Mplus Users Guide v6.. - Muthén & Muthén

Examples: Multilevel Modeling With Complex Survey DataThe decomposition can be expressed as,x wij = x ij - x bj ,which can be viewed as an implicit, latent group-mean centering of thelatent within-level covariate. To obtain results that are not group-meancentered, a linear transformation of the within and between slopes can bedone as described below using the MODEL CONSTRAINT command.In the MODEL command, the label gamma10 in the within part of themodel and the label gamma01 in the between part of the model areassigned to the regression coefficients in the linear regression of y on xin both parts of the model for use in the MODEL CONSTRAINTcommand. The MODEL CONSTRAINT command is used to definelinear and non-linear constraints on the parameters in the model. In theMODEL CONSTRAINT command, the NEW option is used tointroduce a new parameter that is not part of the MODEL command.This parameter is called betac and is defined as the difference betweengamma01 and gamma10. It corresponds to a “contextual effect” asdescribed in Raudenbush and Bryk (2002, p. 140, Table 5.11).EXAMPLE 9.2: TWO-LEVEL REGRESSION ANALYSIS FOR ACONTINUOUS DEPENDENT VARIABLE WITH A RANDOMSLOPETITLE: this is an example of a two-levelregression analysis for a continuousdependent variable with a random slope andan observed covariateDATA: FILE = ex9.2a.dat;VARIABLE: NAMES = y x w xm clus;WITHIN = x;BETWEEN = w xm;CLUSTER = clus;CENTERING = GRANDMEAN (x);ANALYSIS: TYPE = TWOLEVEL RANDOM;MODEL:%WITHIN%s | y ON x;%BETWEEN%y s ON w xm;y WITH s;243