Structural Equation Modeling: Applications Using Mplus

5.3 Multi-Group LGM

In applications of LGMs discussed in Chapter 4 it is assumed that individuals are randomly sampled from a single target population. In many cases, however, researchers encounter the fact that individuals can be identified as belonging to different populations (e.g., rural drug users in Ohio vs. Kentucky in our example) or groups (e.g., intervention vs. control groups) in their studies. To study differences in outcome growth trajectory over time between different known populations/groups, the LGM can be extended to multi-group LGM where the same LGM will be implemented simultaneously for each of the populations/groups. The estimated latent growth factors (i.e., latent growth intercept and slope factors) that determine the outcome growth trajectory may vary by population/group. Invariance of the growth trajectory across populations/groups can be tested in multi-group LGM.

The data (data file 2_Site_Longitudinal.dat) used for demonstration of multi-group LGMs are also selected from the samples of the rural drug user studies in Ohio and Kentucky (Wang et al., 2007). The data set 2_Site_Longitudinal.dat were collected from four interviews (baseline, 6-month, 12-month, and 18-month after baseline) in the two studies. The outcome measures (i.e., y₁ − y₄) are crack-cocaine use frequency in the past 6 months prior to each interview, which was measured on a seven-point scale from 0 (no use), 1 (less than 4 times per month), 2 (about once a week), 3 (about 2–6 times a ...