Including Time-Invariant Covariates in the Latent Growth Curve Model

Within the latent growth curve model, time-invariant covariates are generally modeled on the subject level, thereby estimating the effect of the covariate on the latent growth parameters. Incorporating the time-invariant covariate in this manner may have some advantages regarding the interpretation of the effect but may also be incorrect in certain instances. In this article we discuss a more general approach for modeling time-invariant covariates in latent growth curve models in which the covariate is directly regressed on the observed indicators. The approach can be used on its own to get estimates of the growth curves corrected for the influence of a 3rd variable, or it can be used to test the appropriateness of the standard way of modeling the time-invariant covariates. It thus provides a test of the assumption of full mediation, which states that the relation between the covariate and the observed indicators is fully mediated by the latent growth parameters.