Random coefficient and latent growth curve modeling are currently the dominant approaches to the analysis of longitudinal data in psychology. The application of these models to longitudinal data assumes that the data-generating mechanism behind the psychological process under investigation contains only a deterministic trend. However, if a process, at least partially, contains a stochastic trend, then random coefficient regression results are likely to be spurious. This problem is demonstrated via a data example, previous research on simple regression models, and Monte Carlo simulations. A data analytic strategy is proposed to help researchers avoid making inaccurate inferences when observed trends may be due to stochastic processes. (Contains 4 figures, 2 footnotes and 4 tables.)