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I have a mimic model with some direct effects between indicators and covariates ,and other effects are between indicators. Part of program is as follows. Analysis: type is complex; estimator is wlsmv; Model: factor1 BY f1f3 f6 f1@1; factor2 BY f7 f12 f13 f7@1; factor1 factor2 ON age sex2; !direct effects f7 ON age; f2 ON age; f10 ON sex2; f1 with f2; f13 with f7; How could I interpret "f1 with f2" and "f13 with f7" under "model" statement well? Thanks! 


From the MODEL command, f1 WITH f2 is a residual covariance. From your MODEL command, f13 WITH f7 is also a residual covariance. Note that you have two factor loadings fixed to one in your BY statements. 

Alex Zammit posted on Tuesday, August 05, 2008  5:22 am



When I run a MIMIC model with the following statement: FACTR1 ON AGE GENDER SEVERITY ACCDAYS LITIGATE EDUCN; the model results for GENDER are: Estimate S.E Est/S.E. 0.452 0.184 2.453 I believe the Est/s.e. of 2.453 means the regression of FACTR1 on GENDER is significant. However, if I change the above statement to FACTR1 ON Gender; the model results for GENDER are: Estimate S.E Est/S.E. 0.092 0.146 0.631 Now it seems the regression is no longer significant. Why does the significance change when the additional covariates are removed? 


In the first case, the coefficient for gender is a partial regression coefficient controlling for age, severity, accdays, litigate, and educn. In the second case, it is not a partial regression coefficient. Another issue is sample size. It may have changed between the two analyses. 

Alex Z posted on Tuesday, August 05, 2008  4:08 pm



Thanks for your response. It would then seem that using GENDER as a partial regression coefficient, controlling for age, severity, etc., would be the correct way to demonstrate the significance of the effect of GENDER on FACTR1? is this because all other effects have been eliminated and GENDER is being considered in isolation? regards, 


Yes, the gender effect "controlling for" age, severity, etc would seem like the proper quantity to consider. 


1) I'm having difficulty understand "why" a significant effect of "u1 ON covariate" indicates differential item functioning. It is my understanding that would simply indicate that one group endorses that item at a higher rate. It's possible that higher rates of endorsement do not indicate DIF. 2) Also, my second concern is how to interpret the DIF result. For example, if I had a 1factor model (f1) where u1 ON covariate (male = 0, female =1) was significant (estimate = .433). How would that be interpreted as affecting the difficulty parameter by sex? Thank you for your help with this? 


1) The "u1 on covariate" effect is only half of it. It is not a matter of a marginal difference in u1 ("higher rates of endorsement") at certain covariate values, but instead the conditional difference in u1 at certain covariate values given a certain factor value. In other words, for two people with the same factor value, the u1 probability differ depending on their covariate value. 2) See our handout for the Topic 2 course on our web site where we go through the ASB example and gender differences in shoplifting. This course is also available for free viewing as a video on the web  see our home page. 


Hello, I have a very basic question about CFA with covariates (MIMIC) to assess DIF. I am trying to use a MIMIC model in a paper for the first time using Mplus. In my case, I have a single factor, a single covariate, and binary items. I am using the default WLSMV estimator. In the short course handout, the first step involves establishing the model without covariates. In the ASB example, all indicator errors are uncorrelated. Would anything change in the following steps (i.e., add covariates, add direct effects suggested by modification indices, and interpret the model) if a model includes factor indicators with one or more correlated errors? Thanks in advance, Rick 


No, nothing would change. 


Thank you. I didn't think so, but I didn't want to make any assumptions. Thanks again. 

ic8 posted on Monday, April 02, 2012  9:55 am



Hello Drs. Muthen, I am attempting to run a MIMIC model in a MC simulation. I would like to have the mean/variance of the latent variable differ between groups, while simultaneously being able to regress the latent variable/indicators onto the grouping variable (hence MIMIC model). Is it possible to do this in MPlus? I would appreciate any help on this matter. Thanks! 


See the Monte Carlo counterpart of Example 5.8. The input is called mcex5.8.inp. 

JW posted on Thursday, November 20, 2014  9:04 am



Hi Drs Muthen, I have data collected in 6 different hospitals across 27 teams and would like to conduct a CFA on some of the data. I use the cluster option to account for clustering at the team level and would like to adjust the model for the 6 hospital sites. It appears I can do this using the CFA with covarites (MIMIC) approach. I have written the following script which seems to run correctly and produce a sensible output but I still wanted to doublecheck with you that the script is fine: cluster = team; USEVARIABLES are bQPR1 bQPR2 bQPR3 bQPR4 bQPR5 bQPR6 bQPR7 bQPR8 bQPR9 bQPR10 bQPR11 bQPR12 bQPR19 bQPR21 bQPR22 wave ; ANALYSIS: TYPE = complex; estimator =mlr; MODEL: TOT15 by bQPR1  bQPR22; bQPR1bQPR22 ON wave@0; TOT15 on wave ; Many thanks 


If you have 6 hospitals it seems that you should regress the factor on 5 dummy variables. 

JW posted on Friday, November 21, 2014  2:15 am



Hi Bengt, Thanks for your reply. I have changed the script accordingly after creating 6 dummy variables for the clinics. I am now regressing just the factor onto these dummys BUT not the individual indicator items, is that OK? MODEL: TOT by bQPR1 bQPR22; TOT on wave2wave6; 


That's a reasonable start. But you could also see if some direct effects indicate measurement noninvariance over hospitals. 

JW posted on Friday, November 21, 2014  7:55 am



Thanks Bengt, how would I do that? and is it really necessary? 


Regress one TOT indicator at a time on all the Wave2Wave6 dummies (I assume these are the hosptials) and see if you have a significant effect. 

JW posted on Friday, November 21, 2014  8:25 am



Great  thank you! so should I run bQPR1 ON wave2wave6; and then run a separate script for each of the 14 indicators  correct? what would I do if there are any significant effects? 


Look at our Topic 1 handout video on MIMIC modeling. 

lee posted on Monday, June 15, 2015  6:31 pm



Dear Drs, I have a quick question about specifying covariates (Xs) in a mimic model. If I have some Xs with missingness while the others don't, do I need to mention the variance of all X or just the Xs with missingness in the syntax? Because if I only mention covariates with missingness, the results shows the covariates without missingness are not correlated with covariates with missingness. I am not sure if I understand how to interpret this and your help is appreciated. 


You must mention the full set of observed exogenous covariates. 


Hi Dr. Muthen, For MIMIC/CFA with Covariates, is it typically necessary to examine the multicollinearity/high correlations of the covariates, like in regression studies? Particularly when covariates are nominal in nature. I have read classic MIMIC studies (Jöreskog & Goldberger, 1975; Muthén, 1979, 1981, 1982) and haven't found any researchers addressing this topic. Any reference will be greatly appreciated! Thank you for your advice! 


For instance, in "Age Differences in the Symptoms of Depression: A Latent Trait Analysis (Gallo, Anthony, Muthén, 1994), a total of 7 covariates were included in the MIMIC model: Age, Sex, Minority, Education, NMSE scores, Work, and Spouse. Is there any research on how many covariates could be included in a MIMIC model? 


Examining multicollinearity risks is always useful. How many covariates can be included depends on the sample size. You typically don't want to estimate more parameters than number of subjects in the data. 

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