When modeling with variables identified as categorical, I understand that the choice of scaling of the latent item response variances (to 1.0) or the item residual variances (to 1.0) is somewhat arbitrary.
With WLSMV estimation, it appears that the delta parameterization is used as a default (latent item response variances are set to 1.0).
With ML estimation (with numerical integration), when requesting LINK=PROBIT, it appears that the theta parameterization is used (item residual variances are set to 1.0).
Is this correct? Is there any particular reason why this is the case? Thank you!
In maximum likelihood, scale factors are not used and residual variances are fixed to one for probit and pi squared divided by three for logit. The former is not the Theta parameterization because in multiple group or growth models, the residual variances cannot be estimated. They are fixed in all groups and at all timepoints.