Determining the Number of Latent Classes in Single- and Multi-Phase Growth Mixture Models.

Stage-sequential (or multiphase) growth mixture models are useful for delineating potentially different growth processes across multiple phases over time and for determining whether latent subgroups exist within a population. These models are increasingly important as social behavioral scientists are interested in better understanding change processes across distinctively different phases, such as before and after an intervention. One of the less understood issues related to the use of growth mixture models is how to decide on the optimal number of latent classes. The performance of several traditionally used information criteria for determining the number of classes is examined through a Monte Carlo simulation study in single- and multi-phase growth mixture models. For thorough examination, the simulation was carried out in two perspectives: the models and the factors. The simulation in terms of the models was carried out to see the overall performance of the information criteria within and across the models, while the simulation in terms of the factors was carried out to see the effect of each simulation factor on the performance of the information criteria holding the other factors constant. The findings not only support that sample size adjusted BIC (ADBIC) would be a good choice under more realistic conditions, such as low class separation, smaller sample size, and/or missing data, but also increase understanding of the performance of information criteria in single- and multi-phase growth mixture models.