The broad goal of this project is improve services research and intervention, particularly for people who are homeless and mentally ill, through the use of latent group-trajectory analytic approaches. As an R34 Exploratory Development project, the study has two specific purposes. One is to examine the utility of latent group-trajectory analysis for improving services research for people who are homeless and mentally ill. The other is to compare two techniques for such analyses to understand how each may be best used in the context of services research.