Interactions with categorical indicators PreviousNext
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 Sun Kim posted on Wednesday, April 11, 2012 - 12:13 am
Dear Drs. Muthen,

I am trying to test some interactions in an SEM model where type= complex and my indicators are categorical (WLSMV estimator), with indirect effects (model indirect).

I have two questions:
(1) Can I test interactions between two continuous latent variables (but with categorical indicators)? I couldn't find how to do test for interactions using WLSMV estimator, since only ML estimation is allowed with the specification "type= random," which is shown to be used in the User Guide. Furthermore, it seems I cannot test for interactions using categorical indicators as this returns and ERROR message.

(2) How can I compare the interaction results to the full model using log-likelihood, since I cannot fit interactions and indirect paths at the same time?

Thank you so much for your time, as always.

Regards,
Sun
 Linda K. Muthen posted on Wednesday, April 11, 2012 - 12:05 pm
To test a latent variable interaction you must use maximum likelihood estimation. You can do this when the factor has categorical factor indicators. I don't know what error you received so I can't comment on that.

When you cannot use MODEL INDIRECT for indirect effects, you can instead use MODEL CONSTRAINT.
 Sun Kim posted on Thursday, April 12, 2012 - 4:57 pm
Dear Dr. Muthen,

Thank you so much for your response.
I think the problem is that my model is a complex model with individual-level weights. In the variable command, I have categorical indicators with:
cluster = coupleID;
weight is CH02PRWT;

Then, in the Analysis command, I have:
Analysis:
Type= complex ;
estimator= ML;

So I get the warning message:
*** WARNING in ANALYSIS command
Estimator ML is only allowed with TYPE=COMPLEX and replicate weights.
Default estimator will be used.

Thank you.

Regards,
Sun
 Linda K. Muthen posted on Friday, April 13, 2012 - 8:23 am
We don't allow weights with ML because with weights the standard errors are not ML. Use MLR or another maximum likelihood estimator when you have weights.
 Sun Kim posted on Friday, April 13, 2012 - 8:27 am
Dear Dr. Muthen,

I did that, but I still had problems fitting the model.

Also, I am noticing that I am not getting any of the fit indices. Is this normal? Here is a simplified version of my command (just three latent variables that serve as mediators):

Categorical are sch1d sch23d sch45d sch6d sch7d sch8d hom2d ac1d ac2d;


cluster = coupleID;
weight is CH02PRWT;



Analysis:
Type= complex ;
estimator= MLR;


Model:
schoolF by sch1d sch23d sch45d sch6d sch7d sch8d ;

homeF by hom1d hom2d hom3d hom4d;

acF by ac2d ac1d;

Thank you!

Regards,
Sun
 Linda K. Muthen posted on Friday, April 13, 2012 - 8:32 am
You will not get chi-square and related fit statistics with maximum likelihood and categorical outcomes. This is because means, variances, and covariances are not sufficient statistics for model estimation.
 Sun Kim posted on Friday, April 13, 2012 - 8:43 am
Dear Dr. Muthen,

Thank you so much for your quick response.
In such case, can I just report those I got with the WLSMV estimator? Since I really need to use maximum likelihood estimator because I want to test for interactions, I am thinking of reporting the WLSMV estimator fit statistics at each step in my paper, then in the final test of interaction, use MLR.
How would I justify this, and do you think this is acceptable?

I saw in a previous post "You can also use MLR and create your own unrestricted covariance matrix model in Mplus to test against, that is do a second run, and then compute chi-square as 2 times the log likelihood difference."
However, this still does not give the CFI, RMSEA and TLI values I would like.
Thank you!

Regards,
Sun
 Sun Kim posted on Friday, April 13, 2012 - 8:46 am
By the way, I forgot to add that in my mediation model, my final outcomes are not categorical-- they are continuous, but my mediators and predictors have some categorical indicators.

Also, the model I posted is just a 3-factor CFA (no outcomes or predictors).
 Linda K. Muthen posted on Friday, April 13, 2012 - 9:31 am
You cannot use WLSMV fit indices with ML results. If you must have these fit indices, you must use WLSMV for fit and results.
 Sun Kim posted on Friday, April 13, 2012 - 10:02 am
Dear Dr. Muthen,

So I understand from your responses that at this stage, using Mplus version 6, it is impossible for me to be estimating interactions in my case (categorical indicators with weights and type= complex model) and get fit indices at the same time.

Thank you!

Regards,
Sun
 Linda K. Muthen posted on Saturday, April 14, 2012 - 9:12 am
It is the case that when means, variances, and covariances are not sufficient statistics for model estimation, chi-square and related statistics cannot be computed because they have not been developed for other situations.
 Sun Kim posted on Saturday, April 14, 2012 - 12:02 pm
Dear Dr. Muthen,

Oh, I see.
Thank you very much for your kind responses, always very helpful.

Regards,
Sun
 Sarah Dermody posted on Tuesday, December 02, 2014 - 12:34 pm
Hello, I am using Mplus Version 7. I have been unable to estimate a model with an interaction between a latent variable (with categorical indicators) and dummy variable using estimator = WLSMV. Based on the thread above, I am not sure if estimating this interaction is possible or if need to use a different estimator.

Thank you for your help.
 Linda K. Muthen posted on Tuesday, December 02, 2014 - 1:26 pm
The XWITH option for latent variable interactions is not available with WLSMV. You can use MLR for this. See Example 5.13.
 Sarah Dermody posted on Thursday, December 04, 2014 - 12:10 pm
Thank you for your help. I hope you could clarify if by taking this approach I would be treating the categorical indicators as continuous? Presently, all my latent factor indicators are ordinal (4 reponse options), but this example is with continuous indicators.
 Bengt O. Muthen posted on Thursday, December 04, 2014 - 3:15 pm
No, using XWITH involving a factor does not imply any statement about the indicators of that factor.

Note also that an interaction between a latent variable and an observed dummy variable could be analyzed as a multipe-group model.
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