Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 7u11 u12 u13 u14u21 u22 u23 u24f1f2In this example, the model shown in the picture above is estimated. Thefactors f1 and f2 represent a univariate variable for each member of thetwin pair. Monozygotic and dizygotic twins are considered in a twogrouptwin model for factors with categorical factor indicators usingparameter constraints and maximum likelihood estimation. Parameterconstraints are used to represent the ACE model restrictions. The ACEvariance and covariance restrictions are placed on two factors instead oftwo observed variables as in Example 7.28. The relationships betweenthe categorical factor indicators and the factors are logistic regressions.Therefore, the factor model for each twin is a two-parameter logisticItem Response Theory model (Muthén, Asparouhov, & Rebollo, 2006).The monozygotic and dizygotic twin groups are represented by latentclasses with known class membership.By specifying ALGORITHM=INTEGRATION, a maximum likelihoodestimator with robust standard errors using a numerical integrationalgorithm will be used. Note that numerical integration becomesincreasingly more computationally demanding as the number of factorsand the sample size increase. In this example, two dimensions ofintegration are used with 225 integration points. The ESTIMATORoption can be used to select a different estimator.In the overall model, the two BY statements specify that f1 is measuredby u11, u12, u13, and u14 and that f2 is measured by u21, u22, u23, andu24. The means of the factors are fixed at zero. In the class-specificmodels, the threshold of the dz variable is fixed at 15 in class one and -15 in class 2.192