WLSMV or DWLS? Lavaan and SEM with categorical variables

[VashiRuki]

Dear LAVAAN Users! MPlus offers WLSMV estimator for SEM with categorical variables. LISREL offers DWLS estimator. B. Muthen says both DWLS and WLSMV estimators have similar philosophies, but use different asymptotic approximations in estimating the asymptotic covariance matrix of the estimated sample statistics used to fit the model. Do you offer DWLS (LISREL approach) or WLSMV (MPlus estimator) estimators in the software? Is there any other estimation technique for SEM with categorical models? I am preparing a very interesting analysis on causes of homelessness. I have some missing data. Could you tell me, if there is any other estimator than WLSMV (DWLS) to estimate structural equation model with categorical variables? I would like to compare results of two estimators. Regards. Christopher

[Terrence Jorgensen]

Do you offer DWLS (LISREL approach) or WLSMV (MPlus estimator) estimators in the software?

WLSMV is just a keyword in the Mplus language that simultaneously requests the DWLS estimator and a mean- and variance-adjusted (MV) chi-squared test statistic.  This can be confusing and misleads many users to conflate an estimator/discrepancy function (DWLS) with an ad hoc robust correction to SEs and test statistics, which are only implemented after estimation is already complete.  lavaan implements the same as Mplus describes in its technical literature (available on their website), which can be requested using the arguments:

lavaan(..., estimator = "DWLS", se = "robust.sem", test = "scaled.shifted")

or, like Mplus, you can use their familiar single keyword to request all 3 at once:

lavaan(..., estimator = "WLSMV")

You can find details about lavaan options on the help page:

?lavOptions

Is there any other estimation technique for SEM with categorical models? 

lavaan also has an experimental marginal maximum likelihood estimator (estimator = "MML"), which is currently the standard estimator for IRT models (some of which are equivalent to reparameterized CFA models).  Expect it to run more slowly because it requires numerical integration, and I think it is more likely to have convergence problems holding sample size constant.  You can also try the ADF estimator (estimator = "WLS"), which does not make any specific distributional assumptions about the data, but it does require very large samples (N > 5000) before you can trust the test statistics and SEs to be unbiased.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

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

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Mauricio Garnier-Villarreal]

Another detail related to your question, you mentioned that you have missing data. Missing data with these estimators cannot do Full Information Maximum Likelihood (FIML), because this is a function of a Maximum Likelihood estimator. FIML is the "automatic" way to handle missing data.

With categorical data you either will be doing listwise deletion (to use complete data) or Multiple Imputation. For Multiple Imputation you can use the semTools functions runMi (cfa.mi, etc), these function do the analysis for all the imputed data sets and return the results combine according to Rubin's rules