Mplus Users Guide v6.. - Muthén & Muthén

Examples: Multilevel Modeling With Complex Survey DataEXAMPLE 9.7: TWO-LEVEL CFA WITH CATEGORICALFACTOR INDICATORS AND COVARIATESTITLE: this is an example of a two-level CFA withcategorical factor indicators andcovariatesDATA: FILE IS ex9.7.dat;VARIABLE: NAMES ARE u1-u4 x1 x2 w clus;CATEGORICAL = u1-u4;WITHIN = x1 x2;BETWEEN = w;CLUSTER = clus;MISSING = ALL (999);ANALYSIS: TYPE = TWOLEVEL;MODEL:%WITHIN%fw BY u1-u4;fw ON x1 x2;%BETWEEN%fb BY u1-u4;fb ON w;OUTPUT: TECH1 TECH8;The difference between this example and Example 9.6 is that the factorindicators are binary or ordered categorical (ordinal) variables instead ofcontinuous variables. The CATEGORICAL option is used to specifywhich dependent variables are treated as binary or ordered categorical(ordinal) variables in the model and its estimation. In the exampleabove, all four factor indicators are binary or ordered categorical. Theprogram determines the number of categories for each indicator. Thedefault estimator for this type of analysis is maximum likelihood withrobust standard errors using a numerical integration algorithm. Note thatnumerical integration becomes increasingly more computationallydemanding as the number of factors and the sample size increase. In thisexample, two dimensions of integration are used with a total of 225integration points. The ESTIMATOR option of the ANALYSIScommand can be used to select a different estimator.In the between part of the model, the residual variances of the randomintercepts of the categorical factor indicators are fixed at zero as thedefault because the residual variances of random intercepts are oftenvery small and require one dimension of numerical integration each.Weighted least squares estimation of between-level residual variances255