Mplus Users Guide v6.. - Muthén & Muthén

Examples: Confirmatory Factor Analysis AndStructural Equation Modelingy7 y8 y9 y10 y11 y12y1y2f1y3y4f3f4y5y6f2In this example, the SEM model with four continuous latent variablesshown in the picture above is estimated. The factor indicators arecontinuous variables.The first BY statement specifies that f1 is measured by y1, y2 and y3.The second BY statement specifies that f2 is measured by y4, y5, and y6.The third BY statement specifies that f3 is measured by y7, y8, and y9.The fourth BY statement specifies that f4 is measured by y10, y11, andy12. The metric of the factors is set automatically by the program byfixing the first factor loading in each BY statement to 1. This option canbe overridden. The intercepts and residual variances of the factorindicators are estimated and the residuals are not correlated as thedefault. The variances of the factors are estimated as the default. Thecovariance between f1 and f2 is estimated as the default because f1 andf2 are independent (exogenous) variables. The other factor covariancesare not estimated as the default.The first ON statement describes the linear regression of f4 on f3. Thesecond ON statement describes the linear regression of f3 on f1 and f2.The default estimator for this type of analysis is maximum likelihood.The ESTIMATOR option of the ANALYSIS command can be used toselect a different estimator. An explanation of the other commands canbe found in Example 5.1.69