The present study proposes and examines the multidimensional vector (MDV) model framework as a modeling schema for choice response times. MDV extends the Thurstonian model, as well as signal detection theory, to classification tasks by taking into account the influence of response properties on stimulus discrimination. It is capable of accounting for stimulus-response compatibility, which is known to be an influential task variable determining choice-reaction performance but has not been considered in previous mathematical modeling efforts. Specific MDV models were developed for 5 experiments using the Simon task, for which stimulus location is task irrelevant, to examine the validity of model assumptions and illustrate characteristic behaviors of model parameters. The MDV models accounted for the experimental data to a remarkable degree, demonstrating the adequacy of the framework as a general schema for modeling the latency of choice performance. Some modeling issues involved in the MDV model framework are discussed. Keywords: Simon effect, psychological scaling, sequential sampling model, Thurstonian model, vector model Task performance is better when stimuli are compatible with the responses than when they are not. For instance, when people are asked to press left and right keys in response to lights that occur on the left and right sides, they typically respond faster when the light locations correspond to the positions of the keys. This stimulus-response compatibility (SRC) effect is robust and obtained in a wide range of task conditions, including those of applied settings such as driving a car and piloting an aircraft (Yamaguchi & Proctor, 2006 , 2011b . Thus, SRC has been one of the major principles in designing tools and systems (Proctor & Van Zandt, 2008; Proctor & Vu, 2006; Wickens, Lee, Liu, & Gordon-Becker, 2004) . Also, the SRC effect and its variant phenomena (e.g., the flanker compatibility and Stroop effects) are thought to reflect the abilities to control actions and processes underlying them. These effects have been taken as indices of cognitive capabilities, especially in comparing across subject populations of different ages or with distinct psychopathological conditions (e.g., Cagigas, Filoteo, Stricker, Rilling, & Friedrich, 2007) . At the same time, the SRC effect has also served as an experimental tool to investigate cognitive processes and test cognitive theories in a variety of research fields (e.g., Inhoff, Rosenbaum, Gordon, & Campbell, 1984; Leonhard, Ruiz Fernández, Ulrich, & Miller, 2011; McCann & Johnston, 1992) . Additionally, the SRC effect itself has been the subject of active research programs. In particular, researchers in the studies of action and perception have taken it as a central construct in their theorization of cognitive performances (see, e.g., Hommel & Prinz, 1997). Nevertheless, previous theories are concerned mostly with qualitative characteristics of the phenomena, and only limited attempts have been made to approach SRC from a quantitative perspective. Generally speaking, a modeling framework serves three purposes. First, it serves as a metaphorical description of hypothetical cognitive entities and their relations. Examples of metaphorical descriptions in cognitive psychology include theories of attention (e.g., resources, spotlight, etc.), modes and stages of cognitive processing (e.g., automatic/controlled modes, Donders/Sternberg processing stage models), and kinds of memory pools, among numerous others. These metaphorical terms are typically borrowed from the information-processing framework (Newell, Shaw, & Simon, 1958) and physiology (i.e., neurochemical mechanics) but are not limited to them. A metaphor is an effective way to communicate abstract ideas in a tangible manner and helps bridge between different fields of research. The second purpose of a modeling framework is to demonstrate what a theory of cognition is able to do or not to do by simulating hypothesized processes and systems. It is a means to confirm or disconfirm the workability of a theory, and unknown behaviors of the hypothesized systems are often discovered by means of simulations that can also be tested against data. Prominent examples of this nature include architectural models such as the ACT-R theory (Anderson et al., 2004) , EPIC (Meyer & Kieras, 1997), and Soar (Newell, 1990), which are computational extensions of information-processing metaphors, and connectionist models such as the PRP framework (Rumelhart, McClelland, and the PDP Research Group, 1986) , which are physiological metaphors of cognition.
Their work on a multidimensional vector model of SRC REF ) also addresses the issue of task context in the Simon task.
Multidimensional Vector Model of Stimulus-Response Compatibility
Psychological review
Psychological review
Computer Science Medicine