Mplus Users Guide v6.. - Muthén & Muthén

Examples: Multilevel Modeling With Complex Survey DataIn this example, the two-level growth model for a continuous outcome(three-level analysis) shown in the picture above is estimated. In thewithin part of the model, the filled circles at the end of the arrows fromthe within growth factors iw and sw to y1, y2, y3, and y4 representrandom intercepts that are referred to as y1, y2, y3, and y4 in thebetween part of the model. In the between part of the model, the randomintercepts are shown in circles because they are continuous latentvariables that vary across clusters.In the within part of the model, the | statement names and defines thewithin intercept and slope factors for the growth model. The names iwand sw on the left-hand side of the | symbol are the names of theintercept and slope growth factors, respectively. The values on the righthandside of the | symbol are the time scores for the slope growth factor.The time scores of the slope growth factor are fixed at 0, 1, 2, and 3 todefine a linear growth model with equidistant time points. The zero timescore for the slope growth factor at time point one defines the interceptgrowth factor as an initial status factor. The coefficients of the interceptgrowth factor are fixed at one as part of the growth modelparameterization. The residual variances of the outcome variables areconstrained to be equal over time in line with conventional multilevelgrowth modeling. This is done by placing (1) after them. The residualcovariances of the outcome variables are fixed at zero as the default.Both of these restrictions can be overridden. The ON statementdescribes the linear regressions of the growth factors on the individuallevelcovariate x. The residual variances of the growth factors are freeto be estimated as the default. The residuals of the growth factors arecorrelated as the default because residuals are correlated for latentvariables that do not influence any other variable in the model excepttheir own indicators.In the between part of the model, the | statement names and defines thebetween intercept and slope factors for the growth model. The names iband sb on the left-hand side of the | symbol are the names of the interceptand slope growth factors, respectively. The values on the right-hand sideof the | symbol are the time scores for the slope growth factor. The timescores of the slope growth factor are fixed at 0, 1, 2, and 3 to define alinear growth model with equidistant time points. The zero time scorefor the slope growth factor at time point one defines the intercept factoras an initial status factor. The coefficients of the intercept growth factorare fixed at one as part of the growth model parameterization. The271