Linking the diffusion model and general recognition theory: Circular diffusion with bivariate-normally distributed drift rates

The circular diffusion model represents continuous outcome decision making as evidence accumulation by a two-dimensional Wiener process with drift on the interior of a disk, whose radius represents the decision criterion for the task. The hitting point on the circumference of the disk represents the decision outcome and the hitting time represents the decision time. The Girsanov change-of-measure theorem applied to the first-passage time distribution for the Euclidean distance Bessel process yields an explicit expression for the joint distribution of decision outcomes and decision times for the model. A problem with the expression for the joint distribution obtained in this way is that the change-of-measure calculation magnifies numerical noise in the series expression for the Bessel process, which can make the expression unstable at small times when the drift rate or decision criterion is large. We introduce a new method that uses an asymptotic approximation to characterize the Bessel process at short times and the series expression for the large times. The resulting expressions are stable across all parts of the parameter space likely to be of interest in experiments, which greatly simplifies the task of fitting the model to data. The new method applies to the spherical and hyperspherical generalizations of the model and to versions of it in which the drift rates are normally distributed across trials with independent or correlated components.

A note on decomposition of sources of variability in perceptual decision-making

Breast Tissue Density Influences Tumor Malignancy Perception and Decisions in Mammography

A circular analogue of the diffusion model adapted for continuous response tasks is applied to a continuous-outcome source memory task. In contrast to existing models of source retrieval that attribute all of the variability in responding to memory, the circular diffusion model decomposes noise into variability arising from memory and from decision processes. We compared three models: (1) a single diffusion process with trial-to-trial variability in drift rate, (2) a mixture of two diffusion processes, one with positive drift that does not vary from trial-to-trial, and a second zero-drift process that represents discrete guessing, and (3) a hybrid model that mixed positive and zero-drift processes with trial-to-trial variability in the positive drift process. Comparison of model fits to joint response error and response-time (RT) data suggest that a memory strength threshold under which no information is retrieved appears to underlie responding in a continuous-report source memory task. Additionally, we also conditioned participants' source responding on their confidence in an old/new recognition task, ruling out the possibility that participant guessing was only due to unrecognized items. Overall, our findings support an all-or-none or some-or none view of source memory retrieval and pose a challenge to continuous models of source memory.

Categorization training increases the perceptual separability of novel dimensions

to clarify the specific factors that determine how, why, and under what conditions incentives enhance cognitive processing and associated control functions.

A diffusion model analysis of episodic recognition in preclinical individuals with a family history for Alzheimer's disease: The adult children study.

I present a diffusion model for decision making in continuous report tasks, in which a continuous, circularly distributed, stimulus attribute in working memory is matched to a representation of the attribute in the stimulus display. Memory retrieval is modeled as a 2-dimensional diffusion process with vector-valued drift on a disk, whose bounding circle represents the decision criterion. The direction and magnitude of the drift vector describe the identity of the stimulus and the quality of its representation in memory, respectively. The point at which the diffusion exits the disk determines the reported value of the attribute and the time to exit the disk determines the decision time. Expressions for the joint distribution of decision times and report outcomes are obtained by means of the Girsanov change-of-measure theorem, which allows the properties of the nonzero-drift diffusion process to be characterized as a function of a Euclidian-distance Bessel process. Predicted report precision is equal to the product of the decision criterion and the drift magnitude and follows a von Mises distribution, in agreement with the treatment of precision in the working memory literature. Trial-to-trial variability in criterion and drift rate leads, respectively, to direct and inverse relationships between report accuracy and decision times, in agreement with, and generalizing, the standard diffusion model of 2-choice decisions. The 2-dimensional model provides a process account of working memory precision and its relationship with the diffusion model, and a new way to investigate the properties of working memory, via the distributions of decision times. (PsycINFO Database Record

Reading comparisons across transparent and opaque orthographies indicate critical differences that may reveal the mechanisms involved in orthographic decoding across orthographies. Here, we address the role of criterion and speed of processing in accounting for performance differences across languages. We used binary tasks involving orthographic (words–pseudowords), and non-orthographic materials (female–male faces), and analyzed results based on Ratcliff’s Diffusion model. In the first study, 29 English and 28 Italian university students were given a lexical decision test. English observers made more errors than Italian observers while showing generally similar reaction times. In terms of the diffusion model, the two groups differed in the decision criterion: English observers used a lower criterion. There was no overall cross-linguistic difference in processing speed, but English observers showed lower values for words (and a smaller lexicality effect) than Italians. In the second study, participants were given a face gender judgment test. Female faces were identified slower than the male ones with no language group differences. In terms of the diffusion model, there was no difference between groups in drift rate and boundary separation. Overall, the new main finding concerns a difference in decision criterion limited to the orthographic task: English individuals showed a more lenient criterion in judging the lexicality of the items, a tendency that may explain why, despite lower accuracy, they were not slower. It is concluded that binary tasks (and the Diffusion model) can reveal cross-linguistic differences in orthographic processing which would otherwise be difficult to detect in standard single-word reading tasks.

Theories of dynamic decision-making are typically built on evidence accumulation, which is modeled using racing accumulators or diffusion models that track a shifting balance of support over time. However, these two types of models are only two special cases of a more general evidence accumulation process where options correspond to directions in an accumulation space. Using this generalized evidence accumulation approach as a starting point, I identify four ways to discriminate between absolute-evidence and relative-evidence models. First, an experimenter can look at the information that decision-makers considered to identify whether there is a filtering of near-zero evidence samples, which is characteristic of a relative-evidence decision rule (e.g., diffusion decision model). Second, an experimenter can disentangle different components of drift rates by manipulating the discriminability of the two response options relative to the stimulus to delineate the balance of evidence from the total amount of evidence. Third, a modeler can use machine learning to classify a set of data according to its generative model. Finally, machine learning can also be used to directly estimate the geometric relationships between choice options. I illustrate these different approaches by applying them to data from an orientation-discrimination task, showing converging conclusions across all four methods in favor of accumulator-based representations of evidence during choice. These tools can clearly delineate absolute-evidence and relative-evidence models, and should be useful for comparing many other types of decision theories.

The shifted-Wald model is a popular analysis tool for one-choice reaction-time tasks. In its simplest version, the shifted-Wald model assumes a constant trial-independent drift rate parameter. However, the presence of endogenous processes—fluctuation in attention and motivation, fatigue and boredom—suggest that drift rate might vary across experimental trials. Here we show how across-trial variability in drift rate can be accounted for by assuming a trial-specific drift rate parameter that is governed by a positive-valued distribution. We consider two candidate distributions: the truncated normal distribution and the gamma distribution. For the resulting distributions of first-arrival times, we derive analytical and sampling-based solutions, and implement the models in a Bayesian framework. Recovery studies and an application to a data set comprised of 1469 participants suggest that (1) both mixture distributions yield similar results; (2) all model parameters can be recovered accurately except for the drift variance parameter; (3) despite poor recovery, the presence of the drift variance parameter facilitates accurate recovery of the remaining parameters; (4) shift, threshold, and drift mean parameters are correlated.

Diffusion models of decision making, in which successive samples of noisy evidence are accumulated to decision criteria, provide a theoretical solution to von Neumann’s (1956) problem of how to increase the reliability of neural computation in the presence of noise. I introduce and evaluate a new neurally-inspired dual diffusion model, the linear drift, linear infinitesimal variance (LDLIV) model, which embodies three features often thought to characterize neural mechanisms of decision making. The accumulating evidence is intrinsically positively-valued, saturates at high intensities, and is accumulated for each alternative separately. I present explicit integral-equation predictions for the response time distribution and choice probabilities for the LDLIV model and compare its performance on two benchmark sets of data to three other models: the standard diffusion model and two dual diffusion model composed of racing Wiener processes, one between absorbing and reflecting boundaries and one with absorbing boundaries only. The LDLIV model and the standard diffusion model performed similarly to one another, although the standard diffusion model is more parsimonious, and both performed appreciably better than the other two dual diffusion models. I argue that accumulation of noisy evidence by a diffusion process and drift rate variability are both expressions of how the cognitive system solves von Neumann’s problem, by aggregating noisy representations over time and over elements of a neural population. I also argue that models that do not solve von Neumann’s problem do not address the main theoretical question that historically motivated research in this area.

14 - Can Confusion-Data Inform SFT-Like Inference? A Comparison of SFT and Accuracy-Based Measures in Comparable Experiments

We present a new experimental paradigm intended to allow for the acquisition of the data needed for testing strong hypotheses regarding the nature of encoded representations and the real-time processing of those representations using the same set of trials. The design is motivated by two formal theories: general recognition theory (Ashby & Townsend. Psychological Review, 93, 154-179, 1986), which addresses internal representation, and systems factorial theory (Townsend & Nozawa. Journal of Mathematical Psychology, 39, 321-359. 1995), which addresses the foundational characteristics of real-time processing. We show in the results of two experiments, one with very simple and a second with more complex stimuli, that this paradigm is capable of producing data that can allow for inferences regarding both representation and processing from the same set of trials and that those two sets of inferences can be found to be coherent with one another, allowing for the potential for the results of behavioral experimentation to seriously constrain formal and computational modeling. In this sense, the work is coherent with an overarching theme in Mary Peterson's work, specifically as an application of two theory-driven approaches to questions in cognitive representation and processing.

Thatcherisation of facial features is immediately apparent only in upright faces. Detection of Thatcherisation is therefore widely upheld as being dependent on configural processing. Configural processing has clear predictions of perceptual dependence between facial features and of supercapacity processing.<br/><br/>Perceptual dependence: Configurality in General Recognition Theory (GRT, Ashby & Townsend, 1986) can be conceptualized in terms of violations of perceptual independence, in which the perceptions of the eyes and mouth of a single face are positively correlated; for example, the more inverted the eyes look, the more inverted the mouth will look. Participants were briefly presented with normal, partially Thatcherised and fully Thatcherised faces, and were asked to report whether the outline, eyes and mouth were upright or inverted. Consistent with the predictions, multi-dimensional probit models (DeCarlo, 2003) revealed that within-stimulus perceptual interactions occurred more frequently for upright than inverted faces. However, for the Thatcherised stimulus itself, there was no overall correlation between the eyes and the mouth, suggesting a lack of configural processing for this type of stimulus.<br/><br/>Processing capacity: Supercapacity processing is predicted to accompany configural processing (O’Toole, Wenger & Townsend, 2001; Wenger & Townsend, 2001). Therefore, the detection of Thatcherised features in upright faces should be marked by supercapacity processing of inverted eyes and mouths relative to the inversion of only eyes or only mouths. Response times were used to compute measures of processing capacity (capacity coefficient, Townsend & Wenger, 2004; proportional hazards ratio, Wenger & Gibson, 2006) in Thatcherised upright faces. Results demonstrated limited evidence of supercapacity processing, and only in some individuals, implying that configural processing is not necessary for processing of upright Thatcherised faces.<br/><br/>In summary, predictions from GRT and of processing capacity were tested across two separate studies, with little evidence found for perceptual independence or supercapacity processing for Thatcherised face stimuli.