MLM or WLS estimators to analyze non ... PreviousNext
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 SUSANA BARRADAS posted on Wednesday, February 18, 2015 - 6:50 pm
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? Im a bit confused which one to select.
Also, a have a big sample (N=1533), and it seems to be affecting my Chi-square measurements. Should I dismiss Chi-square and concentrate in other measures such as RMSEA, CFI, TLI?

Many thanks!
 Linda K. Muthen posted on Thursday, February 19, 2015 - 5:41 am
Why are your variables non-normal? Are they categorical or continuous?
 SUSANA BARRADAS posted on Thursday, February 19, 2015 - 7:26 am
Variables are continuous. Some of them have problems with skewness, and others with kurtosis (we used likert scales). Thanks for your response!
 Linda K. Muthen posted on Thursday, February 19, 2015 - 9:58 am
If they are all continuous, you cannot use WLS. I would use MLR not MLM.
 Linda K. Muthen posted on Thursday, February 19, 2015 - 10:02 am
If you have Likert variables with floor or ceiling effects, you should treat them as categorical.
 SUSANA BARRADAS posted on Thursday, February 19, 2015 - 4:11 pm
Linda, you really have been very helpful. It seems that with MLR estimator I got a much better adjustment of the models. I dont think the variabled have any floor or ceiling effects, so Ill assume them as continuous. I still have a few questions questions:

(1) how can I activate the DIFFTEST command, cause it seems chi-square can not be interpreted in the same way. Or definitely, because of my sample, I should discard the Chi-square in my interpretation?

(2) Also, whats 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!
 Linda K. Muthen posted on Thursday, February 19, 2015 - 5:27 pm
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 chi-square 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 skew-ness 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?
 Bengt O. Muthen posted on Wednesday, November 11, 2015 - 1:24 pm
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 censored-normal 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 LOG-LIKELIHOOD 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 CHI-SQUARE COULD NOT BE COMPUTED.

THE MODEL ESTIMATION TERMINATED NORMALLY

THE ROBUST CHI-SQUARE 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 CHI-SQUARE COULD NOT BE COMPUTED.

THE ROBUST CHI-SQUARE COULD NOT BE COMPUTED.

THE STANDARD ERRORS FOR THE STANDARDIZED COEFFICIENT
COULD NOT BE COMPUTED.
 Bengt O. Muthen posted on Thursday, November 12, 2015 - 6:07 pm
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 non-censored variables in the model? Thanks.
 Bengt O. Muthen posted on Friday, November 13, 2015 - 5:46 pm
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 non-normality in the non-censored 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 -0.373D-14.
 Bengt O. Muthen posted on Monday, November 30, 2015 - 5:36 pm
Make sure that you have the same number of parameters in the unrestricted 2-group 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?
 Bengt O. Muthen posted on Wednesday, December 02, 2015 - 6:24 pm
ESEM can hold loadings equal across groups. But the non-convergence wouldn't have to do with shifting factor orders in the unrestricted 2-group model.
 Xu, Man posted on Monday, December 07, 2015 - 7:26 am
Actually it turned out that the non-convergence 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 non-normality in the non-censored variables? Thank you.
 Bengt O. Muthen posted on Monday, December 07, 2015 - 1:42 pm
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?
 Linda K. Muthen posted on Tuesday, March 01, 2016 - 6:29 am
At a minimum, each group should have the same number of factors.
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