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 Anonymous posted on Tuesday, April 03, 2001 - 7:39 am
I am currently testing a model that includes both latent variables that have categorical and continuous indicators and observed variables that are dichotomous. At least one of the variables I would like to treat as observed (rather than latent) is categorical and considered a dependent variable. For example…

categorical observed variable Y1 --> continuous latent variable Y2
continuous latent variable X1 --> continuous latent variable Y2
continuous latent variable X1 --> categorical observed variable Y1

To accomplish this I have indicated the categorical Y1 using the CATEGORICAL statement and used the GENERAL analysis type. I understand that the estimation procedure should be either WLSM or WLSMV. The model runs fine and gives me sensible results.

I have three questions; first does my approach seem sound (i.e., not treating the categorical Y as latent and using mixture modeling)? Second, which estimation procedure, WLSM or WLSMV, is the most appropriate? Can you think of a citation to justify the choice among these two?

Much thanks for the discussion generally and for this issue in particular.
 Linda K. Muthen posted on Tuesday, April 03, 2001 - 11:00 am
I think what you are asking is whether you need to put a latent variable behind a categorical outcome that is used as a dependent variable as you would need to do in some other programs. This is not necessary in Mplus. This is done automatically by the program when needed. I am not sure where mixture modeling comes in unless you mean a combination of latent and observed variables which is not a problem.

We recommend WLSMV for categorical outcomes. You can request the Muthen, DuToit, Spisic paper from bmuthen@ucla.edu. This discusses the two estimtors.

Please continue the discussion if this does not answer your question.
 Anonymous posted on Thursday, April 05, 2001 - 12:04 am
If you treat the categorical Y1 as latent, Mplus
Mixture will not allow:

continuous latent variable X1 --> categorical variable Y1
 Linda K. Muthen posted on Thursday, April 05, 2001 - 9:21 am
In the mixture part of the model, a continuous latent variable cannot influence a categorical latent or observed variable, that is, a latent class indicator.
 Annonymous  posted on Tuesday, February 21, 2006 - 2:51 pm
Hi there,

I have a question regarding probits and making them into Odds Ratios. I am specifying a SEM model where I have a categorical DV being predicted by a number of latent and manifest varaibles (estimator = wlmsv). In turn, I have other manifest variables predicting my ivs.

Here is example code:
catoutcome on x1 x2 x3;
x1 x2 x3 on z1 z2;
I believe I can take the unstandardized beta for x1 in predicting the categorical outome and turn this into an OR (i.e., e to the power of beta). However, I am not sure if I can do this since the default beta is not a logit, but rather a probit when using the WLSMV estimator. Can I use my obtained beta to turn it into an OR?

Thanks in advance!
 bmuthen posted on Tuesday, February 21, 2006 - 3:31 pm
With probit you cannot do the usual

OR = exp(beta)

You can, however, compute an OR by going back to the definition of an OR as the ratio between 2 probabilities for the dependent variable as a function of the predictor. You just compute the estimated probabilities from the probit regression.

Note that since Version 3, Mplus can do this type of path analysis using ML and logit.
 jenny yu posted on Monday, September 04, 2006 - 3:37 pm
Dear Drs. Muthen,

I am running on a MIMIC model with categorical indicators and categorical background variables in Mplus. I used WLS initially as estimator, and later was suggested using WLSMV. May I ask the following questions?

1) When WLSMV is preferred to WLS in a MIMIC model with categorical covariates and indicators?

2) I found I got worse model fit (indices were CFI and RMSEA) after I used WLSMV. I know I need to use DIFFTEST to get Chi-square test results if I use WLSMV. But in order to measure model fit, should I use CFI or RMSEA? Or should I use other indices?

Thank you very much for your time in advance.
 Bengt O. Muthen posted on Monday, September 04, 2006 - 4:06 pm
1) Simulation results suggest that WLSMV is better than WLS in all such cases.

2) CFI seems to work reasonably well according to the Yu dissertation on our web site.
 jenny yu posted on Wednesday, September 06, 2006 - 7:16 am
Dr. Muthen,

Thank you for your quick response.

Could you advise me why I got worse model fit when I change WLS to WLSMV with everything else unchanged?

Though theta is an alternative parameterizatoin, can I use Delta parameterization in my MIMIC model with categorical indicators and categorical background variables?

Thank you very much.
 Bengt O. Muthen posted on Thursday, September 07, 2006 - 8:49 am
WLSMV uses a different weight matrix and therefore gets different test statistics than WLS. The WLSMV results are more trustworthy according to the simulations.

Yes, the Delta parameterization works well - it is the default.
 jenny yu posted on Thursday, September 07, 2006 - 12:42 pm
Dr. Muthen, thank you very much for your answers.
 jenny yu posted on Friday, September 08, 2006 - 8:44 pm
Dr. Muthen,

You mention CFI works well when WLSMV is used as estimator. Then how about RMSEA? Is it still an appropriate index to measure model fit? Do you have some citation on this at hand besides Yu's dissertation?

Thank you very much.
 Linda K. Muthen posted on Saturday, September 09, 2006 - 7:34 am
Yu's dissertation is the only study I know that has looked at WLSMV and fit measures. It also looks at RMSEA.
 Michael Baum posted on Tuesday, January 20, 2009 - 12:22 pm
as i understand Yu's work looked into properties of fit indices for binary indicators, using WLSMV. Should we extent the derived results for this case to the case of ordinal indicators? or do the properties of fit indices in the case of ordinal indicators remain essentially unknown?
 Linda K. Muthen posted on Tuesday, January 20, 2009 - 4:03 pm
We don't know for sure because this has not been studied as far as I know. But given that Yu's cutoffs are very similar if not the same as Bentler's cutoffs for continuous variables, it seems they could be trusted.
 cy posted on Monday, March 30, 2009 - 9:17 pm
Hi,

Is there a reference for WLSMV is generally preferred to WLS?

Thanks
CY
 Linda K. Muthen posted on Tuesday, March 31, 2009 - 7:20 am
See the following paper which is available on our website:

Muthén, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Unpublished technical report.
 Anthony Rosellini posted on Thursday, November 10, 2011 - 8:53 am
Hello,
I am currently examining a measurement model the includes several continuous latent, continuous observed, and categorical observed (dichotomous and ordinal) variables. I have evaluated the model using both the WLSM and WLSMV estimators and although the majority of the results are identical (e.g., strength of factor loadings, majority of fit indices), the model has a much lower CFI using the WLSMV estimate(.83 vs .95). Is their an explanation for such a discrepancy and under what circumstances would one use the WLSM estimator? It appears that you always recommend WLSMV with categorical outcomes.
Thank you,
Anthony
 Bengt O. Muthen posted on Friday, November 11, 2011 - 11:14 am
Our simulation studies indicate that WLSMV gives better chi-square performance than WLSM. Typically, WLSM rejects a true model a bit too often. How that translates into CFI performance I don't know.
 burak aydin posted on Tuesday, November 19, 2013 - 2:26 pm
Hello,
when running a 2 level regression, I would like to use a level-1 predictor (X) in both levels. I am interested in the effect of latent mean. ML and MLR estimators work, however when I try WLSM and WLSMV estimators I have the following error;

*** ERROR in MODEL command
Unrestricted x-variables for analysis with TYPE=TWOLEVEL and ALGORITHM=INTEGRATION
must be specified as either a WITHIN or BETWEEN variable. The following variable cannot exist on both levels: X

Is this a limitation of WLSM?
 Linda K. Muthen posted on Wednesday, November 20, 2013 - 2:11 pm
This has not yet been developed for WLSM and WLSMV.
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