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Hi, I have a non normal distribution in my data. I was using WLS as an estimator, but following Byrne (2012) suggestions I just tried with MLM estimator and I got much better adjustment indices in my models. Which one should I use? I´m a bit confused which one to select. Also, a have a big sample (N=1533), and it seems to be affecting my Chisquare measurements. Should I dismiss Chisquare and concentrate in other measures such as RMSEA, CFI, TLI? Many thanks! 


Why are your variables nonnormal? Are they categorical or continuous? 


Variables are continuous. Some of them have problems with skewness, and others with kurtosis (we used likert scales). Thanks for your response! 


If they are all continuous, you cannot use WLS. I would use MLR not MLM. 


If you have Likert variables with floor or ceiling effects, you should treat them as categorical. 


Linda, you really have been very helpful. It seems that with MLR estimator I got a much better adjustment of the models. I don´t think the variabled have any floor or ceiling effects, so I´ll assume them as continuous. I still have a few questions questions: (1) how can I activate the DIFFTEST command, cause it seems chisquare can not be interpreted in the same way. Or definitely, because of my sample, I should discard the Chisquare in my interpretation? (2) Also, what´s the difference between MLM and MLR, and in which way should I justify using one of them and not the other one? (3) I still have some other models to run, with the same sample but with continuous and categorical variables. In this sense, which estimator will be better to use? Many many thanks, this FAQ is just incredibly helpful! 


If they have skewness, they have floor or ceiling efects. This is a piling up at either end. 1. DIFFTEST is not used with MLR. How to do difference testing with MLR is described on the website. See the left column. The MLR chisquare can be interpreted in the regular way. 2. The difference is in the standard errors. Also MLM does listwise deletion of missing data. MLR uses FIML to use all available information. 3. I would treat the Likert variables as categorical and use WLSMV. WLSMV is good for a combination of continuous and categorical variables. 

Xu, Man posted on Wednesday, November 11, 2015  2:31 am



I am using ESEM to study factor structures in two samples of slightly skewed continuous data. Sample 1 has got some 0 numbers in a few items  it seems this sample contains information below detection level therefore the variables were assigned 0 for some individuals in these variables. But this was not observed in sample 2. So I think under the framework of ESEM, there are three things I need to deal with: 1. how should I deal with the overall skewness of all variables? 2. how to deal with the inflated 0 numbers in sample 1? 3. how to deal with the fact that sample 2 does not have as inflated 0 numbers? For the first two issues, for both samples, I added 1 to all variables (to hide the 0 in sample 1) and took log transformations (to 'correct' the skewness in both samples). For the third issue, in separate analysis of the two samples (I did not use multiple group analysis yet) I have found different number of factors in the EFA analysis. It is difficult to perform multiple group analysis while the EFA results are not consistent. Ultimately it would be interesting for me to do multiple group analysis to establish equivalent factors in the two samples. If the different number of factors is indeed related to the inflated 0, I probably should delete the variables with inflated 0 in order to perform multiple group analysis? Or is there a better way to approach the situation within Mplus? 


1. Just use MLR. 2. Unless the 0's constitute say more than 25%, just let MLR deal with it. 3. If more than 25% floor effect, use censorednormal in both samples. I don't think a weak floor effect would affect the number of factors. 

Xu, Man posted on Thursday, November 12, 2015  8:31 am



Thank you for the suggestion. Actually the zeros are not too bad. Only two items out of sixty have less than 15% of zeros. I tried to use censored regression by specifying CENSORED = i1 i2 (b); but I found that this does not run with ESEM: "The use of EFA factors (ESEM) is not allowed with ALGORITHM=INTEGRATION." Also, when I applied ESTIMATOR = MLR in efa context, I got quite a lot of warnings (below). It seems with mlr, I only get Loglikelihood, Information Criteria, and SRMR for goodness of fit. Is this the case for EFA with MLR, or there is something else going on? I use mplus version 7.11. Thanks! MAXIMUM LOGLIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS 209.258 THE STANDARD ERRORS FOR H1 ESTIMATED SAMPLE STATISTICS COULD NOT BE COMPUTED. THIS MAY BE DUE TO LOW COVARIANCE COVERAGE. THE ROBUST CHISQUARE COULD NOT BE COMPUTED. THE MODEL ESTIMATION TERMINATED NORMALLY THE ROBUST CHISQUARE COULD NOT BE COMPUTED. THE STANDARD ERRORS FOR H1 ESTIMATED SAMPLE STATISTICS COULD NOT BE COMPUTED. THIS MAY BE DUE TO LOW COVARIANCE COVERAGE. THE ROBUST CHISQUARE COULD NOT BE COMPUTED. THE ROBUST CHISQUARE COULD NOT BE COMPUTED. THE STANDARD ERRORS FOR THE STANDARDIZED COEFFICIENT COULD NOT BE COMPUTED. 


As for Censored, you can try WLSMV. As for the error messages I don't think they have to do with EFA but with coverage  if that doesn't explain it you can send the output to Support along with your license number. 

Xu, Man posted on Friday, November 13, 2015  8:24 am



Thank you. I now used WLSMV with the two censored variables. In the EFA, model converged for all number of factors I requested in sample 1, but not so in sample 2 (for example models with 4  10 factors the analysis did not converged  iterations exceeded). But when I tried to run 4 factor model in ESEM set up it was fine (although with a warning that theta matrix is not positive definite). Also I found in ESEM, the intercepts for the two censored items were estimated. No intercepts were estimated in the EFA model, so I am not sure what is happening. I should note also that all variables are standardised already using DEFINE: STANDARDIZE . Finally, to what extent would WLSMV deal with skewness for the other noncensored variables in the model? Thanks. 


If you use version 7.4 you can try STARTS to get the EFA to converge in cases where ESEM converged. ESEM does estimate the mean structure but that part is unrestricted so it doesn't matter really if it is part of the model or not (as in EFA). WLSMV has some robustness to nonnormality in the noncensored variables. 

Xu, Man posted on Monday, November 30, 2015  8:17 am



Thank you. It will be helpful to use STARTS. I will look into the version update. I ran into the situation again where the ESEM model with a specific factor number runs in sample 1 and sample 2 separately (also ok in multiple groups when some equal constraints are applied such as equal loadings) but would not converge when I try to fit a multiple group model with free intercept and free loadings for the same number of factors (warnings below). One information is that the first factor (the factor with the highest eigenvalue) is not necessarily the same one across the two groups. If this is the reason for convergence problems, should I not use multiple group analysis? THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 565. THE CONDITION NUMBER IS 0.373D14. 


Make sure that you have the same number of parameters in the unrestricted 2group run as in the 2 separate runs. If this doesn't help, send to Support along with license number. 

Xu, Man posted on Wednesday, December 02, 2015  8:25 am



Thank you  I have sent the output. Another issue is that, in the case that the order of factors are different  say factor 1 in group 1 is really factor 2 in group 2, and factor 2 in group 1 is factor 1 in group 2. In this case, would it be possible for me to manually constrain factor loadings of factor 1 in grp1 equal to factor 2 in grp 2? 


ESEM can hold loadings equal across groups. But the nonconvergence wouldn't have to do with shifting factor orders in the unrestricted 2group model. 

Xu, Man posted on Monday, December 07, 2015  7:26 am



Actually it turned out that the nonconvergence was mainly due to the latent means not being constrained to be zero  I did not realise this was not the default setting in configurative model. On the other hand, is there a reference as to your earlier comment WLSMV has some robustness to nonnormality in the noncensored variables? Thank you. 


The factor means are fixed at zero in the configural model. No, that's more of a conjecture from me given that a sandwich type of SE estimator is used. 

Xu, Man posted on Tuesday, March 01, 2016  6:08 am



In the ESEM framework, if one finds slightly different number of factors in different populations, is this the end of the multiple group analysis? For example, both populations find five major factors, but one of the population has an additional factor. In this case, is it possible, or is it sensible to look into measurement invariance only for factors in common? 


At a minimum, each group should have the same number of factors. 

Daniel Lee posted on Wednesday, March 21, 2018  11:50 am



Hello, for continuous variables that are zeroinflated (e.g., like an average score of schizophrenia symptoms in the general population), should I use MLR and use the Censor statement (because 40% of cases had a score 0) or use MLR? From reading the posts (unless I misunderstood), WLSMV does not seem like an appropriate approach because the variables are continuous. Thank you! 


MLR would use a linear model which isn't appropriate with a censored outcome. Use the Censor statement. Both ML(R) and WLSMV can handle censored continuous variables. 

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