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 Denis Talbot posted on Tuesday, March 16, 2010 - 1:19 pm
Hi,

I recently read the paper "Exploratory Structural Equation Modeling" from Asparouhov & Muthén and I wanted to try the ESEM approach in Mplus (v5.21) to modelise my data. To keep things simple to start with, I considered subset of my data which has 4 factors having 4 indicators each. When I use the "type = EFA 4 4", the model converges and gives interesting results. However, when I want to use a more complex model (e.g. having paths and correlated residuals), I will have to write the syntax in a different way. Something more like :

ANALYSIS:
type = general;
rotation = geomin(0.0001);

MODEL:

ext BY ext1-ext4*1 mi1-mi4*0 iden1-iden4*0 intro1-intro4*0;
mi BY ext1-ext4*0 mi1-mi4*1 iden1-iden4*0 intro1-intro4*0;
iden BY ext1-ext4*0 mi1-mi4*0 iden1-iden4*1 intro1-intro4*0;
intro BY ext1-ext4*0 mi1-mi4*0 iden1-iden4*0 intro1-intro4*1;

ext WITH intro iden mi;
intro WITH iden mi;
iden WITH mi;

...if I understood right from the example given in the paper. Yet, I receive a "THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED" error when I run the model.

Am I not getting the syntax to do ESEM right?
 Linda K. Muthen posted on Tuesday, March 16, 2010 - 1:54 pm
The syntax is shown in the Version 5.1 Examples and Language Addendums on the website with the user's guide. It should be:

ext mi iden intro BY ext1-ext4 mi1-mi4 iden1-iden4 intro1-intro4 (*1);

The factors will be correlated with oblique rotations.
 Denis Talbot posted on Wednesday, March 17, 2010 - 9:53 am
Thank you very much!
 naomi saito posted on Tuesday, July 13, 2010 - 10:04 am
Hello,

After EFA, I am trying to run ESEM using 16 binary variables with 3 factors. I recently updated Mplus to version6. I can run by using default estimator WLSMV, but it returns error when I use “estimator = MLR”:

*** ERROR in MODEL command
EFA factors are not allowed with ALGORITHM=INTEGRATION.
EFA factors are declared with (*label).

Can we use MLR for categorical variables? Do I need to use CFA if I want to use MLR?
I was hoping use MLR to obtain AIC/BIC to compare models (3 factor model VS latent class models VS factor mixture models).

VARIABLE: NAMES = ID STRATUM weight y1-y16 psu;
USEVAR = y1-y16;
STRATIFICATION = STRATUM;
CLUSTER = psu;
WEIGHT = weight;
CATEGORICAL = y1-y16;
ANALYSIS: type = complex;
estimator = MLR;
MODEL: f1-f3 by y1-y16 (*con);

Thank you for your help.
 Linda K. Muthen posted on Tuesday, July 13, 2010 - 10:26 am
You cannot use MLR with categorical outcomes with the ESEM model. You can use it for regular EFA or for CFA.
 craig neumann posted on Tuesday, April 26, 2011 - 12:27 pm
I recently ran an EFA with my new version of Mplus (6.1) and was delighted to see fit indices. Are these the result of incorporating an ESEM framework into Mplus? If so, then CFI/TLI and SRMR/RMSEA can be interpreted via convention regarding incremental and absolute fit indices, respectively, correct?

thanks for your response...
 Bengt O. Muthen posted on Tuesday, April 26, 2011 - 2:21 pm
EFA (outside ESEM) also has those indices in Mplus. And yes, they are interpreted as usual.
 Christopher T. Allen posted on Thursday, October 20, 2011 - 8:19 am
Drs. Muthen,

First, I would like to thank you both for providing the discussion board for users and responding to inquiries. I have personally found it to be an invaluable resource.

My question is: Will you please explain why, when perfoming an EFA using ESEM, the output does not contain two sets of factor loading matrices (i.e. - pattern and structure)?

Thank you in advance.
 Linda K. Muthen posted on Thursday, October 20, 2011 - 6:26 pm
There is no particular reason that we don't give these.
 Christopher T. Allen posted on Friday, October 21, 2011 - 7:43 am
Thank you for your response.

I have read some articles that have argued that interpretation of both the pattern and structure matrices is necessary for determining the most appropriate factor structure when oblique rotation is used because the factor correlation matrix is not an identity matrix.

Given that ESEM analyses provide significance tests for each loading, would you mind commenting on how using this information provides an improvement over analysis of the structure matrix when oblique rotation is used?
 Bengt O. Muthen posted on Friday, October 21, 2011 - 8:39 am
I would disagree with those articles that this is necessary. Factor structure is Lambda*Psi, that is the covariance between the indicators and the factors. As you say this is different from Lambda when Psi is not the identity matrix, that is, with oblique rotation. However, I personally don't think that knowing this indicator-factor covariance is essential or necessary to interpret the factor analysis solution - studying the pattern (Lambda) together with the factor correlations (Psi) is sufficient, even with oblique rotation. This is why we haven't yet added factor structure to ESEM, although we probably will in the future.

Providing SEs for loadings is useful for both EFA and ESEM.

Two good references are mentioned in our 2009 ESEM article (none uses factor structure):

Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111–150.

Cudeck, R., & O’Dell, L. L. (1994). Applications of standard error estimates in unrestricted factor analysis: Significance tests for factor loadings and correlations. Psychological Bulletin, 115, 475–487.
 Christopher T. Allen posted on Friday, October 21, 2011 - 10:19 am
Thank you both for your time and input. I'll be sure to read the references you provided.
 Thomas A. Schmitt posted on Friday, November 04, 2011 - 9:58 am
Hi,

Is there in reason to expect EFA and ESEM to differ in there results when looking only at a measurement model? I know Mplus used the gradient projection algorithm for ESEM, but I haven't seen any situations where ESEM differs from EFA, which is further evidenced by example 4.1 in the Mplus manual. Thanks,

Tom
 Linda K. Muthen posted on Friday, November 04, 2011 - 10:40 am
ESEM and EFA should agree when using only the measurement model in ESEM as long as the rotations are the same. The measurement model in ESEM is EFA.
 Helen Skerman posted on Sunday, November 06, 2011 - 10:51 pm
Dear Dr Bengt Muthen,
I am most interested in this discussion on the interpretation of an EFA/ESEM solution. Referring to your suggestion to Christopher T Allen, on October 21, 2011, 8:39am, I am unclear as to how to interpret the pattern coefficients together with the factor correlations without referring to the structure coefficients. Could you please expand on this, or more specifically, how to interpret the factor structure by considering both the pattern and structure coefficients?
One recommendation I have read (referenced below) suggests: “attending to the structure coefficients first then evaluating the pattern coefficients to understand the unique factor-variable relationships”.

Bandalos, D. L., & Finney, S. J. (2010). Factor Analysis. In G. R. Hancock & R. O. Mueller (Eds.), The Reviewer's Guide to Quantitative Methods in the Social Sciences. Hoboken: Routledge.


Thank you in advance.
 Bengt O. Muthen posted on Monday, November 07, 2011 - 8:41 am
Simply put, the difference between the factor pattern and the factor structure is akin to the difference between regression coefficients and correlations. Both refer to the relationship between factors and items. The factor model is a regression model, regressing the items on the factors. We know how to interpret regression models - an item's loadings on a set of factors are partial regression coefficients just like regressing a y on a set of x's. And in EFA/ESEM all coefficients are standardized so the interpretation is even easier. This is why I think the factor pattern is sufficient for interpretation of a factor model. It is working with the parameters that we are modeling.

The factor structure tells you about the correlations between the items and the factors. It could be of interest to see how a certain item correlates with certain factors. These are not parameters in the model, but are consequences of the model which may augment the understanding of the model. So I am not against looking at structure, but I don't think it is (1) necessary, or (2) should precede looking at the pattern.
 Helen Skerman posted on Monday, November 07, 2011 - 1:27 pm
Thank you very much for this clarification. It is most helpful.
 Daniel Gucciardi posted on Thursday, January 19, 2012 - 3:20 pm
Drs Muthen,

I collected data on a large pool of items that were designed to capture 6 psych constructs. I am using ESEM for item trimming purposes, and then will cross-validate on an independent sample.

From a statistical standpoint, I’d greatly appreciate your insights into whether it is preferable to focus on the strength of the regression coefficient (i.e., high on one factor only, with low cross-loadings) or whether the loading is significant (or both strength and significance) in determining whether to retain an item. For example, there are instances of items with moderate loadings (e.g., >.40) that are not statistically significant.

Alternatively, any recommended readings would be greatly appreciated.

Regards,
Daniel
 Bengt O. Muthen posted on Thursday, January 19, 2012 - 8:46 pm
You want the loading to be significant - and preferrably also large.

You may want to take a look at

Cudeck, R., & O’Dell, L. L. (1994). Applications of standard error estimates in unrestricted factor analysis: Significance
tests for factor loadings and correlations. Psychological Bulletin, 115, 475–487.
 Daniel Gucciardi posted on Thursday, January 19, 2012 - 9:22 pm
Many thanks - appreciate the prompt response and recommended info/reading.
 Masato Kawabata posted on Thursday, February 16, 2012 - 11:55 pm
Dear the Mplus team,

I have two questions about Mplus output for ESEM.

Q1. What is the difference in factor loadings between ‘ROTATED LOADINGS’ and ‘FACTOR STRUCTURE’ sections?

Q2. Which factor loadings should I report in a paper for publication?

Thank you in advance for your consideration.

Kind Regards,
Masato
 Linda K. Muthen posted on Friday, February 17, 2012 - 1:40 pm
The factor structure is the correlations between the factors and the items.

The rotated loadings should be reported.
 Masato Kawabata posted on Friday, February 17, 2012 - 4:20 pm
Dear Dr Muthen,

Thank you very much for your prompt reply!

Best regards,
Masato
 mark patrick roeling posted on Friday, June 15, 2012 - 3:56 am
Dear Mplus team,

After reading the ESEM-papers of Marsch et al and the Asparouhov & Muthén manual we are now conducting the superior ESEM method on our dataset.

We have to decide on the appropriate number of factors of the ESEM model. Given the distribution of WLSMV, direct chi square comparison is impossible and we have used the Difftest option. However, the type=efa command makes this test impossible:

*** WARNING in SAVEDATA command
DIFFTEST is not available only TYPE=EFA.
Request for DIFFTEST will be ignored.

In the Multigroup analysis presented in the Marsch paper, models are compared based on rmsea/cli/tli and srmr. Given that rmsea is regarded of as the best fit index for the WLSMV, together with the mention in the Asparouhov & Muthén manual that the SRMR should decrease >.001; should we use these fit indices only?

Or is there another way to compare model quality?

Thanks in advance.
Mark Patrick Roeling
 Linda K. Muthen posted on Friday, June 15, 2012 - 12:52 pm
Please send the relevant outputs and your license number to support@statmodel.com.
 emmanuel bofah posted on Thursday, August 02, 2012 - 1:32 pm
I am doing ESEM using the taxonomy in Marsh et al. paper. I have my final model but how to i get the correlation for each group.
what is the difference between F1 and F1_SE Correlations.lastly what are the possible graphs in ESEM.
 Linda K. Muthen posted on Friday, August 03, 2012 - 11:54 am
I think you are saying that you see covariances not correlations. Ask for StdY in the OUTPUT command to see the correlations.
 emmanuel bofah posted on Thursday, August 16, 2012 - 2:04 pm
I am doing ESEM using the 13 taxonomy in Marsh et al. paper. Will like to know if the taxonomy is valid for categorical data as well. if not what are the restriction and any advise on how to go about it.
 Linda K. Muthen posted on Thursday, August 16, 2012 - 3:14 pm
Yes.
 emmanuel bofah posted on Friday, August 17, 2012 - 1:40 am
so i just have to use the WLSMV without any PARAMETRIZATION conditions. e.g Theta
If you look at al the articles on the TAXONOMY chi-SQUARE diff test was not use. so i can also ignore it and use the CFI, RMSEA, TLI arguments.
 emmanuel bofah posted on Friday, August 17, 2012 - 11:02 am
TO correct my post i realized there is a default PARAMETRIZATION of Delta for WLSMV. Can i ignore the chi-sqaure text and use CFI, RMSEA, TLI arguments.I am just confuse because when i use the difftest and i start to use the modification indexes it does not work when i introduce a second misfit always.
I want to send my work but i am using MPLUS on university computer pool. I've treid to the IT center about the license registration so i can add but they dont understand why they should give me the info. Can you explain what i really have to include for verification.
 Linda K. Muthen posted on Friday, August 17, 2012 - 12:46 pm
Support is available to one registered user per license. You must be the registered user of a current license to be eligible for support.
 Zachary Isoma posted on Thursday, March 28, 2013 - 11:06 am
Drs. Muthen-

I am a student, and new user of MPlus. I was able to utilize the user guide to produce an output of my analysis, but am not sure how to interpret the results. Could you point me toward resources that might help guide me through interpretation? Thank you!
 Linda K. Muthen posted on Thursday, March 28, 2013 - 11:22 am
See Chapter 18 of the user's guide. The basic output is described there. If the interpretation is due to not being familiar with the method you are using, see the short course handouts and videos on the website.
 Zachary Isoma posted on Thursday, March 28, 2013 - 1:19 pm
Thank you for responding so quickly. I have found the handouts, videos, and user guides. I will be making thorough use of these.
 seungjin lee posted on Wednesday, June 04, 2014 - 6:37 am
Hello Dr. Muthen,

I am trying to run ESEM using 55 binary variables with 2 factors for ESEM.

I am trying with two ways based on M-plus 7 user guide:

1.
DATA: FILE IS ex.dat;
VARIABLE: NAMES ARE y1-y55;
CATEGORICAL ARE y1-y55;
ANALYSIS: TYPE = EFA 1 2;
OUTPUT: MODINDICES;

2.
DATA: FILE IS ex.dat;
VARIABLE: NAMES ARE y1-y55;
CATEGORICAL ARE y1-y55;
MODEL: f1-f2 BY y1-y55 (*1);
OUTPUT: MODINDICES;

In the first approach, I did not have any problem to use "mlr" or "wlsmv". However,
in the second approach, MLR was not working. Also, you commented above"we cannot use MLR with categorical outcomes with the ESEM model. You can use it for regular EFA or for CFA." Moreover, the results for WLSMV are not really same in both approaches.

If it is true, I am guessing that the first approach is not for ESEM, just EFA.

Am I on the right track?

Thanks you so much in advance,
LEE
 seungjin lee posted on Wednesday, June 04, 2014 - 9:25 am
Hello Dr. Muthen,

I have another question,

In the continuous data for EFA (not ESEM), the following approach could be used based on M-plus 7 users' guide

DATA: FILE IS ex.dat;
VARIABLE: NAMES ARE y1-y55;
ANALYSIS: TYPE = EFA 1 2;
OUTPUT: MODINDICES;

What is different from the approach with SPSS. SPSS produces different model fit indices(?) from the approach(M-plus) above.

Thanks again! :-)

Lee
 Bengt O. Muthen posted on Wednesday, June 04, 2014 - 6:17 pm
Send outputs to Support to show what you mean. Be clear about which output corresponds to what question. Also send the SPSS output in pdf. Plus your license number.
 seungjin lee posted on Wednesday, June 04, 2014 - 6:43 pm
Hello Dr. Muthen

In fact, I have uploaded two messages. I am confused whether your response is for the first message or the second message. I think yours is just for the second one. - -; Your response was for both of them,
please let me know. - -;
I am sorry for the inconvenience.

My first one was:

"I am trying to run ESEM using 55 binary variables with 2 factors for ESEM.

I am trying with two ways based on M-plus 7 user guide:

1.
DATA: FILE IS ex.dat;
VARIABLE: NAMES ARE y1-y55;
CATEGORICAL ARE y1-y55;
ANALYSIS: TYPE = EFA 1 2;
OUTPUT: MODINDICES;

2.
DATA: FILE IS ex.dat;
VARIABLE: NAMES ARE y1-y55;
CATEGORICAL ARE y1-y55;
MODEL: f1-f2 BY y1-y55 (*1);
OUTPUT: MODINDICES;

In the first approach, I did not have any problem to use "mlr" or "wlsmv". However,
in the second approach, MLR was not working. Also, you commented above"we cannot use MLR with categorical outcomes with the ESEM model. You can use it for regular EFA or for CFA." Moreover, the results for WLSMV are not really same in both approaches.

If it is true, I am guessing that the first approach is not for ESEM, just EFA.

Am I on the right track? "
 Linda K. Muthen posted on Thursday, June 05, 2014 - 7:33 am
Send outputs for both.
 QIN Feng posted on Tuesday, October 07, 2014 - 2:26 am
Hello Dr. Muthen,

I am learning ESEM, and attempting to build a model as following:

Title: ESEM of Mach;
DATA: file is Mach2.dat;
Variable: Names are M1-M20;
Model: f1-f3 by M1-M20(*1);
f4 on f1 f2;
f3 with f4;
Output: STDY;
Modindices;

Obviously, f4 became my problem, it was looked as an error in Mplus. I wonder how to write the model correctly. Should I use two level model?

Regards


Harold
 Linda K. Muthen posted on Tuesday, October 07, 2014 - 9:08 am
You have not defined f4 so you cannot use it. What is f4?
 QIN Feng posted on Tuesday, October 07, 2014 - 6:51 pm
f4 was supposed to be an EFA factor which was correlated with f3(on the same level with f3). The model may include 2 levels?
 Linda K. Muthen posted on Tuesday, October 07, 2014 - 7:17 pm
Then you would need to say

Model: f1-f4 by M1-M20(*1);
 QIN Feng posted on Wednesday, October 08, 2014 - 4:30 am
Title: ESEM of Mach;
DATA: file is Mach2.dat;
Variable: Names are M1-M20;
Model: f1-f4 by M1-M20(*1);
f3 on f1 f2;
f3 with f4;
Output: STDY;Modindices;

*** ERROR in MODEL command
EFA factors in the same set as F1 must have the same set of regressions.
Problem with:
F3 ON F1/F1 BY F3
F3 ON F3/F3 BY F3 (not specified or fixed)
F3 ON F4/F4 BY F3 (not specified or fixed)
*** ERROR in MODEL command
EFA factors in the same set as F1 must have the same set of regressions.
Problem with:
F1 ON F1 (not specified or fixed)
F3 ON F1
F3 ON F2
 Bengt O. Muthen posted on Wednesday, October 08, 2014 - 11:05 am
You cannot specify relationships among ESEM factors. You can regress ESEM factors only on other variables and CFA factors.
 Ebrahim Hamedi posted on Thursday, January 08, 2015 - 11:07 pm
Hi
Could one specify a multi-level ESEM?

Many thanks,
Ebi
 Linda K. Muthen posted on Friday, January 09, 2015 - 9:04 am
No. ESEM is available only with TYPE=GENERAL and TYPE=COMPLEX.
 Ebrahim Hamedi posted on Monday, May 04, 2015 - 1:36 am
Hello

1- In comparing ESEM and CFA models, would you recommend using the chi-square diff test or the CFA diff test as a criterion for deciding which model fits the data better? Is there any other statistical procedure to compare fit of ESEM and CFA models? Sometimes a difference exists but is small, so one wonders if the difference is significant. A numerical way to decide would greatly help avoid subjectivity.

2- Is there any statistical test to compare inter-factor correlations produced in CFA and ESEM to see if the inter-factor correlations produced in ESEM are significantly smaller or larger than those produced in CFA? (Again to avoid subjectivity)

Any comments would be greatly appreciated.
Ebi
 Bengt O. Muthen posted on Monday, May 04, 2015 - 7:45 am
1. I recommend using BIC. The ESEM and CFA models are not necessarily nested.

2. Not that I know.
 TA posted on Monday, May 11, 2015 - 3:06 pm
If your ESEM model only contains the measurement models (e.g., f1-f5 by q1-q52 (*1), with the factors being allowed to correlate;), am I just running an EFA then? Does it have to have a structural aspect to be an ESEM model?
 Bengt O. Muthen posted on Monday, May 11, 2015 - 6:21 pm
Q1. Yes.

Q2. Some other variables are needed.
 Helen HL posted on Saturday, May 16, 2015 - 8:24 am
Hi Drs. Muthen,
In my output of ESEM (I used OUTPUT: STDY), I couldn't find ROTATED LOADINGS’ and ‘FACTOR STRUCTURE’ sections as mentioned in previous posts. Did I miss anything? Thanks.
 Linda K. Muthen posted on Saturday, May 16, 2015 - 1:52 pm
Please send the output and your license number to support@statmodel.com.
 Matt Easterbrook posted on Friday, June 05, 2015 - 6:50 am
I am conducting multi-group ESEM and am hoping to save the factor loadings to a file. Is there a way to save the loadings for each group? I have tried saving 'estimates' and 'results' but neither seemed to have worked.

Ultimately, I am going to centre the loadings*item score within each group so each group mean=0. Is there any way to do this automatically in mplus?
Thanks.
 Linda K. Muthen posted on Friday, June 05, 2015 - 8:11 am
The factor loadings should be saved with the RESULTS option. Please send the output where you used the RESULTS option and your license number to support@statmodel.com.

There is no option in Mplus to do this.
 Kathy Greenwood posted on Friday, July 03, 2015 - 3:00 am
Hi

I want to run an ESEM with 16 items and either 2 or 3 factors to work out the best factor structure, using modification indices but I'm struggling to find the complete basic syntax for running an ESEM.

Should this include for example EFA (2-3); for example?
 Linda K. Muthen posted on Friday, July 03, 2015 - 6:32 am
See Example 5.24. If you remove the covariates and direct effects, it is an EFA. Other ESEM examples follow.
 Julie C™tŽ posted on Sunday, August 23, 2015 - 5:13 am
Hi,

I want to test the gender invariance of my model with ESEM but I always receive this error message:

*** ERROR in MODEL command
An EFA factor has been redeclared in a BY statement without (*label). Only one declaration of the factor is allowed. Problem with: F1

Here's a part of my syntax:

GROUPING is sexe (1= feminin 2= masculin);

ANALYSIS:
ESTIMATOR=WLSMV;
PARAMETERIZATION=THETA;
ROTATION=GEOMIN(OBLIQUE, .5)
ITERATIONS = 10000;

MODEL:
F1-F4 BY ALI_R1 ALQ_R1 ALI_R3
ALI_M1 ALI_M2 ALI_M3 ALI_M4
ALI_B2 ALI_B3 ALI_B4
ALQ_S1 ALQ_S2 ALQ_S3 ALQ_S4 (*1);

MODEL masculin:
F1-F4 BY ALI_R1 ALQ_R1 ALI_R3
ALI_M1 ALI_M2 ALI_M3 ALI_M4
ALI_B2 ALI_B3 ALI_B4
ALQ_S1 ALQ_S2 ALQ_S3 ALQ_S4 (*1); !(*) means EFA!

OUTPUT:
TECH1;
STAND;
TECH4;
MOD;
SAMPSTAT;

Can someone help me?

Thanx :-)
 Linda K. Muthen posted on Sunday, August 23, 2015 - 6:24 am
Please send the full output and your license number to support@statmodel.com.
 Bo Y posted on Thursday, September 24, 2015 - 6:15 pm
Hi Dr. Muthen and all,

I need help on these questions about my study.

1. I have three time points in the dataset. T0 is one month after an important event, T1 is three months, T2 is 6 months. Sample size is 100 for T0 but attrition is high, so T2 has 77 left. The set of questionnaires were repeated three times. Is it appropriate for me to use ESEM?


2. If ESEM is applicable, should I do a conventional EFA first before ESEM? I think conventional CFA does not apply, because there is no existing construct to be tested for this exploratory study.


3. If ESEM is not good for my study, would you suggest any other approach?

Many thanks!
 Bengt O. Muthen posted on Thursday, September 24, 2015 - 6:24 pm
I would do EFA for each time point as a first step. But note that even EFA should have variables designed to measure certain factors - it is not a method for blind search of structure among a set of variables for which no structure was contemplated.

If EFA gives reasonable results. You can use ESEM to analyze all time points and impose measurement invariance of varying degrees - we have UG examples of that.
 Bo Y posted on Friday, September 25, 2015 - 5:36 am
Thank you very much for your immediate feedback. Yes, I've noticed the ESEM example and articles. I will try plain EFA for three time points first then.

For the structure in my mind, do I call it hypothesis? sorry about the ignorant question. I just started to learn all these. Originally, the study was not designed to use SEM. Thanks.
 Bengt O. Muthen posted on Friday, September 25, 2015 - 8:06 am
You want to ask these general analysis questions on SEMNET.
 Giovanni Piumatti posted on Wednesday, December 23, 2015 - 3:08 am
Hi,

I want to test the group invariance of my model with ESEM but I receive this error message:

*** ERROR in MODEL command
An EFA factor has been redeclared in a BY statement without (*label).
Only one declaration of the factor is allowed.
Problem with: F1

Here's my syntax:

TITLE: ESEM Betos;


DATA: FILE IS betos_esem_mplus.dat;


VARIABLE: NAMES ARE list nat ov_pr ov_pa ov_f re_pr re_pa re_f co_pr co_pa co_f
st_pr st_pa st_f ph_pr ph_pa ph_f pw_pr pw_pa pw_f es_pr es_pa es_f;

GROUPING IS nat (0 = ITA 1 = SRB);


MODEL: f1-f7 BY ov_pr ov_pa ov_f re_pr re_pa re_f co_pr co_pa co_f st_pr st_pa
st_f ph_pr ph_pa ph_f pw_pr pw_pa pw_f es_pr es_pa es_f (*1);

[f1-f7@0];

MODEL SRB: f1-f7 BY ov_pr ov_pa ov_f re_pr re_pa re_f co_pr co_pa co_f st_pr
st_pa st_f ph_pr ph_pa ph_f pw_pr pw_pa pw_f es_pr es_pa es_f (*1);

[ov_pr ov_pa ov_f re_pr re_pa re_f co_pr co_pa co_f st_pr st_pa st_f
ph_pr ph_pa ph_f pw_pr pw_pa pw_f es_pr es_pa es_f];


OUTPUT: TECH1;


Thanx
 Linda K. Muthen posted on Wednesday, December 23, 2015 - 6:25 am
Please send the full output and your license number to support@statmodel.com.
 Ebrahim Hamedi posted on Tuesday, February 09, 2016 - 8:58 pm
Hello
It is still not possible to specify a higher-order measurement model under ESEM, am I right?

many thanks
 Tihomir Asparouhov posted on Wednesday, February 10, 2016 - 2:00 pm
For more advanced models we recommend EwC (ESEM-within-CFA) approach described here

http://www.vanderbilt.edu/psychological_sciences/graduate/programs/quantitative-methods/quantitative-content/marsh_morin_parker_kaur_2014.pdf

General higher order ESEM is not available.
 Cheng posted on Saturday, March 19, 2016 - 6:50 pm
Dear Linda,
In ESEM model, do we have “marker item factor loading” (the first item’s loading fixed as 1) like we have in CFA?

If yes, can I test invariance of marker item factor loading in ESEM Mplus?
 Bengt O. Muthen posted on Sunday, March 20, 2016 - 6:50 am
No, no loading is fixed in ESEM. It is just like EFA.
 Cristian Zanon posted on Tuesday, March 29, 2016 - 12:32 pm
Hi,

Is it possible to use VARIMAX or another orthogonal rotation with an ESEM model?
 Linda K. Muthen posted on Wednesday, March 30, 2016 - 11:11 am
All rotations except VARIMAX and PROMAX. Try the CF-VARIMAX rotation.
 Cheng posted on Tuesday, April 19, 2016 - 3:03 pm
Hi,
May I know how to fix this problem "(*1)(L1-L22)". I received warning when I run it in Mplus. I need to get the L1-L13 for the CR formula below.



Model:
STRES RECOV by R1 R2 R3 R4 R5 R6 R7
R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 (*1) (L1-L22); !the first 13 items have high loading on GENSTRES

STRES@1;
R1 R2 R3 R4 R5 R6 R7
R8 R9 R10 R11 R12 R13 (THETA1-THETA13);

MODEL CONSTRAINT: NEW(COMP_REL);
COMP_REL =(L1+L2+L3+L4+L5+L6+L7+L8+L9+L10
+L11+L12+L13)**2/((L1+L2+L3+L4+L5+L6+L7+L8+L9+L10+L11+L12+L13)**2+(THETA1+THETA2+THETA3+THETA4+THETA5+THETA6+THETA7+THETA8+THETA9+THETA10+THETA11+THETA12+THETA13) );

OUTPUT:CINTERVAL;
 Linda K. Muthen posted on Tuesday, April 19, 2016 - 4:36 pm
Please send the output and your license number to support@statmodel.com.
 Paulo Alexandre Ferreira Martins posted on Tuesday, October 04, 2016 - 5:56 am
Hello!

After respecificate my 3 Factor Model, i manage to get rid off the previous warning messages and almost attained conventioned cut-offs on default test of "goodness of fit models".

In order to see if there were minor, but significant cross-loadings that could justify the "gap" between the hypothesised model and sample data , i ran ESEM.

However, results from CFA measurement model were quite different from ESEM...e.g:

CFA:
As intended, apart from "reference indicators" (@1 on each of the 3 LVs), other observed variables strongly loaded on each of its LVs.
As supposed, cross-loadings suggestions from "Mod Indices" were weaker than previous ones (besides not significative).


ESEM:
All previous "reference indicators" showed not significative loads.
Besides, "ESEM" showed high and significative cross-loadings with other observed variables even stronger than previous ones...

Thank you,
 Bengt O. Muthen posted on Tuesday, October 04, 2016 - 2:14 pm
Trust the ESEM results. Good CFA solutions are not contradicted by ESEM results, so your CFA model sounds weak.
 Ebrahim Hamedi posted on Saturday, October 08, 2016 - 7:29 pm
Hello mplus team
I carefully studied all the main articles on ESEM, but one question remains for me. In CFA we can specify all significant secondary loadings to be freely estimated using the modification indexes. So, do we really need ESEM? ESEM estimates trivial cross-loadings and thus may be considered not parsimonious enough. Why an ESEM model is better than a modified CFA model?

Thank you so much for responding to my question.

Ebi
 Bengt O. Muthen posted on Sunday, October 09, 2016 - 11:09 am
The problem with a CFA that needs many adjustments using modification indices is that the starting point may be too far from the true model so that the adjustments may lead to the wrong model. ESEM uses the EFA rotation approach to finding a simple structure; all you do is specify the number of factors and you say nothing about where the zero/small loadings are. The strength of ESEM over EFA is that the EFA measurement model can be placed in a general SEM context such as including covariates or multiple groups.

BIC is a good way to determine statistically if the ESEM model is better than the CFA model.
 Ebrahim Hamedi posted on Monday, May 29, 2017 - 12:04 am
Hi
can ESEM be used with mixture modeling?

thanks
 Linda K. Muthen posted on Monday, May 29, 2017 - 6:44 am
No. It is available only for TYPE=GENERAL and TYPE=COMPLEX.
 Cristian Zanon posted on Friday, June 16, 2017 - 7:39 am
Dear Drs Muthén,

I would like to test the invariance of a measure for a group that answered it under two distinct conditions. Is it possible to do it through exploratory structural equation modeling (using the multi-group approach)?
 Bengt O. Muthen posted on Friday, June 16, 2017 - 8:08 am
It's not multi-group because the observations in the two different settings aren't independent. Instead, use the single-group longitudinal approach of UG ex 5.26.
 Deniz  posted on Sunday, June 18, 2017 - 9:40 am
Hi,
I have specified a five factor esem. Five of the items are inverse (i.e. "lazy" for low conscientiousness"). For my model I want these inverse items to have negative loadings on their corresponding latent factor. This is the case for three of the latent factors. However, for the other two latent factors the factor loadings are just the other way around (inverse items have positive loadings, while positive items have negative loadings). In a next step, I want to conduct a regression analysis based on the latent factors. In this regression analysis, I need the factors to have the correct orientation (i.e. positive relationship between conscientiousness and my dependent variable should have positive regression coefficients). I have specified a method factor, so I want to leave the items in their original metric (I don't want to reverse them before conducting the ESEM). Is there any way to achieve that inverse items have negative loadings? Or do you have any other advice how to handle this?

F1 BY
BFE -0.634 0.029 -22.201 0.000
BFEI 0.841 0.029 29.427 0.000
BFOI -0.040 0.014 -2.785 0.005
...
(BFEI is the inverse item and should have a negative loading, while BFE should have a positive loading)
 Cristian Zanon posted on Monday, June 19, 2017 - 6:57 am
Thank you very much for your answer, Dr. Muthén! I would like to test the configural, metric, variance and covariance levels of invariance using this approach. To test the configural level I removed the "1" inside the (*t1 1) and the (*t2 1), am I right?

The exemple presents the test for the metric level, right?

How can I test if the variances and covariances are equal from time 1 to time 2? My output indicates of variances are equal to 1 on both times.
 Bengt O. Muthen posted on Monday, June 19, 2017 - 5:35 pm
Q1: Yes

Q2: Yes

Q3: Borrow ideas from UG ex 5.27
 Cristian Zanon posted on Tuesday, June 20, 2017 - 11:04 am
Thanks again for your help, Dr. Muthén. I figured out how to set covariances to be equal across times using f1-f5 WITH f6-f10 (1);

but still don`t know how to constrain factor variances to be equal. I tried different possibilities that do not work. Could you help me again, please?

Can I trust the output with this message?

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE
DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A
LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES.
CHECK THE TECH4 OUTPUT FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE F7.
 Deniz  posted on Tuesday, June 20, 2017 - 1:36 pm
Dear Dr. Muthén, you might have overlooked the question I posted in this thread, on sunday (June 18, 2017 - 9:40 am). It would be great if you could give me some advice.
Thank you so much.
 Bengt O. Muthen posted on Tuesday, June 20, 2017 - 5:22 pm
Answer to Sunday question by Deniz:

I think the easiest approach is to simply switch the signs of your estimates when reporting the results. The fit of such a model is the same.
 Katherine Schaumberg posted on Wednesday, August 09, 2017 - 7:01 am
Hi,

I am having an issue where I am getting a model with 5 factors that fits my data well in an EFA portion of an ESEM model. When I introduce covariates that the factors are then regressed on, the factor structure seems to change significantly --. the fifth factor does not have any significant factor loadings and the items that were loading well onto that factor are integrated into the fourth factor. I then specified a four factor model and the same thing seems to occur - the fourth factor that is present in the EFA portion of the model no longer has significant item loadings after introducing covariates. I'm wondering what the next steps are in order to most accurately specify the model.

Thanks,
Katherine
 Bengt O. Muthen posted on Wednesday, August 09, 2017 - 3:38 pm
Please send your outputs with and without covariates to Support along with your license number.
 Ebrahim Hamedi posted on Tuesday, October 17, 2017 - 3:30 am
Hello,
You have commented that the CFA/SEM and ESEM models are not nested models and it is better to use BIC to compare them. Just want to make sure this applies to all situations. for example, what if ESEM is being used to test an exploratory factor analysis model (with no structural section). Again the ESEM model and the corresponding CFA model are not nested and BIC should be used for comparison?

thanks
 Tihomir Asparouhov posted on Wednesday, October 18, 2017 - 9:16 am
It does not apply to all situations. For example a CFA with m factors is always nested within the ESEM model with m factors. Using the chi-square is preferable when the models are nested. In most situations it is known if the models are nested but it is hard to give a simple rule. If you are not sure about your situation a simple montecarlo procedure can help. Generate large sample from the more restricted model and then analyze it with the less restricted model. The less restricted model should always give better log-likelihood value with any set of parameters generating the data.
 WEN Congcong posted on Wednesday, December 13, 2017 - 5:16 pm
Dear professors,

Hello! I wrote a monte carlo simulation study to compare ESEM and CFA, tell readers when to use them. I took the degree of the factor covariance, the degree of the cross-loadings, the cross-loadings’ positions and the degree of the covariate into consideration in 2 factor 7 or 8 items 1 or 2 cross- loadings models to identify the parameter biases difference between ESEM and CFA. I also investigated the optimal sample size for ESEM’s fitting. But in my opinion, I did not go beyond previous studies. Could you please give me some indications about future research with regard to the parameter biases difference between ESEM and CFA , and when to use them?

I really want to do a new research, but don’t know what should I do now. Thank you very much!
 Tihomir Asparouhov posted on Thursday, December 14, 2017 - 3:46 pm
You can probably get some research ideas when you apply a methodology to a real data sets. Simulations studies though can be used to figure out which rotation criterion works bets with different level of matrix complexity. Also using ESEM-within-CFA (see http://statmodel.com/download/Marsh%20Nagengast%20Morin%202012%20Big5%20Inv%20ESEM%20la%20dolce%20viita%20effect%20DevPsych.pdf) one can migrate/merge ESEM with other modeling techniques such as DSEM for example.
 WEN Congcong posted on Saturday, December 16, 2017 - 7:04 am
Thanks for your advice! I know what I should do now!
 Victoria Narine posted on Thursday, April 12, 2018 - 8:09 pm
Hi professors,

I'm using ESEM to investigate the measurement invariance of a scale. My grouping variable is ethnicity. Do I have to dummy code the grouping variable?

Thanks.
 Bengt O. Muthen posted on Friday, April 13, 2018 - 4:19 pm
Look at UG ex 5.27 which show multiple-group ESEM.
 Victoria Narine posted on Sunday, April 15, 2018 - 10:00 pm
Hi professors,

I'm testing the measurement invariance of a scale with 4 factors, 54 items. All items are categorical with WSLMV estimation.
I've included item thresholds for all items and the second threshold is exclamated out for each item.
I keep getting this error message:

The following MODEL statements are ignored:
* Statements in the GENERAL group:

and:
Statements in Group ASIAN:

Do I have to include all thresholds in the general model and the comparison model when testing for configural invariance?
I appreciate any help I can get. Thanks.
 Victoria Narine posted on Sunday, April 15, 2018 - 10:21 pm
An amendment to my previous post:

When I look at the error report in the output, only the last category of each item is being ignored. For example:

[ V6$6 ]
[ V8$6 ]
[ V11$6 ]
[ V13$6 ]

There are 6 categories for each item. Why is the last category being ignored?

Thanks.
 Bengt O. Muthen posted on Tuesday, April 17, 2018 - 4:28 pm
Please send your output to Support along with your license number.
 Lim Si Hui Regina posted on Thursday, July 12, 2018 - 1:28 am
Hi Professors,

I performing a hierarchical ESEM using ESEM-within-CFA model. I understand that in writing the syntax, one item per factor has all cross loadings on non-target factors constrained to be exactly equal to their ESEM values (using @).I did this but my model did not converge. I then went on to constraining all non-target factors to their ESEM values (using @) and my model converged. Am I doing it right? I would like to know how does mplus read the two differently.

Would really appreciate your help as I am very new to mplus.
 Bengt O. Muthen posted on Thursday, July 12, 2018 - 3:45 pm
Send your 2 outputs to Support along with your license number.
 Ashley Duguay posted on Friday, March 01, 2019 - 1:06 pm
Hi Drs. Muthen,

I am testing the validity of an emotional competence questionnaire (50 items and 10 expected factors [2 expected higher-order factors]) with athletes. I am using both CFA and ESEM approaches in Mplus. At present, I am testing a 50-item, 10 factor model however in both the CFA and ESEM I have several items that are loading negatively on their intended factor. (There are also items loading negatively on unintended factors). Could you provide some insight on what these negative factor loadings may mean?

Sample from output (notice the negative loading on intended factor for UTOTE4):

F10 BY

UTOTE1 0.841
UTOTE2 0.753
UTOTE3 0.656
UTOTE4 -0.084
UTOTE5 0.588

Thank you for your time and expertise,

Ashley
 Bengt O. Muthen posted on Friday, March 01, 2019 - 6:05 pm
Check if the sample correlations between UTOTE4 and the other 4 items on that factor have positive correlations.
 Ashley Duguay posted on Friday, March 01, 2019 - 7:19 pm
Hi Dr. Muthen,

Thank you for your prompt response! I included the output option SAMPSTAT and checked the sample correlations. The correlations between UTOTE4 and the other 4 items on that factor are as follows:

UTOWE5 - UTOWE1 = -0.073
UTOWE5 - UTOWE2 = 0.347
UTOWE5 - UTOWE3 = 0.361
UTOWE5 - UTOWE4 = 0.389
 Ashley Duguay posted on Friday, March 01, 2019 - 7:27 pm
*CORRECTION*

Hi Dr. Muthen,

My apologies, I posted the wrong items. Here are the sample correlations (output option SAMPSTAT) for UTOTE4:

UTOTE4 - UTOTE1 = 0.030
UTOTE4 - UTOTE2 = 0.187
UTOTE4 - UTOTE3 = 0.066
UTOTE4 - UTOTE5 = -0.003
 Ashley Duguay posted on Saturday, March 02, 2019 - 5:24 am
Hi Dr. Muthen,

Just to follow-up on my post directly above, the negative sample correlation between UTOTE4 and UTOTE5 (-0.003) indicates that they are inversely related correct? Would you then suggest removing UTOTE4 in the ESEM post-hoc modifications of the model? If so, in an attempt to improve model fit, would you suggest removing these negative factor loadings on intended factors first? (Before, for instance, low factor loadings on intended factors or high cross-loadings on unintended factors)?

Thank you for your insight!
 Bengt O. Muthen posted on Saturday, March 02, 2019 - 10:22 am
Given its small size, I would think the UTOTE4 item does not load significantly on the factor and could therefore be removed. This is also supported by the low sample correlations.
 Hailey Lee posted on Monday, October 14, 2019 - 5:01 pm
Hi Dr. Muthen,

I am running a series of multi-group ESEM invariance models. From a configural invariance model to strong invariance model, changes in chi-square were significant, indicating that the invariance did not hold. However, the values in CFI/TLI/RMSEA didn't much change. For example, the change in CFI was less than .01. In this case, should I still reject invariance?
 Bengt O. Muthen posted on Wednesday, October 16, 2019 - 7:09 am
This general analysis strategy question is suitable for SEMNET.
 craig neumann posted on Saturday, November 09, 2019 - 3:11 pm
Curious about DFs for ESEM.

Have 28 items and ran 4-factor ESEM using ML. The Mplus output says there are 272 DFs.... however,

given I have 28(29)/2 = 406 data points, and am estimating,

28 * 4 loadings
28 error variances
6 factor correlations
(factor variances fixed to 1)

shouldn't the DFs = 406 - 146 = 260?
 Bengt O. Muthen posted on Saturday, November 09, 2019 - 4:40 pm
ESEM, like EFA, has M^2 indeterminacies. So you subtract 16 from the number of parameters. You already subtracted 4 (=m) by noting that the factor variances are fixed at 1 so you should subtract 12 more. That means that the df increases by 12 so 260+12=272 and all is ok.
 Deniz  posted on Monday, April 13, 2020 - 8:17 am
Dear Dr. Muthén,
I have specified an esem to model five latent personality traits. I would also like to report latent means of these five personality traits. I have tried to obtain these means by including:
[factor1];
[factor2];

However, when I include these statements the model doesn’t converge anymore.

In a CFA, I would assume that I have to fix one item of each factor to one.
[f1_1@0];

However, this probably wouldn’t give meaningful latent means in an ESEM model – do you agree? I haven’t found any paper reporting latent means of esem models. Is there any other way to obtain latent means within an esem?
Thank you so much in advance
 Bengt O. Muthen posted on Monday, April 13, 2020 - 5:29 pm
Latent means are not really meaningful unless you have measurement invariance across multiple groups or several time points. They are zero.
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