Can MIMIC be incoperated in SEM? PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Daniel posted on Tuesday, August 26, 2003 - 12:21 pm
Hi Dr. Muthen,

1. Can MIMIC be incorperated in SEM? Is there any problem on interpreting the result? For example,

f1 by y1-y5;
f2 by y6-y10;
f3 by y11-y15;
f4 by y16-y20;

f2 on f1;
f3 on f2 f1;
f4 on f3 f2;

f1 f2 f3 f4 on x1-x3;

2. By the way, in SEM, the minimum number of indicators for a factor is two, not one. Am I right? If I want to treat a independent variable as a latent variable in SEM, how to do it?

 Linda K. Muthen posted on Tuesday, August 26, 2003 - 1:41 pm
1. Yes. No.

2. You can have one indicator. If the residual variance is zero, then the factor and the indictor are identical. If the residual variance is a function of reliability, measurement error can be accounted for by fixing the residual variance. A two indicator factor model is not identified unless there are other factors in the model. At least three indicators is desirable.
 Daniel posted on Sunday, December 07, 2003 - 6:50 pm
Hello Dr. Linda,

In question 1 in discuss August 26, 2003, if x1-x3 are categorical covariates e.g., sex, school race, is the model in question 1 meaningful? I do not think covariates can be incoorperated in SEM at present developmental level of SEM, am I right?

Daniel Meng
 Linda K. Muthen posted on Monday, December 08, 2003 - 6:38 am
I must not understand your question because covariates are a meaningful part of SEM and have been for a long time. Please clarify.
 Anonymous posted on Monday, May 24, 2004 - 6:35 pm
Dear Dr. Muthen,

I am learning MIMIC now and notice that you are one of the pioneers who explored to use this technique. May I request here a copy of some of your articles? My email address is

Thank you very much.

1)Muthén, B. (1989). Latent variable modeling in heterogeneous populations. Psychometrika, 54, 557-585. (#24)

2)Gallo, J.J., Anthony, J. & Muthen, B. (1994). Age differences in the symptoms of depression: a latent trait analysis. Journals of Gerontology: Psychological Sciences, 49, 251-264. (#52)
 Linda K. Muthen posted on Monday, May 24, 2004 - 7:11 pm
You should request these papers by emailing
 Lois Downey posted on Friday, January 27, 2006 - 5:08 pm
This is a question about nomenclature. How do MIMIC models differ from SEM models? Must MIMIC models have at least some predictors that are measured, and SEM models have at least some predictors that are latent? Or is there some other distinction?
 Linda K. Muthen posted on Saturday, January 28, 2006 - 9:11 am
I'm not sure there is a definition that everyone uses. We see any model with a latent variable where there are observed or latent predictors as an SEM model. So for us, bringing predictors into a CFA model makes it an SEM model. The MIMIC model is a CFA with covariates. It is therefore an SEM model.
 johanna posted on Tuesday, March 04, 2008 - 7:54 pm
Hi Dr Muthen

I started a SEM course and I made multiple researches and read some articles but I was not able de find a simple definition of the MIMIC model. Would you be please able to help in explaining the concept in simple words and shematize it if it's possible?
Thank you and best regards, Johanna
 Linda K. Muthen posted on Wednesday, March 05, 2008 - 6:05 am
A MIMIC model is a confirmatory factor analysis model with covariates.
 Kihan Kim posted on Wednesday, February 04, 2009 - 2:34 pm
Hi Dr Muthen:

I would like to test a structural model in which an endogenous latent variable is predicted by a dichotomous covariate (such as gender). In other words, I want to control for the impact of x (gender) on the endogenous variable in SEM.

Is this possible? For example..

F1 y1 y2 y3;
F2 y4 y5 y6;
F3 by y7 y8 y9;
F3 on F1 F2;
F3 on x;

(x is a dichotomous variable like gender).

 Linda K. Muthen posted on Wednesday, February 04, 2009 - 3:20 pm
 Kihan Kim posted on Wednesday, February 04, 2009 - 5:21 pm
Thank you Linda, As follow-up of the previous question, I want to double check a few things:

1. Can I use a continuous variable (instead of dichotomous variable) as covariate?

2. If I want to a structural model with a covariate, then I should use the same covarate predicting the same latent variable in the measurement model. Am I right?

3. If you know an article that tests a structural model with a covariate, could you share with me the reference?

Thank you.
 Linda K. Muthen posted on Thursday, February 05, 2009 - 10:13 am
You can use either a binary or continuous observed variable as a covariate. See the topics MIMIC and SEM under References on the website for papers on these topics.
 Erika Wolf posted on Tuesday, May 19, 2009 - 4:50 pm
I have a good fitting CFA model and I'm running a modified MIMIC model now where I regress some of my latent factors from my CFA on several demographic covariates--these include binary covariates (gender, etc) and continuous (age). I seem to be running into a problem with the age variable, I think because its variance is so much bigger than anything else in the model. The model will not run and I get an error message indicating there is a problem with the age variable in the psi matrix. Can you advise me how to handle this? Thanks. The model runs fine if I remove this variable and it is definitely reading the data in correctly.
 Linda K. Muthen posted on Tuesday, May 19, 2009 - 7:22 pm
You can try rescaling the age variable by dividing in by a constant using the DEFINE command. Otherwise you need to send your input, data, output, and license number to
 Erika Wolf posted on Wednesday, May 20, 2009 - 6:05 am
I did try rescaling the age variable in a few different ways, but I continued to get error messages related to the rescaled variable. I'll send you the requested info, thanks.
 Jurgen Becker posted on Monday, March 28, 2011 - 1:48 pm
Dear prof Linda and Bengt

I have a question regarding IRT and SEM. I am planning to used Rasch rating scale measures as indicators in SEM. However, I am running into some problems with emperical under identification because the Rasch measures are expressed for the entire scale and not for individual items comprising a scale.

As indicated above, I know that it is possible to fit an SEM model with single indicators. However, I am testing moderation in SEM, thus I need to compute item parcels to capture the interaction effect.

Firstly, is it possible to convert lambda factor loading into interval Rasch rating scale measures for individual items and, secondly, if this conversion is possible, is it methodologically prudent to combine these Rasch rating scale measures to create interaction effect parcels in MPLUS
 Bengt O. Muthen posted on Monday, March 28, 2011 - 4:42 pm
I am not clear on your questions because I don't see how moderation requires item parcels or how factor loadings relate to a Rasch scale. It seems like it would be best to work with the responses to the individual items if you have them. SEM in Mplus can handle an IRT measurement model and can handle interactions with the latent variable that the IRT model defines.
 Sarah Ryan posted on Tuesday, September 20, 2011 - 3:21 pm
I am working with a model including:
4 binary and 1 continuous control covariates(x1-x5)
2 observed exogenous predictors (z1-z2)
3 latent exogenous predictors (L1-L3)
1 latent mediator (LM1)
1 observed ordinal outcome (y)

The structural part of the input syntax is:
L1 with L2 L3;
L2 with L3;
L1 on z1-z2 x1-x5 (the "on z1-z2" b/c my understanding is that this is the syntax for correlating a LF with an observed predictor)
L2 on z1-z2 x1-x5;
L3 on z1-z2 x1-x5;
LM1 on x1-x5 z1-z2 L1-L3;
Y on x1-x5 z1-z2 L1-L3 LM1;

y IND L1;
y IND L2;
y IND L3;
y IND z1;
y IND z2;

Does this accurately reflect a model in which 3 LF's and 2 z's predict LM1; the LF's, z's and LM predict y; and the model is estimated conditional on x1-x5?
 Bengt O. Muthen posted on Tuesday, September 20, 2011 - 6:49 pm
Looks right to me.
 Anonymous posted on Thursday, January 05, 2012 - 2:54 pm
Hi. This is a follow-up to the question asked by S. Ryan; Sept 20, 2011.

Rather than regressing all of the latent covariates on the observed covariates, what if one just wants to treat it like basic regression, so that the respective regression estimates for both the observed and latent covariates reflect the effects, after controlling for all the covariates in the model (irrespective of being latent or observed).

From some prior posts (and the ats.ucla site), it seems like one does this by including both the latent and observed covariates as predictors in a model statement (e.g., Y on F1 F2 ObservedX1). One doesn’t have to model the covariances between the observed and latent covariates by, say, adding the variances of the observed covariates to the model statement. Is this correct?

If so, I’m wondering why I might get very different estimates for the effects of the observed covariates, when I do choose to estimate the covariances between the predictors, compared to when I don’t. In the latter case, the regression parameters for the observed covariates look as though they’re controlling for the effects of the latent covariates. Without including the covariances between the observed and latent covariates, it seems as though the effects of the observed variables fail to adjust for the effects of the latent covariates. Any thoughts would be very appreciated. Thanks!
 Linda K. Muthen posted on Friday, January 06, 2012 - 10:11 am
Please send the two outputs and your license number to
 Samuel Greiff posted on Monday, February 06, 2012 - 2:40 am
Dear Dr. Muthen,

i have one short question about the standardized output in a MIMIC analysis.

When running the User Guide example “ex5_17.inp” with the standardized output option, only STdYX estimates were printed in the output file.

Is there any possibility to not only get StdYX estimates, but also S.E., Est./S.E. and Two-Tailed P-Values? For instance, in order to report the standardized path coefficients and p-values for covariates.
 Linda K. Muthen posted on Monday, February 06, 2012 - 1:46 pm
With covariates in the model and weighted least squares estimation, we don't give all of the standardized estimates nor do we give standard errors.
 Sascha posted on Tuesday, February 21, 2012 - 1:10 am
Might you shortly explain why standardized estimates were not reported?
 Linda K. Muthen posted on Tuesday, February 21, 2012 - 1:44 pm
We did not have easy access to the covariance matrix of the covariates in this part of the program.
 Kathryn Degnan posted on Thursday, October 04, 2012 - 4:15 pm
I understand the MIMIC model is when a CFA and an indicator of the CFA are regressed onto a covariate simultaneously. However, what sort of model might have an outcome regressed onto a CFA and indicator simultaneously?

I've heard that there are examples of this sort of model, but I have not been able to find one. Can someone point me in the right direction?
 Bengt O. Muthen posted on Friday, October 05, 2012 - 9:45 am
If a certain indicator has a stronger influence on an outcome than the rest of the indicators, there may be a need to have not only the factor predicting the outcome but also that indicator predicting the outcome.

No articles of this kind come to mind, but I would think they exist.
 neslihan kahyalar posted on Sunday, July 07, 2013 - 2:28 pm
Dear Dr.Muthen,

I'am trying to calculate size of informal economy using MIMIC model in stata 12. I have 6 cause variables and 2 indicator variables. I tried with following command below and also wanted to identify gdpgr as a scale variable that goes in the same direction with latent variable,IE. However, it seems that i'm doing something wrong.
Can you please let me know how do i identify the scale variable and fit the MIMIC model in stata.

Thank you very much,


sem (IE -> gdpgr) (IE -> dlnm1) (dssc -> IE) (dinf -> IE) (dunemp -> IE) (dagricult -> IE) (dintax -> IE) (ddirtax -> I
> E) if gdpgr, covstructure(e.IE e.gdpgr e.dlnm1 , diagonal) latent(IE ) nocapslatent
(1 observations with missing values excluded;
specify option 'method(mlmv)' to use all observations)
 Bengt O. Muthen posted on Sunday, July 07, 2013 - 2:39 pm
This discussion list is for Mplus.
 Sandra Bohmann posted on Friday, October 13, 2017 - 9:08 am
I am trying to estimate the following: 2 Latent variables with effect indicators Le1 & Le2. 1 latent variable with causal indicators (LC1). Both latent variables with effect ind. mediate the effect of the latent variable with cause ind. on 3 outcome variables which are observed (O1, O2, O3) where O1 is continuous and log-transformed while O2 and O3 are categorical.

! effect ind
Le1 by x1-x8 ;(continuous ind)
Le2 by y1-16 ;(categorical ind)
! cause ind
Lc1 on z1@1.000 z2-z5 (categorical causal ind.)
Lc1 by Le1* Le2 ;
! structural
O1 on Le1 Le2 Lc1 O3 gender ;
O2 on Le1 Le2 Lc1 O3 gender ;
O3 on Le1 Le2 Lc1 gender ;
! cor
Le1 with Le2;
z1 with z2-z5 ;
z2 with z3-z5 ;
z3 with z4-z5 ;
z4 with z5 ;

I get an error message that PSI is not positive definite and the Lc1 is the problem and another error message that the standard errors could not be estimated due to O3.

I looked at Tech 4 there are no correlations > 1 between the latent variables but Lc1 has a negative residual variance. All of the causal indicators for Lc1 have a variance of 1.

Can you help me with this?
In a next step I would like to include an interaction between Lc1 and Le1 and one between Lc1 and Le2 for each of the outcome variables. But I want to get this model right beforehand.
many thanks
 Bengt O. Muthen posted on Friday, October 13, 2017 - 2:26 pm
Your Lc1 factor should have its residual variance fixed at zero.
 Sandra Bohmann posted on Friday, October 13, 2017 - 6:25 pm
Dear Bengt, thank you for your response. Setting the variance of Lc1 to 0 works for the mediation model above. If I interact Lc1 with Le1, however, this no longer makes sense, does it? When running the model with the interactions I only get this message.



without the restriction to 0, I obtain results but with a warning that the estimation has reached a saddle point and I am back to all the causal indicators having a variance of 1.

Can you recommend any papers that are dealing with a similar problem? I only found papers on latent interactions involving cause indicators using the pls method.
 Bengt O. Muthen posted on Saturday, October 14, 2017 - 11:15 am
Why would you want to interact Lc1 with Le1; why not just regress Le1 on Lc1?
 Sandra Bohmann posted on Saturday, October 14, 2017 - 11:29 am
I do regress Le1 on Lc1 but I want to test not only mediation but moderated mediation - hence the interaction effect. The moderated mediation is one of the hypotheses I would like to test.
The hypothesis would be that the strength (and possibly even the direction) of the effect of Le1 on O3 depends on the level of Lc1. I thought the way to test this would be an interaction term Le1xLc1 (using XWITH). Is there another way?

Many thanks. Sandra
 fatima bouharaoui posted on Monday, January 22, 2018 - 9:26 am
I am trying to test a MIMIC model with 4 indicators, one latent variable and 3 covariates , but in order to compare with PLS method, I want to fox the residual variance of the latent variable in 0, how can I do that ?

 Bengt O. Muthen posted on Monday, January 22, 2018 - 10:39 am
I think you are after a "formative" model where the indicators predict the factor. That's not a MIMIC model. You may want to discuss this on SEMNET.
 ava saleh posted on Tuesday, August 07, 2018 - 3:12 am
Hi all, I'm new to SEM and I really need some help.

I have a 3 factor CFA model. I want to see whether my covariates of interest; consumption, age and race, predict these factors.

Prior to running a MIMIC model, I conducted some correlations in SPSS between the covariates and the factor items. Significant correlations (all of them) were included in the model.

Now, the problem comes when I perform the MIMIC model. My model results are showing negative regression coefficients when correlations were positive for all factor items (even when looking at each covariate separately). I'm wondering if theres a problem in my syntax:

control BY EA EB EC;
efficacy BY SA SB SC;
protection BY PA PB PC;

control efficacy protection ON black high mod age;

estimator= wlsmv;

standardized sampstat residual ;

race 1= black 0=white
dummy variables for:
high consumption 1 = high 0= not high
moderate consumption 1=moderate 0=not moderate
low consumption 1=low 0 = not low (reference group)

Please help! Thank you so much

Kind regards,
 Bengt O. Muthen posted on Tuesday, August 07, 2018 - 11:15 am
Perhaps your factor loadings are negative. If not, perhaps you need many direct effects from covariates to factor indicators.
 ava saleh posted on Tuesday, August 07, 2018 - 4:01 pm
thank you for your reply!

how is this done?

 Bengt O. Muthen posted on Tuesday, August 07, 2018 - 4:54 pm
Try regressing one factor indicator at a time on all the covariates ("y on x") to see which ones are significant.

Alternatively, for p y's and q x's, say

y1-yp on x1-xq@0;

and look at the modindices to see which ones are large.
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