Modeling Heterogeneity of Latent Growth Depending on Initial Status

In this article, a heterogeneous latent growth curve model for modeling heterogeneity of growth rates is proposed. The suggested model is an extension of a conventional growth curve model and a complementary tool to mixed growth modeling. It allows the modeling of heterogeneity of growth rates as a continuous function of latent initial status and time-invariant covariates. A quasi-ML parameter estimation method and a likelihood-ratio test for heterogeneity of growth is developed, and the new methodology is applied to an empirical example on math achievement data. The example illustrates that the proposed model gives more accurate confidence intervals for the prediction of future math achievement than a conventional growth curve model and identifies the subgroup of subjects which show the most homogeneous growth.