The Standardization of Linear and Nonlinear Effects in Direct and Indirect Applications of Structural Equation Mixture Models for Normal and Nonnormal Data.

The application of mixture models to flexibly estimate linear and nonlinear effects in the SEM framework has received increasing attention (e.g., Bauer, 2005; Jedidi, Jagpal, & DeSarbo, 1997b; Kelava & Brandt, 2014; B. O. Muthen & Asparouhov, 2009, 2014; Wall, Guo, & Amemiya, 2012). The advantage of mixture models is that unobserved subgroups with class-specific relationships can be extracted (direct application), or that the mixtures can be used as a statistical tool to approximate nonnormal (latent) distributions (indirect application). Here, we provide a general standardization procedure for linear and nonlinear interaction and quadratic effects in mixture models. The procedure can also be applied to multiple group models or to single class models with nonlinear effects like LMS (Klein & Moosbrugger, 2000). We present an empirical example from education science applying the proposed procedure.