Two-choice response times are a common type of data, and much research has been devoted to the development of process models for such data. However, the practical application of these models is notoriously complicated, and flexible methods are largely nonexistent. We combine a popular model for choice response times-the Wiener diffusion process-with techniques from psychometrics in order to construct a hierarchical diffusion model. Chief among these techniques is the application of random effects, with which we allow for unexplained variability among participants, items, or other experimental units. These techniques lead to a modeling framework that is highly flexible and easy to work with. Among the many novel models this statistical framework provides are a multilevel diffusion model, regression diffusion models, and a large family of explanatory diffusion models. We provide examples and the necessary computer code.Keywords: response time, psychometrics, hierarchical, random effects, diffusion model Supplemental materials: http://dx.doi.org/10.1037/a0021765.suppIn his 1957 presidential address at the 65th annual business meeting of the American Psychological Association, Lee Cronbach drew a captivating sketch of the state of psychology at the time. He focused on the two distinct disciplines that then existed in the field of scientific psychology. On the one side, there was the experimental discipline, which concerned itself with the systematic manipulation of conditions in order to observe the consequences. On the other side, there was the correlational discipline, which focused on the study of preexisting differences between individuals or groups. Cronbach saw many potential contributions of these disciplines to one another and argued that the time and opportunity had come for the two dissociated fields to crossbreed: "We are free at last to look up from our own bedazzling treasure, to cast properly covetous glances upon the scientific wealth of our neighbor discipline. Trading has already been resumed, with benefit to both parties" (Cronbach, 1957, p. 675). Two decades onward, Cronbach (1975) saw the hybrid discipline flourishing across several domains.In the area of measurement of psychological processes, there exists a schism similar to the one Cronbach pointed out in his presidential address. Psychological measurement and individual differences are studied in the domain of psychometrics, whereas cognitive processes are the stuff of the more nomothetic mathematical psychology. In both areas, statistical models are used extensively. There are common models based on the (general) linear model, such as analysis of variance (ANOVA) and regression, but we focus on more advanced, nonlinear techniques.Experimental psychology has, for a long time, made use of process models to describe interesting psychological phenomena in various fields. Some famous examples are Sternberg's (1966) sequential exhaustive search model for visual search and memory scanning, Atkinson and Shiffrin's (1968) multistore model for memory,...