Decision making on spatially continuous scales.

Abstract

A new diffusion model of decision making in continuous space is presented and tested. The model is a sequential sampling model in which both spatially continuously distributed evidence and noise are accumulated up to a decision criterion (a 1D line or a 2D plane). There are two major advances represented in this research. The first is to use spatially continuously distributed Gaussian noise in the decision process (Gaussian process or Gaussian random field noise) which allows the model to represent truly spatially continuous processes. The second is a series of experiments that collect data from a variety of tasks and response modes to provide the basis for testing the model. The model accounts for the distributions of responses over position and response time distributions for the choices. The model applies to tasks in which the stimulus and the response coincide (moving eyes or fingers to brightened areas in a field of pixels) and ones in which they do not (color, motion, and direction identification). The model also applies to tasks in which the response is made with eye movements, finger movements, or mouse movements. This modeling offers a wide potential scope of applications including application to any device or scale in which responses are made on a 1D continuous scale or in a 2D spatial field.

Stimulus reliability automatically biases temporal integration of discrete perceptual targets

“…Further studies, most likely in combination with hierarchical computational modelling (49), would be necessary to address this issue conclusively. At present, computational models of decision-making in reproduction tasks are just beginning to appear (50,51), and more research will be needed before applying these models to integrative decision-making tasks.…”

Reconciling similarity across models of continuous selections

“…Unfortunately, the CDM cannot predict multimodal distributions of responses, where selections are clustered in more than one main area. These types of distributions appear in continuous response tasks when the stimulus is driven by multiple targets (Ratcliff, 2018) or when there is conflict between two sources of information such as a stimulus and a predecision cue (Kvam, 2019b). Multimodal distributions and the relative concentration of responses at different modes are often theoretically important, as they reflect potentially interesting properties of the generating process.…”

“…A number of recent papers proposing new computational models have targeted a long-standing problem in decision-making, which is that dynamic theories of choice only account for selections between a small number of options (most often, sets of 2-3). Continuous-response paradigms are prevalent across cognitive sciences and psychology, including perception and memory of color (Awh et al, 2007;van den Berg et al, 2014;Zhang & Luck, 2008) and orientation (Rademaker et al, 2012;Kvam, 2019b), simple studies of brightness detection (Ratcliff, 2018), and more applied cognitive tasks like spatial navigation and wayfinding (Blanchard et al, 1987;Montello & Pick Jr, 1993), pricing (Mellers et al, 1992;Kvam & Busemeyer, 2018) and preference or confidence rating tasks (Sniezek & Henry, 1989;Harvey, 1997). Despite this, theories of the cognitive processes underlying selections in continuous-report paradigms were under-developed or non-existent until the recent advent of the circular diffusion model (Smith, 2016), the spatially continuous diffusion model (Ratcliff, 2018), the more general geometric framework for constructing models (Kvam, 2019a), and extensions and generalizations of these approaches (Kvam, 2019b;Smith & Corbett, 2018;Smith, 2019).…”

“…Another approach to modeling continuously-distributed responses was provided by Ratcliff (2018) with the spatially continuous diffusion model (SCDM). Instead of the circular distributions typically encountered in color and orientation tasks, it was aimed at predicting performance in tasks where responses could fall along a line or plane, such as function learning tasks (DeLosh et al, 1997) or spatial location tasks (Naveh-Benjamin, 1987).…”

“…Although Ratcliff (2018) noted some differences between the models in terms of what they could predict, the structure of these models have not been thoroughly compared. In part, this is because the CDM has been applied to tasks with a circular / wrapped response space and the SCDM has been applied to tasks where responses fall within a fixed range on a line or plane.…”