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Structural Equation Mixture Models(SEMMs) are latent class models that permit the estimation of a structural equation model within each class. Fitting SEMMs is illustrated using data from one wave of the Notre Dame Longitudinal Study of Aging. Based on the model used in the illustration, SEMM parameter estimation and correct class assignment are investigated in a large scale simulation study. Design factors of the simulation study are (im)balanced class proportions, (im)balanced factor variances, sample size, and class separation. We compare the fit of models with correct and misspecified within-class structural relations. In addition, we investigate the potential to fit SEMMs with binary indicators. The structure of within-class distributions can be recovered under a wide variety of conditions, indicating the general potential and flexibility of SEMMs to test complex within-class models. Correct class assignment is limited.
Tueller et al. (Tue,) studied this question.