WLSMV with some continuous variables

[Lucas Sempe]

Dear Lavaan team,

Thanks for all your work! It is invaluable for many of us! My PhD will have to acknowledge this forum too!

I have a technical question of how lavaan deals with continuous data when WLSMV is used. 

I have an SEM were the vast majority of my variables are ordered. Therefore I've chosen a WLSMV estimator. One manifest variable is used in the structural part.

Following Yves presentation (https://personality-project.org/r/tutorials/summerschool.14/rosseel_sem_cat.pdf),  my question: am I correct to assume that stage 1 (estimation of thresholds) is omitted, that stage 2 estimates a polyserial/biserial correlation and finally stage 3 is estimated?

I've read few papers and many posts on why WLSMV is better for ordinal data rather than ML. But should I worry of the opposite (WLSMV not being proper to deal with a continuous variable)?

Thanks a lot, 

Lucas

[Terrence Jorgensen]

am I correct to assume that stage 1 (estimation of thresholds) is omitted

No, that step still occurs because some variables do have thresholds.  Stage 2 estimates a correlation matrix that contains polychorics among ordered variables as well as polyserials between the ordered and continuous variables (as well as the continuous variable's variance, not fixed to 1 like the ordered variables' variances).  If there are multiple continuous variables, their covariances are also estimated.

?lavCor

WLSMV is appropriate when even a single endogenous variable is ordered/binary.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Lucas Sempe]

Hello Terrence, thanks your answer. 

A follow-up question. How the continuous variables are treated under wlsmv?

Thanks, Lucas

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[Terrence Jorgensen]

How the continuous variables are treated under wlsmv?

I thought I answered that above.  They are treated as continuous.  It might help to be more specific.  WLSMV is not a thing, it is shorthand for 3 things:

estimator = "DWLS"
se = "robust.sem"
test = "scaled.shifted" # "mean.var.adjusted" also available, which is what "MV" stands for

You can request estimator = "wls" for models with only continuous variables, but that is the ADF estimator described by Browne (1984), not the 3-stage estimator for models with any ordered variables for which we must assume a latent underlying distribution:

1. estimate thresholds from 1-way contingency tables
2. estimate polychoric/serial correlations from thresholds and 2-way tables
3. fit SEM to polychoric/serial matrix

The robust "MV" correction is to account for the uncertainty of estimates in steps 1 and 2 when fitting the model in step 3.  That is not an issue for (full) WLS/ADF with continuous variables only.

[joh4nd]

Is it in such cases (WLSMV and, hence, a subset of DWLS estimates) that robust fit criteria are preferred?