Mplus Users Guide v6.. - Muthén & Muthén

Examples: Multilevel Modeling With Complex Survey Datacovariate x. The within-level residual variance in the regression of y onx is estimated as the default.In the between part of the model, the ON statement describes the linearregressions of the random intercept y and the random slope s on theobserved cluster-level covariates w and xm. The intercepts and residualvariances of s and y are estimated as the default. The residuals arecorrelated as the default. The default estimator for this type of analysisis maximum 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.Following is the second part of the example that shows an alternativetreatment of the observed covariate x.TITLE: this is an example of a two-levelregression analysis for a continuousdependent variable with a random slope anda latent covariateDATA: FILE = ex9.2b.dat;VARIABLE: NAMES = y x w clus;BETWEEN = w;CLUSTER = clus;ANALYSIS: TYPE = TWOLEVEL RANDOM;MODEL:%WITHIN%s | y ON x;%BETWEEN%y s ON w x;y WITH s;The difference between this part of the example and the first part of theexample is that the covariate x is latent instead of observed on thebetween level. This is achieved when the individual-level observedcovariate is modeled in both the within and between parts of the model.This is requested by not mentioning the observed covariate x on theWITHIN statement in the VARIABLE command. When a random slopeis estimated, the observed covariate x is used on the within level and thelatent variable covariate x bj is used on the between level. TheESTIMATOR option of the ANALYSIS command can be used to selecta different estimator. An explanation of the other commands can befound in Example 9.1.245