Ordinal data
Message/Author
 Eric Teman posted on Friday, June 17, 2011 - 4:20 pm
Is there an article or other reference that explains how Mplus imputes ordinal data?
 Tihomir Asparouhov posted on Friday, June 17, 2011 - 4:42 pm
Mplus use multivariate probit model by default but there are other options. See http://statmodel.com/download/Imputations7.pdf
 Eric Teman posted on Friday, June 17, 2011 - 8:46 pm
Thanks Tihomir. I read the pdf and have a question. On page 13, it reads, "Note here that the ML estimation method can also
be used for the estimation of this data directly. However the ML estimation
method would heavily rely on the fact that the data is generated from a
one factor analysis model. In general the true model could have many more
factors and residual correlations. So in that respect the ML method would
not be an appropriate substitute for the imputation methods, because the
ML estimation method will be computationally very intensive and does not
support residual correlations."

I am unclear as to why ML is inappropriate. Is it only inappropriate with the H0 model or with all the models?
 Bengt O. Muthen posted on Saturday, June 18, 2011 - 12:38 pm
The argument is made that H1 imputation is safer than H0 imputation because it does not rely on the H0 model being correct. Also, Table 6 shows that the "H1-Cov Imputed WLSMV" column gives almost as good results as the two H0 columns. ML would have to use an H0 model because with categorical outcomes it cannot do an H1 model due to too many dimensions of integration.

If the H0 model is correct and can be estimated by ML, ML H0 imputations will be excellent.
 Eric Teman posted on Saturday, June 18, 2011 - 4:39 pm
Oh, OK. So this has nothing to do with using full information maximum likelihood in place of MI?
 Bengt O. Muthen posted on Sunday, June 19, 2011 - 12:11 pm
No, it does have to do with that. FIML = ML and ML is a possible alternative to MI, but not necessarily a practical one for the reasons I gave.
 Eric Teman posted on Monday, June 27, 2011 - 6:10 pm
I read http://statmodel.com/download/Imputations7.pdf and do not see where it discusses the multivariate probit model used to impute missing ordinal data. Is there another reference?
 Eric Teman posted on Monday, June 27, 2011 - 6:28 pm
Also, is the multivariate probit model a new approach to imputing ordinal data or is it discussed in the literature?
 Tihomir Asparouhov posted on Monday, June 27, 2011 - 9:25 pm
Equations (1) and (2) and the first 15 rows in Section 2.1 define the multivariate probit model.

This is a new approach unique to Mplus and it is based on a breakthrough for estimating large correlation matrices via MCMC.
 Eric Teman posted on Monday, June 27, 2011 - 11:51 pm
That is great news. Is the technical document the only reference you have to this new approach?
 Tihomir Asparouhov posted on Tuesday, June 28, 2011 - 9:21 am
The above reference describes the unrestricted model Mplus uses for imputation. The actual estimation is described in