Mplus Users Guide v6.. - Muthén & Muthén

CHAPTER 10In this example, the two-level latent transition analysis (LTA) with acovariate shown in the picture above is estimated. This example issimilar to Example 8.13 except that the categorical latent variables areallowed to have random intercepts that vary on the between level. Thismodel is described in Asparouhov and Muthén (2008a). In the withinpart of the model, the random intercepts are shown in the picture asfilled circles at the end of the arrows pointing to c1 and c2. They arereferred to as c1#1 and c2#1 on the between level. The randomintercepts c1#1 and c2#1 are shown in circles in the between part of themodel because they are continuous latent variables that vary acrossclusters (between-level units).In the overall part of the between part of the model, the first ONstatement describes the linear regression of the random intercept c1#1 ona cluster-level covariate w. The second ON statement describes thelinear regression of the random intercept c2#1 on the random interceptc1#1 and the cluster-level covariate w. The residual variances of therandom intercepts c1#1 and c2#1 are estimated instead of being fixed atthe default value of zero.The default estimator for this type of analysis is maximum likelihoodwith robust standard errors using a numerical integration algorithm.Note that numerical integration becomes increasingly morecomputationally demanding as the number of factors and the sample sizeincrease. In this example, two dimensions of integration are used with atotal of 225 integration points. The ESTIMATOR option of theANALYSIS command can be used to select a different estimator. Anexplanation of the other commands can be found in Examples 8.13, 10.1,and 10.2.332