Using mixture models with known class membership to address incomplete covariance structures in multiple-group growth models.

Multi-group latent growth modelling in the structural equation modelling framework has been widely utilized for examining differences in growth trajectories across multiple manifest groups. Despite its usefulness, the traditional maximum likelihood estimation for multi-group latent growth modelling is not feasible when one of the groups has no response at any given data collection point, or when all participants within a group have the same response at one of the time points. In other words, multi-group latent growth modelling requires a complete covariance structure for each observed group. The primary purpose of the present study is to show how to circumvent these data problems by developing a simple but creative approach using an existing estimation procedure for growth mixture modelling. A Monte Carlo simulation study was carried out to see whether the modified estimation approach provided tangible results and to see how these results were comparable to the standard multi-group results. The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. We also present a real data example and demonstrate that the proposed estimation approach can be used for the chi-square difference test to check various types of measurement invariance as conducted in a standard multi-group analysis.