Mplus Users Guide v6.. - Muthén & Muthén

Examples: Multilevel Modeling With Complex Survey Datapart of the model. In the between part of the model, the randomintercepts and random slope are shown in circles because they arecontinuous latent variables that vary across clusters.By specifying TYPE=TWOLEVEL RANDOM in the ANALYSIScommand, a multilevel model with random intercepts and random slopeswill be estimated. By specifying ALGORITHM=INTEGRATION, amaximum likelihood estimator with robust standard errors using anumerical integration algorithm will be used. Note that numericalintegration becomes increasingly more computationally demanding asthe number of factors and the sample size increase. In this example, fourdimensions of integration are used with a total of 10,000 integrationpoints. The INTEGRATION option of the ANALYSIS command isused to change the number of integration points per dimension from thedefault of 15 to 10. The ESTIMATOR option of the ANALYSIScommand can be used to select a different estimator.In the within part of the model, the BY statement specifies that fw ismeasured by the factor indicators y1, y2, y3, and y4. The metric of thefactor is set automatically by the program by fixing the first factorloading in each BY statement to one. This option can be overridden.The residual variances of the factor indicators are estimated and theresiduals are uncorrelated as the default. The variance of the factor isestimated as the default.In the within part of the model, the | symbol is used in conjunction withTYPE=RANDOM to name and define the random slope variables in themodel. The name on the left-hand side of the | symbol names therandom slope variable. The statement on the right-hand side of the |symbol defines the random slope variable. Random slopes are definedusing the ON option. In the | statement, the random slope s is defined bythe linear regression of the dependent variable y5 on the within factorfw. The within-level residual variance of y5 is estimated as the default.In the between part of the model, the BY statement specifies that fb ismeasured by the random intercepts y1, y2, y3, and y4. The metric of thefactor is set automatically by the program by fixing the first factorloading in the BY statement to one. This option can be overridden. Theresidual variances of the factor indicators are fixed at zero. The varianceof the factor is estimated as the default. The ON statement describes thelinear regressions of the random intercept y5 and the random slope s on265