Mplus Users Guide v6.. - Muthén & Muthén

Examples: Mixture Modeling With Cross-Sectional Datau1u2f1f2In this example, the model shown in the picture above is estimated. Thevariables u1 and u2 represent a univariate outcome for each member of atwin pair. Monozygotic and dizygotic twins are considered in a twogrouptwin model for categorical outcomes using maximum likelihoodestimation. Parameter constraints are used to represent the ACE modelrestrictions. The ACE variance and covariance restrictions are placed onnormally-distributed latent response variables, which are also calledliabilities, underlying the categorical outcomes. This model is referredto as the threshold model for liabilities (Neale & Cardon, 1992). Themonozygotic and dizygotic twin groups are represented by latent classeswith known class membership.The CATEGORICAL option is used to specify which dependentvariables are treated as binary or ordered categorical (ordinal) variablesin the model and its estimation. In the example above, the variables u1and u2 are binary or ordered categorical variables. The programdetermines the number of categories for each indicator. TheKNOWNCLASS option identifies cdz as the categorical latent variablefor which latent class membership is known. The information inparentheses following the categorical latent variable name defines theknown classes using an observed variable. In this example, the observedvariable dz is used to define the known classes. The first class consistsof the monozygotic twins who have the value 0 on the variable dz. Thesecond class consists of the dizygotic twins who have the value 1 on thevariable dz.By specifying ALGORITHM=INTEGRATION, a maximum likelihoodestimator with robust standard errors using a numerical integration189