Mplus Users Guide v6.. - Muthén & Muthén

ANALYSIS Commandleast one observed dependent variable is categorical, and weighted leastsquares estimation is used in the analysis. The second purpose is tochange from the default logit regression parameterization to thealternative loglinear parameterization when TYPE=MIXTURE and morethan one categorical latent variable is used in the analysis.DELTA VERSUS THETA PARAMETERIZATIONThere are two model parameterizations available whenTYPE=GENERAL is used, one or more dependent variables arecategorical, and weighted least squares estimation is used in the analysis.The first parameterization is referred to as DELTA. This is the defaultparameterization. In the DELTA parameterization, scale factors forcontinuous latent response variables of observed categorical outcomevariables are allowed to be parameters in the model, but residualvariances for continuous latent response variables are not. The secondparameterization is referred to as THETA. In the THETAparameterization, residual variances for continuous latent responsevariables of observed categorical outcome variables are allowed to beparameters in the model, but scale factors for continuous latent responsevariables are not.The DELTA parameterization is the default because it has been found toperform better in many situations (Muthén & Asparouhov, 2002). TheTHETA parameterization is preferred when hypotheses involvingresidual variances are of interest. Such hypotheses may arise withmultiple group analysis and analysis of longitudinal data. In addition,there are certain models that can be estimated using only the THETAparameterization because they have been found to impose improperparameter constraints with the DELTA parameterization. These aremodels where a categorical dependent variable is both influenced by andinfluences either another observed dependent variable or a latentvariable.To select the THETA parameterization, specify the following:PARAMETERIZATION = THETA;535