Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 7u11 u12 u13u21 u22 u23c1c2fIn this example, the second-order factor model shown in the pictureabove is estimated. The first-order factors are categorical latentvariables and the second-order factor is a continuous latent variable.This is a model that can be used for studies of twin associations wherethe categorical latent variable c1 refers to twin 1 and the categoricallatent variable c2 refers to twin 2.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, one dimension ofintegration is used with 15 integration points. The ESTIMATOR optioncan be used to select a different estimator. When a model has more thanone categorical latent variable, MODEL followed by a label is used todescribe the analysis model for each categorical latent variable. Labelsare defined by using the names of the categorical latent variables.In the overall model, the BY statement names the second order factor f.The ON statement specifies that f influences both categorical latentvariables in the same amount by imposing an equality constraint on thetwo multinomial logistic regression coefficients. The slope in themultinomial regression of c on f reflects the strength of association172