Mplus has 3 different estimators for categorical dependent variables: least squares, maximum likelihood, and Bayes. Some of these have different options that affect the scale of the parameter estimates. There are three versions of parameterizations/links that produce parameter estimates on the same scale. They are:
ESTIMATOR=WLSMV; PARAMETERIZATION=THETA;)ESTIMATOR=MLR; LINK=PROBIT; )ESTIMATOR=BAYES;)Unless there are compelling reasons, it is a good idea to default to one of these three estimator options, as it makes it easy to move among them. We commonly will use WLSMV/theta or MLR/probit for parameter estimation and then switch to Bayes for factor score estimation. MLR/probit has the advantage of invoking the missing-at-random assumption in the presence of missing data, whereas WLSMV/theta invokes the more restrictive MCAR. So, if there are missing data, MLR/probit is a good choice. The advantage of WLSMV/theta is that limited information fit statistics (model Chi-square, CFI, RMSEA, SRMR) are defined and produced. The advantage of Bayes is increased speed in high dimensional situations and the ability to generate plausible values as factor score estimates.
See this note from Rich and this note from Doug for an explication of the parameterizations and relationship to the typical 2PL IRT metric.
Least squares always uses the probit link function but has two different parameterizations, referred to as “theta” and “delta”. These labels refer to parameterizations of the scale and variance of the residual for the latent response variables (continuous unobserved variables assumed to underly observed and categorical response variables). Maximum likelihood does not make use of latent response variable formulation and is therefore indifferent to theta and delta. However, the ML procedure can use either the the probit or logit link function. Similarly Bayes does not care about theta/delta, but unlike ML does not allow for specification of a link function. Bayes uses the probit link.
Rich Jones (rnjones@brown.edu)
8 May 2021