Message/Author 


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 ext1ext4*1 mi1mi4*0 iden1iden4*0 intro1intro4*0; mi BY ext1ext4*0 mi1mi4*1 iden1iden4*0 intro1intro4*0; iden BY ext1ext4*0 mi1mi4*0 iden1iden4*1 intro1intro4*0; intro BY ext1ext4*0 mi1mi4*0 iden1iden4*0 intro1intro4*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? 


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 ext1ext4 mi1mi4 iden1iden4 intro1intro4 (*1); The factors will be correlated with oblique rotations. 


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 y1y16 psu; USEVAR = y1y16; STRATIFICATION = STRATUM; CLUSTER = psu; WEIGHT = weight; CATEGORICAL = y1y16; ANALYSIS: type = complex; estimator = MLR; MODEL: f1f3 by y1y16 (*con); Thank you for your help. 


You cannot use MLR with categorical outcomes with the ESEM model. You can use it for regular EFA or for CFA. 


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... 


EFA (outside ESEM) also has those indices in Mplus. And yes, they are interpreted as usual. 


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. 


There is no particular reason that we don't give these. 


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? 


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 indicatorfactor 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. 


Thank you both for your time and input. I'll be sure to read the references you provided. 


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 


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. 


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 factorvariable 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. 


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. 


Thank you very much for this clarification. It is most helpful. 


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 crossvalidate 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 crossloadings) 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 


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. 


Many thanks  appreciate the prompt response and recommended info/reading. 


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 


The factor structure is the correlations between the factors and the items. The rotated loadings should be reported. 


Dear Dr Muthen, Thank you very much for your prompt reply! Best regards, Masato 


Dear Mplus team, After reading the ESEMpapers 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 


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


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. 


I think you are saying that you see covariances not correlations. Ask for StdY in the OUTPUT command to see the correlations. 


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. 


Yes. 


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 chiSQUARE diff test was not use. so i can also ignore it and use the CFI, RMSEA, TLI arguments. 


TO correct my post i realized there is a default PARAMETRIZATION of Delta for WLSMV. Can i ignore the chisqaure 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. 


Support is available to one registered user per license. You must be the registered user of a current license to be eligible for support. 


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! 


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. 


Thank you for responding so quickly. I have found the handouts, videos, and user guides. I will be making thorough use of these. 


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 Mplus 7 user guide: 1. DATA: FILE IS ex.dat; VARIABLE: NAMES ARE y1y55; CATEGORICAL ARE y1y55; ANALYSIS: TYPE = EFA 1 2; OUTPUT: MODINDICES; 2. DATA: FILE IS ex.dat; VARIABLE: NAMES ARE y1y55; CATEGORICAL ARE y1y55; MODEL: f1f2 BY y1y55 (*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 


Hello Dr. Muthen, I have another question, In the continuous data for EFA (not ESEM), the following approach could be used based on Mplus 7 users' guide DATA: FILE IS ex.dat; VARIABLE: NAMES ARE y1y55; ANALYSIS: TYPE = EFA 1 2; OUTPUT: MODINDICES; What is different from the approach with SPSS. SPSS produces different model fit indices(?) from the approach(Mplus) above. Thanks again! Lee 


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. 


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 Mplus 7 user guide: 1. DATA: FILE IS ex.dat; VARIABLE: NAMES ARE y1y55; CATEGORICAL ARE y1y55; ANALYSIS: TYPE = EFA 1 2; OUTPUT: MODINDICES; 2. DATA: FILE IS ex.dat; VARIABLE: NAMES ARE y1y55; CATEGORICAL ARE y1y55; MODEL: f1f2 BY y1y55 (*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? " 


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 M1M20; Model: f1f3 by M1M20(*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 


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? 


Then you would need to say Model: f1f4 by M1M20(*1); 

QIN Feng posted on Wednesday, October 08, 2014  4:30 am



Title: ESEM of Mach; DATA: file is Mach2.dat; Variable: Names are M1M20; Model: f1f4 by M1M20(*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 


You cannot specify relationships among ESEM factors. You can regress ESEM factors only on other variables and CFA factors. 


Hi Could one specify a multilevel ESEM? Many thanks, Ebi 


No. ESEM is available only with TYPE=GENERAL and TYPE=COMPLEX. 


Hello 1 In comparing ESEM and CFA models, would you recommend using the chisquare 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 interfactor correlations produced in CFA and ESEM to see if the interfactor 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 


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., f1f5 by q1q52 (*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? 


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. 


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


I am conducting multigroup 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. 


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. 


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 (23); for example? 


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: F1F4 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: F1F4 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 


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! 


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. 


You want to ask these general analysis questions on SEMNET. 


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: f1f7 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); [f1f7@0]; MODEL SRB: f1f7 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 


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


Hello It is still not possible to specify a higherorder measurement model under ESEM, am I right? many thanks 


For more advanced models we recommend EwC (ESEMwithinCFA) approach described here http://www.vanderbilt.edu/psychological_sciences/graduate/programs/quantitativemethods/quantitativecontent/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? 


No, no loading is fixed in ESEM. It is just like EFA. 


Hi, Is it possible to use VARIMAX or another orthogonal rotation with an ESEM model? 


All rotations except VARIMAX and PROMAX. Try the CFVARIMAX rotation. 

Cheng posted on Tuesday, April 19, 2016  3:03 pm



Hi, May I know how to fix this problem "(*1)(L1L22)". I received warning when I run it in Mplus. I need to get the L1L13 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) (L1L22); !the first 13 items have high loading on GENSTRES STRES@1; R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 (THETA1THETA13); 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; 


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


Hello! After respecificate my 3 Factor Model, i manage to get rid off the previous warning messages and almost attained conventioned cutoffs on default test of "goodness of fit models". In order to see if there were minor, but significant crossloadings 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, crossloadings 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 crossloadings with other observed variables even stronger than previous ones... Thank you, 


Trust the ESEM results. Good CFA solutions are not contradicted by ESEM results, so your CFA model sounds weak. 


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 crossloadings 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 


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. 

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