The authors analyzed longitudinal data from a cognitive training experiment—Advanced Cognitive Training for Independent and Vital Elderly—using several alternative contemporary statistical models to test dynamic hypotheses based on latent change scores. The analyses focused on pretest and posttest data for only the group who received Reasoning training compared with the No-Contact (control) group. The initial structural equation modeling (SEM) path model isolated several training effects and an important source of transfer of training, Near→Far, but this transfer was not increased due to training. The subsequent models, which accounted for pretest differences and latent changes, implied that only the Near measurements were influenced by training, and the change transfer was small. Introduction of common factors for both Near and Far measurements showed the factor patterns were unaffected by training or time and suggested training was a broader effect than in any single variable. The bivariate analysis of common factors did not appear to alter the previous results. Addition of demographic covariates and latent mixture analysis of the trained group led to further results. The uses of contemporary SEMs with experimental data are discussed.