Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 17because BY statements are used to name the continuous latent variables.BY statements also provide a set of convenient defaults.Observed factor indicators for continuous latent variables can becontinuous, censored, binary, ordered categorical (ordinal), or counts.Factor indicators can also be continuous latent variables or the inflationpart of censored and count variables. Combinations of all factorindicator types are allowed. With TYPE=TWOLEVEL andTYPE=TWOLEVEL MIXTURE, factor indicators for continuous latentvariables can be between-level random effects. These factor indicatorscan appear only on the BETWEEN level.CONFIRMATORY FACTOR ANALYSIS MODELINGIn this section the use of the BY option for confirmatory factor analysis(CFA) models is described. Following are the two BY statements thatdescribe how the continuous latent variables in the figure above aremeasured:f1 BY y1- y5;f2 BY y6- y9;The factor loading of any observed variable mentioned on the right-handside of the BY statement is free to be estimated with the exception of thefactor loading of the first variable after the BY option. This factorloading is fixed at one as the default. Fixing a factor loading of anindicator of a continuous latent variable sets the metric of the continuouslatent variable. Setting the metric can also be accomplished by fixingthe variance of the continuous latent variable to one and freeing thefactor loading of the factor indicator that is fixed at one as the default.In the example above, the factor loadings of y1 and y6 are fixed at one.The other factor loadings are estimated using default starting values ofone.Following is an example of how to set the metric of the continuous latentvariable by fixing the variance of the continuous latent variable to oneand allowing all factor loadings to be free:f1 BY y1* y2- y5;f2 BY y6* y7- y9;f1@1 f2@1;574