Structural Equation Modeling: Applications Using Mplus

4.1 Linear LGM

A common practice in applications of LGMs is to assess features of outcome growth trajectory, such as the form of the latent growth trajectory (e.g., linear or nonlinear), the initial level of the outcome measure, the rate of outcome change, the association between the rate of change and the initial level of outcome, as well as the determinates of trajectory variations. A simple unconditional linear LGM is described in Figure 4.1, where y_0i − y_5i are observed outcomes measured at six different time points (e.g., t₀ − t₅); and are the latent intercept and slope growth factors, respectively; the former represents the initial level of outcome measure, and the latter represents the rate of outcome change over time. The latent intercept and slope growth factors capture the information of the overall growth trajectory, as well as individual trajectories. The observed outcome measures y_0i − y_5i are treated as the multiple indicators of these two latent growth factors.¹ The factor loadings on the intercept growth factor are all fixed to 1.0, and the factor loadings on the slope growth factor are called time scores. The time scores play three roles: (1) time scores determine ...