Modeling the complex relationship between task difficulty, accuracy, response time, and confidence

Kurzfassung/Abstract

Confidence, a subjective evaluation about the correctness of one's own decision, is influenced by many aspects of the decision itself, for example the level of difficulty. Empirically, the time it takes to make a decision is also related to confidence, such that faster decisions are usually accompanied with higher confidence compared to slower decisions. The mathematical framework of sequential sampling models offers a way to formalize a unified theory of the complex relationship between task difficulty, response times, and confidence judgments. The three studies in this thesis utilized the sequential sampling framework to yield insight into the decision dynamics and computations that give rise to confidence judgments in perceptual decisions.

In Study 1 and 2, a variety of dynamical confidence models are compared with respect to their fit to empirical data from experiments comprising different visual discrimination tasks with a difficulty manipulation. In Study 1, I formulated the dynamical weighted evidence and visibility (dynWEV) model and in Study 2, I refined the model to the dynamical visibility, time, and evidence model (dynaViTE) model. The dynaViTE model describes the decision process as a drift diffusion model. In addition, dynaViTE assumes a period of post-decisional accumulation of evidence and a parallel accumulation of visibility evidence, which accrues evidence about task difficulty. In dynaViTE, confidence is determined by a combination of decision evidence and visibility evidence in the form of a weighted sum, penalized by the duration of evidence accumulation.

In Study 1, I compared different dynamical confidence models, which are based on either a race of accumulators or the drift diffusion model, on their fit to data from two experiments comprising different visual discrimination tasks with a difficulty manipulation. The newly proposed dynWEV model outperformed all competitors suggesting that confidence is not only determined by evidence about stimulus identity but is influenced by independent evidence about task difficulty, which is conveyed by choice-irrelevant stimulus features.

Study 2 examined the role of the duration of evidence accumulation in the computation of confidence. Theoretically supported by a formal analysis of confidence in a Bayesian optimal observer model, I generalized the dynWEV model to include a penalization of the time it takes to accumulate evidence and form a decision in the computation of confidence, resulting in the dynaViTE model. The dynaViTE model is compared against three of its special cases that either ignore accumulation time, visibility evidence, or both accumulation time and visibility evidence in the computation of confidence. We used previously published empirical data from four experiments, three visual discrimination tasks with a difficulty manipulation, and one visual two-alternative forced choice task with a difficulty and a speed-accuracy manipulation. The results suggest that human observers indeed explicitly consider accumulation time when making confidence judgments. However, depending on the task at hand, either visibility accumulation or accumulation time may be less relevant in the formation of confidence, which suggests that some stimuli or experimental tasks leads to different strategies in confidence computations. The third study showcases the R package dynConfiR, which includes an implementation of several dynamical confidence models together with high-level functions for parameter estimation and prediction of response time distributions. The package offers an efficient and intuitive model fitting function, which simplifies the workflow for modeling studies with confidence and response time data to calling a few lines of code. Thus, the dynConfiR package provides useful tools for analyzing response time and confidence data across a variety of experiments.

In sum, the dynaViTE model forms a computational model, which formalizes the relationship between task difficulty, choice, response time, and confidence judgment. The dynaViTE model extends previous theories of confidence by including the parallel assessment of independent evidence about task difficulty and the incorporation of accumulation time in the computation of confidence. The studies presented in this thesis deliver substantial evidence in supporting both features, the parallel accumulation of visibility and the incorporation of accumulation time in the computation of confidence. This thesis thus forms an important contribution to the growing research on decision mechanics and confidence and thereby improve our understanding how confidence arises in perceptual decisions.