Mplus Users Guide v6.. - Muthén & Muthén

Examples: Multilevel Modeling With Complex Survey DataxyWithinwBetweenyxmIn this example, the two-level regression model shown in the pictureabove is estimated. The dependent variable y in this regression iscontinuous. Two ways of treating the covariate x are described. In thispart of the example, the covariate x is treated as an observed variable inline with conventional multilevel regression modeling. In the secondpart of the example, the covariate x is decomposed into two latentvariable parts.The within part of the model describes the regression of y on anobserved covariate x where the intercept is a random effect that variesacross the clusters. In the within part of the model, the filled circle at theend of the arrow from x to y represents a random intercept that isreferred to as y in the between part of the model. In the between part ofthe model, the random intercept is shown in a circle because it is acontinuous latent variable that varies across clusters. The between partof the model describes the linear regression of the random intercept y onobserved cluster-level covariates w and xm. The observed cluster-levelcovariate xm takes the value of the mean of x for each cluster. Thewithin and between parts of the model correspond to level 1 and level 2of a conventional multilevel regression model with a random intercept.239