the last country to the 3rd model, CFI and TLI were over .90 and SRMR and RMSEA were below .05. Luk Bruyneel 


Take a look at the ESEM and BSEM approaches I discussed in Utrecht in August on Day 1. See end of the day under the heading "Multiplegroup BSEM. Crosscultural comparisons". There is a video and a handout on our web site. I had similar problems with CFA in the 34 countries. 

Juliette posted on Friday, March 01, 2013  12:53 pm



Hello, I wanted to follow up regarding the question at the top of this thread. You suggested using ML or Bayes with KNOWNCLASS to do a twolevel multigroup CFA with categorical indicators. I am not what the syntax should look like. Do you have an example? Should TYPE=MIXTURE and ESTIMATOR=BAYES or ML? what would the CLASSES and KNOWNCLASS statements look like for a 6 group comparison? Thank you. 


KNOWNCLASS requires TYPE=MIXTURE; Use the ESTIMATOR option to select BAYES or ML. See Example 7.21 for the CLASSES and KNOWNCLASS options. It is for two classes but is easily generalized. 


I would like to conduct a multiplegroup twolevel CFA with ordered categorical indicators testing measurement invariance for three groups. Each group consists of 150200 clusters with 10 observations per group (5000 observations in total, the twolevel CFA model results in good model fit). The WLSM/V estimator is currently not available for multiple group analysis of TYPE=TWOLEVEL, and the Bayes estimator is currently not available for multiple group analysis of TYPE=TWOLEVEL MIXTURE using the CLASSES and KNOWNCLASS options. I would appreciate if you could give an advice. 


If there are not too many latent variable dimensions, you can try ML which uses Knownclass for the multiple groups, where the class variable is put on the Between list. You can use integration=montecarlo(5000); 

Dexin Shi posted on Thursday, April 18, 2013  9:04 pm



Hi Dr. Muthens, I'd like to conduct a multiple group multilevel CFA model using Bayes estimator; as TYPE=TWOLEVEL MIXTURE using the CLASSES and KNOWNCLASS options is not available, I was wondering is there any alternative coding approaches I can fit the multigroup multilevel CFA model with ordered categorical outcomes using bayes as estimator ? if not, How about the continuous case? Thanks. 


This is not possible in Mplus with Bayes for either categorical or continuous variables. 


I used successfully MLR which uses Knownclass for the multiple groups, where the class variable is put on the Between list to conduct multiplegroup twolevel CFA with ordered categorical indicators testing measurement invariance for three groups. Unfortunately I have problems to assess the model fit. I tried to request the VuongLoMendellRubinTest (TECH11) and the BootstrapLikelihoodRatioDifferencesTest (TECH14), but they are not available: *** WARNING in OUTPUT command TECH11 option is not available for TYPE=MIXTURE with the KNOWNCLASS option. Request for TECH11 is ignored. *** WARNING in OUTPUT command TECH14 option is not available for TYPE=MIXTURE with the KNOWNCLASS option. Request for TECH14 is ignored. I would be very gratefully if you could tell me how I can assess the model fit of the multiple group model. 


In this case you have to work with "neighboring models", that is, compare your model with one that is less restricted and compute the LR chisquare as 2 times the logL difference. 

Jinxin ZHU posted on Friday, October 17, 2014  12:24 am



Dear Bengt, I am now runing a multigroup twolevel CFA with ordinal data, and want to have the variance of between level latent facor varied across groups. However, when I use KNOWNCLASS with TWOLEVEL and MIXTURE, I got the error that "Variances of betweenlevel variables are not allowed to vary across classes". 1. Is the asumption of variance of between level latent facor varying across groups reasonable? 2. Is what I want workable using Mplus? 3. Would you please suggest what I should do? Thank you so much. 


Are the groups level1 groups or level2 groups? 

Jinxin ZHU posted on Saturday, October 18, 2014  2:13 am



Level2 (between level). Variances for latent factor in level1 (within level) can be set varied across groups. 


To get the variance of the betweenlevel factor to vary across classes, you need to use a trick. Try expressing the factor variance in the Beta matrix instead of in the Psi matrix. For instance, f by y1y10; ftrick by; ftrick@1; ftrick with f@0; f on ftrick; where you mention f on ftrick in each class so that this slope varies. This classvarying Beta matrix slope then lets the f variance vary across classes. 

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