Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 9and individuals with g equal to 2 are assigned the label g2. These labelsare used in conjunction with the MODEL command to specify modelstatements specific to each group. The grouping variable should be acluster-level variable.In multiple group analysis, two variations of the MODEL command areused. They are MODEL and MODEL followed by a label. MODELdescribes the model to be estimated for all groups. The factor loadingsand intercepts are held equal across groups as the default to specifymeasurement invariance. MODEL followed by a label describesdifferences between the overall model and the model for the groupdesignated by the label.In the within part of the model, the BY statements specify that fw1 ismeasured by y1, y2, and y3, and fw2 is measured by y4, y5, and y6. Themetric of the factors is set automatically by the program by fixing thefirst factor loading in each BY statement to one. This option can beoverridden. The variances of the factors are estimated as the default.The factors fw1 and fw2 are correlated as the default because they areindependent (exogenous) variables. In the between part of the model,the BY statements specify that fb1 is measured by y1, y2, and y3, andfb2 is measured by y4, y5, and y6. The metric of the factor is setautomatically by the program by fixing the first factor loading in eachBY statement to one. This option can be overridden. The variances ofthe factors are estimated as the default. The factors fb1 and fb2 arecorrelated as the default because they are independent (exogenous)variables.In the group-specific MODEL command for group 2, by specifying thewithin factor loadings for fw1 and fw2, the default equality constraintsare relaxed and the factor loadings are no longer held equal acrossgroups. The factor indicators that are fixed at one remain the same, inthis case y1 and y4. The default estimator for this type of analysis ismaximum likelihood with robust standard errors. The ESTIMATORoption of the ANALYSIS command can be used to select a differentestimator. An explanation of the other commands can be found inExample 9.1.268