Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 6y33. The metric of the three factors is set automatically by the programby fixing the first factor loading in each BY statement to one. Thisoption can be overridden. The residual variances of the factor indicatorsare estimated and the residuals are not correlated as the default.A multiple indicator growth model requires measurement invariance ofthe three factors across time. Measurement invariance is specified byholding the intercepts and factor loadings of the factor indicators equalover time. The (1-2) following the factor loadings in the three BYstatements uses the list function to assign equality labels to theseparameters. The label 1 is assigned to the factor loadings of y21, y22,and y23 which holds these factor loadings equal across time. The label 2is assigned to the factor loadings of y31, y32, and y33 which holds thesefactor loadings equal across time. The factor loadings of y11, y21, andy31 are fixed at one as described above. The bracket statements refer tothe intercepts. The (3) holds the intercepts of y11, y12, and y13 equal.The (4) holds the intercepts of y21, y22, and y23 equal. The (5) holdsthe intercepts of y31, y32, and y33 equal.The | statement is used to name and define the intercept and slope factorsin the growth model. The names i and s on the left-hand side of the | arethe names of the intercept and slope growth factors, respectively. Thevalues on the right-hand side of the | are the time scores for the slopegrowth factor. The time scores of the slope growth factor are fixed at 0,1, and 2 to define a linear growth model with equidistant time points.The zero time score for the slope growth factor at time point one definesthe intercept growth factor as an initial status factor. The coefficients ofthe intercept growth factor are fixed at one as part of the growth modelparameterization. The residual variances of the factors f1, f2, and f3 areestimated and allowed to be different across time, and the residuals arenot correlated as the default.In the parameterization of the growth model shown here, the interceptsof the factors f1, f2, and f3 are fixed at zero as the default. The mean ofthe intercept growth factor is fixed at zero and the mean of the slopegrowth factor is estimated as the default. The variances of the growthfactors are estimated as the default, and the growth factors are correlatedas the default because they are independent (exogenous) variables. Thedefault estimator for this type of analysis is maximum likelihood. TheESTIMATOR option of the ANALYSIS command can be used to select122