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Mplus Discussion > Categorical Data Modeling >
 Leigh Roeger posted on Sunday, January 09, 2000 - 4:53 pm
When applying a MIMIC model researchers have typically tested first whether items are unidimensional. So for example in the Gallo, Anthony and Muthen (1994) paper 15 depression symptom items when subjected to a EFA were found to load on to a single factor (depression).

My question is what happens when you are working with a depression scale such as the CES-D or BDI which when factor analysed (EFA) will invariably produce three or four factors (eg depressed affect, positive affect, somatic). Does it make any sense to model this as a second order model and then carry out the MIMIC analysis. This means we would be saying that for the same level on the second order factor of depression one group (say women) are more likely to endorse a particular item than are men. Does this sound plausible or would it be better to go back to the scale and remove items with a view to producing unidimensionality.

Any views would be very much appreciated.
 Linda K. Muthen posted on Monday, January 10, 2000 - 1:29 pm
It is not necessary to have a single dimension to study direct effects using a MIMIC model. If you have four factors, you can regress them on the background variables and also regress the factor indicators on the background variables to study direct effects.
 Anonymous posted on Tuesday, September 19, 2000 - 3:00 pm
1. In MIMIC modeling, could the cause/background variables (X) be categorical? The examples in the MPlus manual for MIMIC models do not contain one for categorical X.

2. Can we combine a MIMIC model with a multi-layer
structural equation in MPlus? For example, is it possible to have the following:

CATEGORICAL ARE y1-y12 x1-x3;
f1 BY y1-y2;
f2 BY y3-y5;
f3 BY y6-y8;
f4 By y9-y10;
f5 BY y11-y12;
f1 ON x1;
f2 ON x2;
f3 ON x3;
f4 ON f1 f2 f3;
f5 ON f4;
 bmuthen  posted on Thursday, September 21, 2000 - 8:52 am
Yes to both questions. The distribution of the covariates does not matter because the model is for the outcomes as a function of the covariates. And, factors can be regressed on other factors and the model still have all the usual MIMIC features including direct effects from covariates. As long as the model is identified and makes sense.
 Randy MacIntosh posted on Friday, October 13, 2000 - 8:22 am
Is it possible to test for factor loading invariance across groups using a MIMIC model? Or does that have be done using a multi-group model?
 Linda K. Muthen posted on Friday, October 13, 2000 - 9:33 am
You cannot compare models with and without factor loading invariance using the MIMIC model. There is no way to relax the assumption that the factor loadings are the same for two groups, say males and female. Only the intercepts can vary. I think the only way to test factor loading invariance is multiple group analysis.
 Anonymous posted on Thursday, December 20, 2001 - 4:12 am
I'm trying the MIMIC model with categorical data.
I would like to examine the regression of the second-order factor model
of cognitive test on background variables gender, age.

Because the gender (1=male/2=female) is binary,
I used "CATEGORICAL" command to treat gender
as categorical variables in the model.

However, following error message was shown,
and I could'nt go ahead with the analysis.

*** ERROR in Variable command
CATEGORICAL option is used for dependent variables only.
GENDER is not a dependent variable.

I don't think that the M-plus could not treat the categorical
independent variables.

Should I use another analytic methods like multiple group analysis?
 Linda K. Muthen posted on Thursday, December 20, 2001 - 7:43 am
The CATEGORICAL statement is used to identify dependent variables that are categorical. The scale of the independent variables can be categorical or continuous but this information is not important in the estimation of the model. All you need to do is remove the independent variables from the CATEGORICAL statement.
 Mesfin Mulatu posted on Wednesday, November 27, 2002 - 1:44 pm
I am estimating a single group MIMIC model with categorical variables. I noticed that the model fit improves a great deal when analysis type=MEANSTRUCTURE as opposed to analysis type=GENERAL. I found this by accident but I am not sure I understand exactly what the implications of it is. Would you please explain what meanstructure single group MIMIC model means?


- Mesfin
 Linda K. Muthen posted on Wednesday, November 27, 2002 - 3:30 pm
If you have unstructured means in your model, you should get the same chi-square as when you have no means. I just ran a categorical MIMIC to confirm this. If you are only adding MEANSTRUCTURE and doing nothing else, you should get the same chi-square. If you send your outputs, I will be happy to see what the explanation is.
 Anonymous posted on Tuesday, October 14, 2003 - 5:58 am
I am conducting a CFA with bacground variables
to test my single-factor model(n=1358).

The measurement model has ten indicators and are regressed
by three background variables (sex, age, diagnosis).
I am estimating the parameters using the WLSMV for binary and categorical
data, because the indicators are dichotoumous and categorical.

When I run the analysis, the following error message was shown:


As a result, I can not admit the correlation between sex and age.
Of course, I know that dependent categorical variables does not need to
be declared as continuous.

I don't know what to do to solve this problem.

Any suggestions would be appreciated.
 Linda K. Muthen posted on Tuesday, October 14, 2003 - 6:23 am
Please send the complete output to support@statmodel.com. I need to see how you specified your model.
 yang posted on Friday, April 21, 2006 - 1:03 pm
I am fitting a MIMIC model, in which the unidimensional latent variable (f) is continuous, while all of its indicators (u1-u12) are binary (0/1), and the only one covariate (x) is also binary (0/1). Since I could not find a program ¡°template¡± from the User¡¯s Guide or Handouts, I composed the following codes, but I am not sure whether it is correct. Would you mind to have a look at it? Thanks.

TITLE: MIMIC with binary indicators and covariate;

DATA: FILE IS "123.dat";


MODEL: f BY u1-u12;
f ON x;
u1-u12 ON x;

OUTPUT: standardized modindices (3.84);
 yang posted on Friday, April 21, 2006 - 1:31 pm
I got a report of problem after running the previous codes:


The sample size pretty large (>1000), and I am fitting a unidimensional struture. What's wrong? Thanks a lot.
 Linda K. Muthen posted on Friday, April 21, 2006 - 1:44 pm
I see two problems. You have set the metric of the factor twice. Once because the default in Mplus is to hold the first factor loading to one to set the metric of the factor. In addition, you have fixed the factor variance to one. See the BY statement in the user's guide for a discussion of this.

The identification problem is because you cannot identify a model with all of the direct effects. A better way to do this is to use the statement:

u1-u12 ON x@0;

and ask for modification indices to find large direct effects.
 yang posted on Friday, April 21, 2006 - 2:50 pm
I see. Thank you very much!
 Marisa Schlichthorst posted on Monday, May 15, 2006 - 6:32 am
I am estimatig a one-factor-MIMIC-model with binary x-variables and categorical y-variables in order to explore heterogeneity. In the first model all relations between x-variables and y-variables are set to zero. Only relations between the factor and the x-variables are estimated. With respect to modificationindices a second model is estimated by relaxing the restriction and setting one relation between x- and y-variable free. Doing so the paper Muthén & Asparouhov (2002) states that the interpretation of a significant direct effect is that the threshold of one group is biased. But in their model they only dealed with binary outcomes with one threshold. I have categorical outcomes with four/five categories and therefore three/four thresholds. Does in this case a positive significant direct effect mean that all thresholds are biased in the way tau-kappa?
 Linda K. Muthen posted on Tuesday, May 16, 2006 - 6:56 am
A significant direct effect with an ordered categorical outcome applies to all thresholds.
 jenny fan posted on Thursday, June 15, 2006 - 1:36 pm
Dear Drs. Muthen,

I am using MIMIC to investigate DIF effect of some demographic characteristics (x1-x3) on the items (y1-y10). Besides x1-x3, I included some clinical conditions (x4-x6) as exogenous variables in the MIMIC model. The quesion is -- do I need to create the direct path from x4-x6 to the items considering the potential DIF of x4-x6 on the items? If we don't create extra direct paths other than for the grouping variables of interest, does it impact the model results and interpretation?

Specifically in the codes --

f1 by y1-y10;
x1-x6 on f1;
to add the direct effect, should I use
y1 on x1-x3 OR y1 on x1-x6 ?

Another question is --
if all exogenous variables are dichotomous, is it true that multi-group MIMIC is not necessary because multi-group MIMIC requires categorical variables?

Thank you for your time in advance.
 Linda K. Muthen posted on Friday, June 16, 2006 - 9:48 am
You don't need to include direct paths for all of the variables. In fact, the model would not be identified if you did. I suggest adding y1-y10 ON x1-x6@0; to the MODEL command and run this asking for modification indices. The modification indices will show you where direct effects may be needed.

I don't undersatnd your second question. The scale of the covariates is not an issue in model estimation.
 yang posted on Friday, December 15, 2006 - 7:53 am
Drs. Muthen,

How to evaluate/estimate the magnitude of DIF in MIMIC model? Thanks.
 Linda K. Muthen posted on Friday, December 15, 2006 - 10:46 am
A significant direct effect, a factor indicator regressed on a covariate, indicates differential item functioning.
 Roger Brown posted on Sunday, March 18, 2007 - 3:32 pm
I have also encountered the following error message, as previously posted by an anonymous poster:

Previous post (October 14, 2003 - 5:58 am)
I am conducting a CFA with bacground variables
to test my single-factor model(n=1358).

The measurement model has ten indicators and are regressed
by three background variables (sex, age, diagnosis).
I am estimating the parameters using the WLSMV for binary and categorical
data, because the indicators are dichotoumous and categorical.

When I run the analysis, the following error message was shown:


As a result, I can not admit the correlation between sex and age.
Of course, I know that dependent categorical variables does not need to
be declared as continuous.

I don't know what to do to solve this problem.

I did not see a response posted, was there a solution to this MIMIC model using a dichotomous variable? Thanks.

Roger Brown
 Linda K. Muthen posted on Monday, March 19, 2007 - 10:16 am
I think the problem is that you have put the covariates on the CATEGORICAL list. This list is for dependent variables only.
 Roger Brown posted on Monday, March 19, 2007 - 11:02 am
Thanks Linda, I didn't have the covariates in the CATEGORICAL list, but did seem to solve my MIMIC problem. I originally ran my problem on my home machine, where I had an earlier version of MPlus. When I just ran the same problem here at work using V 4.1, everything was fine. So, must have been something in an earlier version? I will run these problems on my home machine to confirm my suspicion. Thanks for the response.

 Linda K. Muthen posted on Monday, March 19, 2007 - 11:04 am
That may be the case. It's always best to use the newest version.
 Gemma vilagut posted on Thursday, May 10, 2007 - 5:45 am
I am running a MIMIC model with one dummy covariate(begenl). The model results show that the loadings of the covariate on the two of the factors (MOBILT and PARTIC) seem to be significant (Est./S.E.=4.173 and 2.116, repectively), however, their stdXY are small (<0.120)>0.98). The modification indices suggest that there is a direct effect of the covariate on item FD20 (Est./S.E.=7.506). When I compare Chisq of model with direct effect with that without it is signifficant. Although the chis-q test is signifficant and the parameters seem to be signifficant too, the effect of the covariate on the factors and on item FD20 seems small to me. What do you think? Would you say there is non invariance of Item FD20 and population haterogeneity?

Estimates S.E. Est./S.E. Std StdYX
BEGENL 0.221 0.053 4.173 0.227 0.112

BEGENL 0.090 0.043 2.116 0.106 0.052

BEGENL -0.414 0.055 -7.506 -0.414 -0.201

Residual Variances
MOBILT 0.935 0.009 101.243 0.987 0.987
PARTICI 0.724 0.025 29.006 0.997 0.997

 Linda K. Muthen posted on Thursday, May 10, 2007 - 9:26 am
The significant direct effect of fd20 on begenl indicates measurement non-invariance. It sounds like you have confirmed that with a chi-square difference test.

For a binary covariate, the standardized estimate should be divided by the sample standard deviation of the covariate. Then it will represent the change from one category to the other rather than a standard deviation change.
 Gemma vilagut posted on Friday, May 11, 2007 - 8:25 am
 Carol M. Woods posted on Monday, June 11, 2007 - 9:25 am

I am fitting a one-factor MIMIC model. All indicators are binary (these are items and some have DIF) and I'm using the IRT parameterization with MLR.

There are 6 binary covariates. One for gender (1 = female), and 5 dummy indicators to code a 6-category nominal ethnicity variable (white is the reference group). Items with DIF are regressed on all 6 covariates (as is the factor).

In my final model, there is one threshold parameter estimate for every item. For items with DIF, the threshold depends on the group.

My question concerns how to interpret the estimated threshold for an item with DIF. Is it for when all covariates = 0, which would be white men? Or something else?

 Linda K. Muthen posted on Monday, June 11, 2007 - 11:03 am
The threshold printed in the output for for all x's equal to zero. If you are interested in a threshold for a particular set of x values, you would need to compute that by hand.
 Andrea Vocino posted on Tuesday, April 15, 2008 - 4:41 am
Hi Linda,

in a previous post you state: "The CATEGORICAL statement is used to identify dependent variables that are categorical. The scale of the independent variables can be categorical or continuous but this information is not important in the estimation of the model".

My question is why?

In a type I (fixed) regression the dichotomous/ordinal/polytomous exogenous variables do not create a problem because they are not random variables. In SEM however they are random and when using normal theory ML they are supposed to follow a normal distribution.

LISREL, for instance, has a FI option on the model line where all exogenous variables can be configured as having fixed effects as in a type I (fixed) regression. Could you please explain how does Mplus work?

Thanks in advance.
 Linda K. Muthen posted on Tuesday, April 15, 2008 - 8:51 am
To be more clear about what I said, in regression covariates can be binary or continuous. Both binary and continuous covariates are treated as continuous variables in model estimation.

In LISREL using the FI option and in Mplus with TYPE=GENERAL for continuous outcomes, the means. variances, and covariances of the exogenous observed variables are fixed at their sample values. This is done because in this case if they were estimated using ML, they would be estimated at their sample values.
 Andrea Vocino posted on Tuesday, April 15, 2008 - 2:15 pm
Thanks Linda -- what happens if I use MLM estimation instead?
 Linda K. Muthen posted on Tuesday, April 15, 2008 - 2:49 pm
Same thing.
 Andrea Vocino posted on Tuesday, April 15, 2008 - 3:37 pm
Thnx again. My probelm is that I have a MIMIC model whith covariates that are ordinal. In particular Age, which is coded as follows:

1=under 18

11=over 65

How do I model such variable where scale intervals aren't the same size?
 Linda K. Muthen posted on Tuesday, April 15, 2008 - 4:11 pm
When you have a covariate like that if you don't want to treat it as continuous, you need to create 10 dummy variables just as in regression? Covariates in regression can be binary or continuous.
 wenjun zhong posted on Tuesday, September 30, 2008 - 3:28 pm
Hi Linda and Bengt, I met a question with my MIMIC models that I can not figure out by reading the posts.

I'm using Mplus version 4.21. I want to check whether age sex and other indicators can have effects on the self-reported hearing, vision and other symptoms. I have three factors.

When using age, sex and education as the indicators, the MIMIC model fit well: CFI:0.927, TLI:0.913, RMSEA=0.047. No warning or error messages.

However, when I further add another indicator (general health score), I got a warning: "the residual covariance matrix is not positive definite. this could indicate a negative variance/residual variance for an observed variables..." And it indicated that the problem involving one item "hearing problem". In the output, the residual variance for this item was 0, and the R-square was "undefined".

From the correlation matrix output by Mplus, I found that this item had high correlations to item "hearing aide (yes, no)", coefficient=0.817, and item "ears problem", coefficient=0.793.
 wenjun zhong posted on Tuesday, September 30, 2008 - 3:28 pm
Are these correlations the polychoric correlation? I checked the items correlation (spearman), they were not that high (<0.4). If these high correlations are the causes for the 0 residual variance for item "hearing problem", why the program went well when I only use age, sex and education as the indicators?

How can I fix this problem?

Thank you very much!!

 Linda K. Muthen posted on Wednesday, October 01, 2008 - 8:43 am
Please send your files and license number to support@statmodel.com.
 RDU posted on Sunday, December 07, 2008 - 4:03 pm
Hi. I am trying to run a MIMIC model using ordinal indicators with 2 continuous factors. The estimation method is the default of WLSMV.

I know that in MIMIC models the covariates used to predict both the latent factors and the observed indicators are usually binary(0/1). Though, I was wondering how one would treat a combination of binary and continuous covariates? Would the continuous covariates be specified such that their residual variances are set to 0 (i.e., factor1 on covariate1@0))?

Thank you.
 Linda K. Muthen posted on Monday, December 08, 2008 - 8:54 am
You treat binary and continuous covariates the same in a MIMIC model. It is not necessary or even recommended to put a factor behind the covariate. You would simply say:

f ON x1 x2;
y1 ON x1 x2;

if x1 is binary and x2 in continuous.
 Hsien-Yuan Hsu posted on Sunday, March 01, 2009 - 10:10 pm
Drs. Muthen,

In the Ex.11.1, let's say X2 is a grouping variable since X2 is a binary variable (0=group1 or 1=group2). How could I control the sample ratio by variable X2 in Monte Carlo study?

Or do I need to generate multiple group dataset (e.g., Monte Carlo study example 5.15)? If yes, the grouping variable I generate is 1 and 2. In Monte Carlo study, how could I define this grouping variable as 0 and 1?

Thanks in advance.
 Linda K. Muthen posted on Monday, March 02, 2009 - 10:46 am
If you want to generate multiple group data, you should follow mcex5.15.inp. Grouping information is given using the NGROUPS and NOBS options of the MONTECARLO command.
 Novice Researcher posted on Monday, April 13, 2009 - 7:47 am
How do I test for non-uniform DIF with a MIMIC model in Mplus? I am using a model with several categorical items measuring a single factor and a dummy coded group variable.
 Linda K. Muthen posted on Monday, April 13, 2009 - 1:41 pm
If by non-uniform DIF, you mean testing both intercept and factor loading invariance, this is best done using multiple group analysis.
 Matthew Diemer posted on Friday, November 06, 2009 - 7:41 am

I have a question re: extending MIMIC to structural models.

I am analyzing data that includes White youth and youth of color; theory suggests the constructs I am studying will not be invariant across groups. Due to small samples for some racial/ethnic groups and convention in MIMIC modeling, I collapsed youth from different groups into a dichotomous variable – White and non-White youth – rather than conduct multiple group analyses to test for measurement invariance. This group membership was used as the external covariate in a MIMIC model. The MIs suggested one direct effect from racial/ethnic group to one indicator – which was significant and improved the fit of the MIMIC model, suggesting DIF for this indicator. The MIMIC model also suggested some latent mean differences; overall, “partial” measurement invariance, I think.

I therefore want to attend to racial/ethnic differences when fitting the structural model. I could further subdivide the population into White and non-White subsamples, run the structural model for each, and compare the model fit and pattern of relationships for each racial/ethnic subsample.

What if I included these paths from the MIMIC model in the structural model, running analyses with the population of White and non-White youth? My understanding is that this doesn’t test for group differences in path coefficients. Does this “control” for race/ethnicity and attend to DIF in the structural model?
 Bengt O. Muthen posted on Friday, November 06, 2009 - 8:44 am
I am not clear on the question - if you analyze a single subgroup in what you call a "structural model" (which MIMIC also is) you cannot include paths from a race/ethnic dummy variable because the dummy variable won't have variation in that group. It is correct that MIMIC dummy covariate effects do not moderate slopes - which would be the path coefficients you refer to.
 Matthew Diemer posted on Friday, November 06, 2009 - 9:06 am
Let me clarify - my sample consists of White AND non-White youth. The exogeneous covariate is a 0/1 variable where 0 = non-White and 1 = White. I modeled this covariate in a traditional MIMIC model (CFA with covariates) and am considering doing so in a structural model where I am interested in examining paths between latent constructs while controlling for this exogeneous racial/ethnic group variable as a covariate (recognizing MIMICs are also structural by nature).

Because the MIMIC CFA model was "mostly" invariant, it doesn’t seem necessary to then proceed to fit separate structural models in a multiple groups analysis (by racial/ethnic group).

Rather, this would entail fitting a structural model with one sample (both White and non-White youth) where racial/ethnic group is an exogeneous covariate.

I've just read your 1989 Psychometrika paper on this topic.

Thank you, Bengt.
 oliver lin posted on Thursday, May 26, 2011 - 5:02 am
Hi Bengt and/or Linda,
when I run WLSMV with the DIFFTEST command, I get the message:
I want to detect DIF on item 1 ,could you please give me hand? thank you very much.

[H1 model]
NAMES ARE group i1-i20;
USEVARIABLES ARE group i1-i20;
f by i1-i20;
f on group;
i1 on group;
DIFFTEST is deriv.dat ;

[H0 model]
NAMES ARE group i1-i20;
USEVARIABLES ARE group i1-i20;
ANALYSIS: DIFFTEST is deriv.dat;
f by i1-i20;
f on group;
i1-i20 on group @0;
 Linda K. Muthen posted on Thursday, May 26, 2011 - 10:50 am
It may be the following:

i1-i20 on group @0;


i1 on group @0;

If this does not help, please send the relevant files and your license number to support@statmodel.com.
 AK22 posted on Tuesday, September 13, 2011 - 1:56 pm
Can the Std estimate for the direct effect of a binary covarite on a factor indicator be interpreted like an effect size based on Cohen's guidelines? If not do you have any suggestions on how to determine if a statistically significant direct effect has practical significance when your sample size is really large?
 Bengt O. Muthen posted on Wednesday, September 14, 2011 - 10:34 am
You need to divide the unstandardized estimate with the standard deviation of the factor indicator to get a Cohen-like result.
 Jaume Aguado Carné posted on Wednesday, October 26, 2011 - 12:08 pm
I have recently performed a CFA and added covariates that have an effect on the factors (MIMIC). I have four factors and the indicators are ordinal and defined as categorical in Mplus (WLSMV used). I have two question about this model:

1- How must I interpret the coefficients of the covariates regressed on the factors. As usual regression coefficients? and those of dummy created variables when there are various categorical variables that have been coded as dummies?

2- Is it possible to assess the effect of the factor on an observed variable that is binary? I want to study how the factors relate to an outcome variable three months later while keeping in the model the covariates I mentioned in 1 and the measurement part. And one last thing, can I have a logistic type coefficient in that model so I can obtain an Odds ratio with it?

Thank you
 Linda K. Muthen posted on Wednesday, October 26, 2011 - 1:19 pm
1. The regression of the factor on a covariate is a linear regression. The regression of a categorical indicator on a factor in a probit regression with WLSMV.

2. I'm unclear on the first part of your question. You can have logistic regression with maximum likelihood estimation.
 Jaume Aguado Carné posted on Thursday, October 27, 2011 - 4:42 am
Let me try to make it more clear.

Can I have a MIMIC model with categorical indicators in the measurement part and then add an observed binary variable in the following way?


Where NEWOBSVAR is the binary variable and Fx are the factors.

If this is possible, my question is:
is there a way to obtain Odds Ratios for that part of the model without changing the estimation method for the whole model?
I hope it is clearer now.
Thank you.
 Linda K. Muthen posted on Thursday, October 27, 2011 - 9:58 am
With WLSMV,you would obtain a probit regression coefficient for the regression of NEWOBSVAR ON F1 F2 F3 F4. This cannot be exponentiated. You would need to use the ML or MLR estimator if you want logistic regression and odds ratios.
 Jaume Aguado Carné posted on Thursday, October 27, 2011 - 10:51 am
Thank you. But then what would it be the effect on the measurement part? Would I be considering the indicators as continuous? I assume I leave the categorical command as it is now in the program.
 Linda K. Muthen posted on Thursday, October 27, 2011 - 12:21 pm
You change nothing but the estimator. Maximum likelihood is not only for continuous outcomes.
 AK22 posted on Friday, October 28, 2011 - 9:28 pm
Does MPLUS output scale reliability so one can calculate a standard error of measurement as a way to compare the difference between a MIMIC model accounting for DIF and a mis-specified model?
 Linda K. Muthen posted on Monday, October 31, 2011 - 4:37 pm
I think you are asking about standard errors of factor scores. Yes, Mplus does provide these.
 UM posted on Sunday, November 18, 2012 - 6:24 pm

Is it possible for Mplus to compute the VIF to check multicollinearity among covariates in MIMIC models?
 Linda K. Muthen posted on Monday, November 19, 2012 - 10:38 am
Mplus does not compute the VIF. You can use TYPE=BASIC to look at the correlations among the covariates.
 Sebastian Köhler posted on Wednesday, January 16, 2013 - 8:56 am
Dear Drs Muthén,

this might a rather trivial question, but I would appreciate your help. I have run a MIMIC model that regresses 9 covariates on a depression factor in a sample with neurological disease using a WLSMV estimator. The covariates are of any kind (binary, ordered categorical, continuous) and can be grouped into disease-specific (n=3) and disease-nonspecific variables (n=6). The model fits well. I now want to compare the relative contribution of the combined disease-specific versus the combined disease non-specific variables for the depression outcome, but I am unsure about how to proceed. Would it be correct to do a Wald test using the MODEL TEST option in the following way?

depr ON u1 (p1)
u2 (p2)
u3 (p3)
u4 (p4)
x1 (p5)
x2 (p6)
x3 (p7)
x4 (p8)
x5 (p9) ;

Model test:
0 = (p1+p2+p3+p4+p5+p6) - (p7+p8+p9) ;

where p1 to p6 = disease nonspecific factors
and p7 ot p9 = disease specific

Covariates were coded so that their parameters are all of the same sign (positive).

Can you please advice?

Best wishes, Seb
 Bengt O. Muthen posted on Thursday, January 17, 2013 - 8:52 am
I don't think you can do this adding of regression coefficients because the covariates are all correlated. Instead, perhaps you can try to form 2 factors and see which factor has the largest standardized coefficient. The factors can be either formative or regular.
 Sebastian Köhler posted on Friday, January 18, 2013 - 2:21 am
Thank you very much for this. I made separate factors for disease specific and nonspecific indicators:

depr BY a01-a17 ;
a02 WITH a03 ;
a02 a03 WITH a09 ;
a05 WITH a06 a04 ;
a07 a14 WITH a17 ;
a10 WITH a11 ;
a12 WITH a16 ;

f1 BY u1-u4 x1-x2 ;
f2 BY x3-x5 ;

depr ON f1 (p1)
f2 (p2) ;

Model test:
0 = p1 - p2 ;

Does this look correct? The standardized coefficients show the expected direction (f1 > f2), which is confirmed by the Wald test (chi-sq = 11.911, df = 1, p = .0006). So my conclusion would be that disease-nonspecific risk factors contribute more to variation in depression outcome than disease-specific risk factors.

Best wishes, Seb
 Bengt O. Muthen posted on Friday, January 18, 2013 - 3:14 pm
You may want to set the factor metric by factor variances @1 instead of factor loadings @1. In this way, your f1, f2 predictors are on the same scale and p1 and p2 are comparable.
 Sebastian Köhler posted on Monday, January 21, 2013 - 3:56 am
Thank you so much!
 secilarslan posted on Thursday, January 16, 2014 - 8:50 am
Dear Dr Muthen;
I watched Topic 1 and 2 videos. They are very usefull for me. I ran analysis by inputs which you talk about in those videos. I want to ask you Do we use these inputs for detecting uniform DIF?
And one more question is Can we talk about an effect size for MIMIC model? Is there any relationship with R squares and effect size?

I am studing with Simulated data set. So I must do the same analyses again and again. Is there any way to do these analyses automatically by MPlus program? Thank you for your help.

Secil Arslan
 Bengt O. Muthen posted on Thursday, January 16, 2014 - 9:12 am
Yes, MIMIC focuses on uniform DIF, that is, for the intercepts/difficulties of the factor indicators.

Don't know which effect you are interested in - on the factor or on an item, but you can always describe an effect size as the ratio of a difference divided by its SD.

Mplus offers Monte Carlo simulations; see UG Chapter 12.
 secilarslan posted on Thursday, January 16, 2014 - 11:23 am
Thank you for your answers.I mean the effect sizes which give us the level of DIF on items. Like standardized regression coefficients(R2)in some other methods.
 Bengt O. Muthen posted on Friday, January 17, 2014 - 8:53 am
If you have a binary item you already have a good scale to present your results in: The difference in probability.
 Sarah Phillips posted on Wednesday, March 26, 2014 - 7:42 pm

I am wondering how to interpret significant effects for my tests of measurement invariance in a MIMIC model. Is it correct to interpret significant relationships between my covariates (in this example gender) and factor indicators as: "Holding the latent construct constant, the intercept for item x was .33 points higher among boys than girls?"

 Linda K. Muthen posted on Thursday, March 27, 2014 - 1:56 pm
 Sarah Phillips posted on Friday, April 18, 2014 - 11:04 am
Thank you!
 Jason Bond posted on Sunday, June 01, 2014 - 1:52 pm

I'm trying to get the correct interpretation of direct effects (DIF) on ICCs. In Carol Woods J Psy Behav 2009 paper (Illustration of MIMIC-Model DIF...), she indicates that, using the Mplus parameterization, negative beta coefs (direct effect of covariates on items) imply tau is smaller for the focal than reference group and she indicates thus that the level of the latent variable required for respondents to respond 'yes' is lower for the focal than reference group (as she says tau is the value of theta such that P(Yes)=.5). However, Muthen, Kao, and Burstein (1991), equation 5 for the difficulty parameter conversion, indicates that (due to the negative sign on the betaj), it is the opposite. Could you help me resolve my confusion? Thanks,

 Bengt O. Muthen posted on Monday, June 02, 2014 - 5:37 pm
Our Topic 2 handout, slide 163 shows this in detail. You see that the key term is tau - kappa*x, that is, a direct effect gets subtracted from the threshold. With a negative direct effect this means that the threshold gets bigger. A bigger threshold means that the probability is smaller for u=1 when x=1 as compared to x=0.
 BOUHARAOUI FATIMA posted on Sunday, July 06, 2014 - 12:08 pm
I'm trying the MIMIC model with categorical data using WLSMV, I have 4 indicators and two reflectives variables . My objectif is to obtain a formative score that I can use in an other analysis, can I obtain a score values in Mplus with MIMIC model? what is the command to obtain this model ? I usually used a lisrel to obtain this score but for continuous indicators.
 Bengt O. Muthen posted on Sunday, July 06, 2014 - 4:16 pm
See FSCORES in the UG.
 Emily Haroz posted on Wednesday, July 16, 2014 - 4:17 pm
I am trying to look at DIF by country on 15 items of a depression scale and have 9 different countries. Is it possible to use a MIMIC model with categorical data using MLR (due to missing values) and a categorical covariate? Or do I have to dummy code the country variable to do a mimic model?

Thank you for your help.
 Bengt O. Muthen posted on Wednesday, July 16, 2014 - 4:25 pm
You need to either dummy code the categorical covariate (if it is nominal) or treat it as continuous (if it is ordinal). In either case you don't put it on the Categorical= list.

Or, you can create C*9 groups, where C is the number of categories in your categorical covariate and then use the new Alignment method to analyze those C*9 groups. See our website under Recent Papers.
 Emily Haroz posted on Thursday, July 17, 2014 - 9:32 am
Thank you Dr. Muthen. I just read about the alignment analysis and looks like it is exactly what I am looking for.

Just to clarify--Can this be done with observed indicators that were recorded on a likert scale (0,1,2,3)?

Thank you for your help! Very exciting stuff.
 Bengt O. Muthen posted on Friday, July 18, 2014 - 4:10 pm
Variables treated as ordered polytomous categorical variables can not yet be handled with alignment. We expect to have this in a few months.
 fatima bouharaoui posted on Tuesday, August 19, 2014 - 11:04 am
I'm trying the MIMIC model with categorical data , I have 4 indicators and two reflectives variables , I used fscores to obtain the score by Mplus, but I want to know how to calculate it, can I use the coefficients obtained by my 4 indicators to estimate the score, if not, what is the formulas used for this?

 Linda K. Muthen posted on Tuesday, August 19, 2014 - 1:25 pm
For categorical data, the estimation of factor scores is iterative. You cannot compute this by hand. See Technical Appendix 11 on the website for further information.
 Megan Brokenbourgh posted on Tuesday, December 16, 2014 - 4:33 pm

I have posted the following message on SEMNET but wanted to multiple opinions:

I have a question regarding sample size for a MIMIC model to test measurement invariance. I am planning to run a MIMIC model in Mplus with ethnicity as my covariate. Originally, my plan was to run a MGCFA, but one of the ethnic groups only has 134 valid cases, which I understand would be less than desirable for a MGCFA. The other ethnic group has 1,248 valid cases. My plan is to randomly select a subset of cases from the larger ethnic group for the MIMIC analysis. I am not sure how many cases I should select from the larger group given the relatively limited sample size of the smaller group. Does anyone know (or can point me in the direction) of any publications regarding whether equal sample size in terms of ethnicity is needed or desirable for a MIMIC model in this case? I came across one article saying that it is preferable, but I am not sure why or how often that is actually applied. In my specific case, randomly selecting 134 valid cases from the larger group to match the 134 valid cases in the smaller group would result in an overall n of less than 400, which I understand is a bit small. Any guidance or advice would be greatly appreciated.
 Bengt O. Muthen posted on Thursday, December 18, 2014 - 12:19 pm
I don't think we know what the best thing to do is here. I would probably keep all cases in the analysis. The 134 cases in the small group can be large enough to have enough power to detect substantively important MIMIC-type non-invariance, that is, direct effect corresponding to intercept/thresholds non-invariance. But you can certainly explore the sample size issue by sampling say 250 cases (enough to work well in a single group) from the 1,248, (perhaps even sample twice).

What did SEMNET say?
 Megan Brokenbourgh posted on Thursday, December 18, 2014 - 1:24 pm
Thank you very much for your prompt response. SEMNET recommended running a power analysis simulation to determine what differences across groups will be detectible. However, I have never done this sort of analysis before and am not sure about the procedure. For now I think I will explore the issue as you recommended. Thank you again and please feel free to share any thoughts about the SEMNET suggestion.
 Fran posted on Tuesday, September 13, 2016 - 1:40 pm
Dear Drs.Muthen,

I am running a DIF test with the MIMIC model on the CESD scale. Is a significant direct path from a covariate (e.g. sex) to an individual item sufficient evidence that this item has DIF, or I have to run a separate LRT test of the nested models allowing this specific direct path versus not allowing this specific direct path?

A followup question is: if the answer to previous question is yes a significant direct path suffices as evidence of DIF, can I test multiple items at the same time?

Thanks you so much for your time to read and answer all our questions.


 Fran posted on Tuesday, September 13, 2016 - 2:31 pm
Dear Drs.Muthen,

Sorry to bother again, another followup question:

I am running the DIF test with the MIMIC model based on a national survey with complex survey design, which means my sample size is huge.

My questions are:
1. Given the sample size,is there a preference of choice between Multiple Group CFA vs MIMIC for testing DIF?
2. Given the sample size, is there any standard of interpreting the magnitude of DIF as meaningful?

Thank you so much! Any information is appreciated!


 Bengt O. Muthen posted on Tuesday, September 13, 2016 - 6:45 pm
First post:

Q1. Yes

Q2. You can't do all of them because that model is not identified. I would do one at a time.

Second post:

Q1. I don't think so. But multiple group analysis can find other kinds of non-invariance such as for loadings.

Q2. That's a tough question. You can compute the effect size - that is, the difference between the 2 groups in intercepts divided by SD of the item. This can be done using Model Constraint. That could tell you more about how substantively important the DIF is. You may also want to ask about this on SEMNET.
 Fran posted on Wednesday, September 14, 2016 - 6:56 am
Dear Dr. Muthen,

Appreciate your timely reply! That clarifies my problem.

All the best

 Jeremie Smith posted on Wednesday, January 25, 2017 - 8:24 am
Dear Dr. Muthen,

I did MIMIC analysis and asked for modification indices. If I fix the variance of latent variable at 1 and intercept at 0, Mplus produces modification indices over 10. If I don't fix the values, it says that there is no modification indices above the minimum value.

Can you explain what is the difference between the two cases? I added the last two line.

Dep by dep1-dep10;
Dep on gender;
dep1-dep10 on gender@0;

Thank you,
 Linda K. Muthen posted on Thursday, January 26, 2017 - 6:50 am
In once case, the factor variance is free to be estimated. In the other, you fix it to one. The intercept is fixed at one as the default so that makes no change. You have now set the factor metric by both fixing the factor loading to one or fixing the factor variance to one not both.

If you send the two outputs and your license number to support@statmodel.com, I can tell you why you get modification indices in one case and not the other.
 Samuli Helle posted on Tuesday, December 12, 2017 - 11:02 am
In a previous post (7/16/2104), Bengt said that: "You need to either dummy code the categorical covariate (if it is nominal) or treat it as continuous (if it is ordinal)". I have three ordinal covariates (actually causal indicators), ranging from 1-4 in my MIMIC model. If I treat these variables as continuous, only one of them is statistically associated with the latent. If I dummy code them, 8 out 9 coefficients are significant. Does this indicate non-linearity or is there something else going on?

 Bengt O. Muthen posted on Tuesday, December 12, 2017 - 3:01 pm
Hard to tell. It could indicate that the ordinal variable does not have interval-scaled categories or that ordinality doesn't hold with respect to its relationship with the DV.
 Jeremy Zhang posted on Wednesday, June 13, 2018 - 11:58 am
Hi Drs. Muthen,

I have set up a MIMIC/CFA with eight covariates model to test measurement invariance of a Competency scale in Mplus. My dissertation methodologist insisted that I should test correlations of the eight covariates, which are all categorical (nominal), such as Professional identity (1 = Evaluator; 2=Other), Highest degree (1=Doctoratel 2=Bachelor & Master); Jobsetting (1=College/University; 2=Other). He argued that MIMIC model is essentially regression model and the multicollinearity of these covariates can be problematic. My question is, should I be be concerned about the multucollinearity issue, given all my covariates are nominal in nature? How can I accomplish that in Mplus? Would you please kindly suggest any references on this topic?

Second question is, when categorical covariates have three or more categories, e.g. education background, (1= Doctorate; 2 = Masters; 3 = Bachelor; 4= High School), how would you interpret the results across the four subgroups?

Thank you so much for your guidance!
 Bengt O. Muthen posted on Wednesday, June 13, 2018 - 5:02 pm
You need to break your multicategory nominal covariates into a set of dichotomous dummy variables. So with C nominal categories, you create C-1 dummies. Then you can use Type=Basic for the set of covariates to see how highly they are correlated.
 Lois Downey posted on Tuesday, April 09, 2019 - 12:56 pm
I am trying to use a MIMIC model to test a latent variable measured with 2 reflective indicators and 4 causal indicators:
F by X1 X2;
F on X3-X6;

All 6 of the indicators are ordered categorical variables (although I am permitted to declare only the reflective indicators as such).

The model that is produced shows no indication of correlations among the causal indicators. If I add "with" statements,
X3 with X4-X6;
X4 with X5-X6;
X5 with X6;
I do get covariances/correlations between the causal indicators, but the variables are assumed to be linear (the output shows means and variances). Am I correct in assuming that the correlations are Pearson, rather than polychoric? Is there a way to get polychoric correlations in this case?

Thank you.
 Bengt O. Muthen posted on Tuesday, April 09, 2019 - 5:26 pm
You can declare causal indicators as Categorical if you like.

Causal indicators (that is, covariates) are correlated but those parameters are not part of the model. See our FAQ: Analysis conditional on covariates.

Regarding your last 2 questions:

Q1: Yes.

Q2: You can mention them on the Categorical list.
 Lois Downey posted on Tuesday, April 09, 2019 - 7:50 pm
Thank you. Actually, I tried listing the causal indicators on the CATEGORICAL list, thinking that that might work when the correlations were included. But even with the correlations included in the model, I still get the message "The CATEGORICAL option is used for dependent variables only. The following variable is an independent variable in the model ...." Do you have any idea what I'm doing incorrectly?

 Bengt O. Muthen posted on Thursday, April 11, 2019 - 10:18 am
Mention them on the Categ list and mention them in WITH statements. The latter makes them dependent variables in the eyes of Mplus.
 Lois Downey posted on Thursday, April 11, 2019 - 10:49 am
Yes. I did that. My input instructions included the following lines:

ANALYSIS: type=complex;
Depress by PHQ2 PHQ1;
Depress on PHQ4-PHQ8;
PHQ4 with PHQ6-PHQ8;
PHQ6 with PHQ7-PHQ8;
PHQ7 with PHQ8;

That produced the error messages indicating, "The CATEGORICAL option is used for dependent variables only...."
 Bengt O. Muthen posted on Thursday, April 11, 2019 - 1:32 pm
Send your output to Support along with your license number.
 Lois Downey posted on Thursday, June 18, 2020 - 1:48 pm
I have a latent variable measured with 3 categorical effect indicators and 2 continuous causal indicators:
QOC by A, B, C;
QOC on D, E;

I want to use a 2-group model to test for differences between groups (control and intervention) on the resulting latent variable. The output provides intercepts for the two groups, but I don't know the syntax for adding in the effects of the two causal indicators in order to get estimated latent variable MEANS for the two groups. Could you please show me how to do that, or direct me to some place where it is published online?

 Bengt O. Muthen posted on Thursday, June 18, 2020 - 4:14 pm
The mean of QOC can be expressed in Model Constraint as

M(QOC) a + b1*M(D) + b2* M(E)

where a, b1, and b2 are parameter labels given in the Model command (intercept and slopes in the QOC regression).
 Lois Downey posted on Friday, June 19, 2020 - 12:05 pm
Got it! Thanks very much for the spoon-feeding!
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