A Heterogeneous Growth Curve Model for Nonnormal Data.

The heterogeneous growth curve model (HGM; Klein & Muthén, 2006 ) is a method for modeling heterogeneity of growth rates with a heteroscedastic residual structure for the slope factor. It has been developed as an extension of a conventional growth curve model and a complementary tool to growth curve mixture models. In this article, a robust version of the heterogeneous growth curve model (HGM-R) is presented that extends the original HGM with a mixture model to allow for an unbiased parameter estimation under the condition of nonnormal data. In two simulation studies, the performance of the method is examined under the condition of nonnormality and a misspecified heteroscedastic residual structure. The results of the simulation studies suggest an unbiased estimation of the heterogeneity by the HGM-R when sample size was large enough and a good approximation of the heteroscedastic residual structure even when the functional form of the heteroscedasticity was misspecified. The practical application of the approach is demonstrated for a data set from HIV-infected patients.