For some time now Collins and colleagues have been studying prevention by developing and applying a new statistical procedure for estimating and testing stage-sequential models of substance use onset and related prevention constructs. This approach, called Latent Transition Analysis (LTA), can be used to estimate the proportion of individuals who start out in a particular stage at the first wave of measurement in a longitudinal study, the probability of transitions between stages over time, and the measurement quality of all manifest variables. These quantities can be compared across groups, as for example to compare the rate of stage transitions between a group that received a prevention program and a control group. In the proposed study we will develop several important new features in LTA that will make it even more useful to prevention researchers. First, there is currently no adequate model selection procedure for LTA. We will implement a new approach to goodness-of-fit testing in latent class and LTA models, based on a Bayesian procedure known as the posterior predictive check distribution. This new procedure will provide LTA users with much more informative goodness-of-fit testing and model selection. Second, the LTA user currently has little information upon which to base a power analysis. We will develop and implement a procedure to assess statistical power for LTA analyses. Third, we will develop a version of LTA for small sample sizes, so that the LTA framework can be used by prevention scientists who do not have the large samples available that are typically recommended. Fourth, we will develop a new class of LTA models that will provide an approach conceptually similar to growth curve modeling for stage-sequential processes. Fifth, throughout the study we will apply the new procedures we have developed to address important prevention questions in empirical data.
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