Mplus Users Guide v6.. - Muthén & Muthén

Examples: Mixture Modeling With Cross-Sectional DataEXAMPLE 7.26: CFA WITH A NON-PARAMETRICREPRESENTATION OF A NON-NORMAL FACTORDISTRIBUTIONTITLE: this is an example of CFA with a nonparametricrepresentation of a non-normalfactor distributionDATA: FILE IS ex7.26.dat;VARIABLE: NAMES ARE y1-y5 c;USEV = y1-y5;CLASSES = c (3);ANALYSIS: TYPE = MIXTURE;MODEL: %OVERALL%f BY y1-y5;f@0;OUTPUT: TECH1 TECH8;In this example, a CFA model with a non-parametric representation of anon-normal factor distribution is estimated. One difference between thisexample and Example 7.17 is that the factor variance is fixed at zero ineach class. This is done to capture a non-parametric representation ofthe factor distribution (Aitkin, 1999) where the latent classes are used torepresent non-normality not unobserved heterogeneity with substantivelymeaningful latent classes. This is also referred to as semiparametricmodeling. The factor distribution is represented by a histogram with asmany bars as there are classes. The bars represent scale steps on thecontinuous latent variable. The spacing of the scale steps is obtained bythe factor means in the different classes with a factor mean for one classfixed at zero for identification, and the percentage of individuals at thedifferent scale steps is obtained by the latent class percentages. Thismeans that continuous factor scores are obtained for the individualswhile not assuming normality for the factor but estimating itsdistribution. Factor variances can also be estimated to obtain a moregeneral mixture although this reverts to the parametric assumption ofnormality, in this case, within each class. When the latent classes areused to represent non-normality, the mixed parameter values are ofgreater interest than the parameters for each mixture component(Muthén, 2002, p. 102; Muthén, 2004). An explanation of the othercommands can be found in Example 7.1.185