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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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6.3 Growth Mixture Model

In Chapter 4 we discussed LGM in which outcome growth trajectory over time is captured by continuous latent variables (i.e., latent intercept and slope growth factors). LGM assumes that all individuals in the sample are from a single homogeneous population, and individual growth trajectories vary randomly around the overall mean growth trajectory. Very often, the assumption of homogeneity in outcome growth trajectory is unrealistic. Ignoring possible growth heterogeneity and focusing on the overall mean growth trajectory can lead to misunderstanding and wrong conclusions about outcome growth. In this chapter we extend LGM to the GMM to assess whether the population under study is comprised of a mixture of identifiable subpopulations/groups based on their growth trajectories (Verbeke and Lesaffre, 1996; Muthén and Shedden, 1999; Muthén and Muthén, 2000; Muthén, 2001, 2002, 2004>, >, >). The GMM model has increasingly gained in popularity in longitudinal studies in different fields of social sciences and public health studies because of its capability of enabling the examination of possible heterogeneity of outcome growth trajectories; classifying individuals into distinctive growth trajectory groups; and relating the heterogeneous growth trajectories to distal outcomes.

Figure 6.5 is helpful to compare growth trajectories modeled in the LGM and the GMM. Figure 6.5a illustrates hypothetical growth trajectories in which each line represents an individual's ...

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