In our first project period we focused on the systematic study of longitudinal latent curve models (LCMs) applied to continuous scale scores with a particular emphasis on challenges that commonly arise in the empirical study of substance use. Despite the many advantages of these LCMs, one limitation is that methods are currently not well developed to fit LCMs to repeated measures that are ordinally scaled, particularly in the presence of missing data. A second limitation stems from the potential violation of a strict set of required assumptions governing the structure of the measurement model of continuous or ordinally observed scale scores over time. To address these limitations, we have drawn upon our findings from the initial project period and have designed the revision of our proposed continuation project around the systematic study of measurement models in latent curve analysis. Our proposed project is organized around four specific aims. In Aim 1 we propose to study existing challenges and identify optimal strategies for fitting LCMs to ordinal manifest scale scores assessed overtime both with complete and missing data. In Aim 2 we plan to study the incorporation of latent factors with continuously scaled indicators in LCMs to allow for tests of measurement invariance and the inclusion of formal measurement models. In Aim 3 we propose extending the findings of Aim 2 to include the incorporation of latent factors with ordinally scaled indicators in LCMs. Finally, in Aim 4 we plan to study the implications of item scaling and measurement invariance across all prior aims with respect to the estimation of statistical power and optimal study design. These project goals will be pursued through the integrated use of analytical review and organization, computer simulation studies, and the analysis of data drawn from an existing longitudinal study of the parental alcoholism effects on the development of drug use in a large sample of adolescent. Taken together, we believe the proposed study has the potential for making significant unique contributions to the field of quantitative methodology and to the rigorous empirical study of developmental trajectories of substance use and abuse.