Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 17short for measured by. ON is used to describe the regressionrelationships among the observed and latent variables in the model. It isshort for regressed on. WITH is used to describe correlational(covariance) relationships in the measurement and structural models. Itis short for correlated with.The model in the following figure is used to illustrate the use of the BY,ON, and WITH options. The squares represent observed variables andthe circles represent latent variables. Regression relationships arerepresented by arrows from independent variables to dependentvariables. The variables f1 and f2 are continuous latent variables. Theobserved dependent variables are y1, y2, y3, y4, y5, y6, y7, y8, and y9.The measurement part of the model consists of the two continuous latentvariables and their indicators. The continuous latent variable f1 ismeasured by y1, y2, y3, y4, and y5. The continuous latent variable f2 ismeasured by y6, y7, y8, and y9. The structural part of the modelconsists of the regression of the two continuous latent variables on nineobserved independent variables. The observed independent variables arex1, x2, x3, x4, x5, x6, x7, x8, and x9. Following is the MODELcommand for the figure below:MODEL:f1 BY y1-y5;f2 BY y6-y9;f1 f2 ON x1-x9;572