Information processing underlying human perceptual decision-making is inherently noisy and identifying sources of this noise is important to understand processing. Ratcliff, Voskuilen, and McKoon (2018) examined results from five experiments using a double-pass procedure in which stimuli were repeated typically a hundred trials later. Greater than chance agreement between repeated tests provided evidence for trial-to-trial variability from external sources of noise. They applied the diffusion model to estimate the quality of evidence driving the decision process (drift rate) and the variability (standard deviation) in drift rate across trials. This variability can be decomposed into random (internal) and systematic (external) components by comparing the double-pass accuracy and agreement with the model predictions. In this note, we provide an additional analysis of the double-pass experiments using the linear ballistic accumulator (LBA) model. The LBA model does not have within-trial variability and thus it captures all variabilities in processing with its across-trial variability parameters. The LBA analysis of the double-pass data provides model-based evidence of external variability in a decision process, which is consistent with Ratcliff et al.’s result. This demonstrates that across-trial variability is required to model perceptual decision-making. The LBA model provides measures of systematic and random variability as the diffusion model did. But due to the lack of within-trial variability, the LBA model estimated the random component as a larger proportion of across-trial total variability than did the diffusion model.

We present a model-based analysis of two-alternative forced-choice tasks in which two stimuli are presented side by side and subjects must make a comparative judgment (e.g., which stimulus is brighter). Stimuli can vary on two dimensions, the difference in strength of the two stimuli and the magnitude of each stimulus. Differences between the two stimuli produce typical RT and accuracy effects (i.e., subjects respond more quickly and more accurately when there is a larger difference between the two). However, the overall magnitude of the pair of stimuli also affects RT and accuracy. In the more common two-choice task, a single stimulus is presented and the stimulus varies on only one dimension. In this two-stimulus task, if the standard diffusion decision model is fit to the data with only drift rate (evidence accumulation rate) differing among conditions, the model cannot fit the data. However, if either of one of two variability parameters is allowed to change with stimulus magnitude, the model can fit the data. This results in two models that are extremely constrained with about one tenth of the number of parameters than there are data points while at the same time the models account for accuracy and correct and error RT distributions. While both of these versions of the diffusion model can account for the observed data, the model that allows across-trial variability in drift to vary might be preferred for theoretical reasons. The diffusion model fits are compared to the leaky competing accumulator model which did not perform as well.

It is important to identify sources of variability in processing to understand decision-making in perception and cognition. There is a distinction between internal and external variability in processing, and double-pass experiments have been used to estimate their relative contributions. In these and our experiments, exact perceptual stimuli are repeated later in testing, and agreement on the 2 trials is examined to see if it is greater than chance. In recent research in modeling decision processes, some models implement only (internal) variability in the decision process whereas others explicitly represent multiple sources of variability. We describe 5 perceptual double-pass experiments that show greater than chance agreement, which is inconsistent with models that assume internal variability alone. Estimates of total trial-to-trial variability in the evidence accumulation (drift) rate (the decision-relevant stimulus information) were estimated from fits of the standard diffusion decision-making model to the data. The double-pass procedure provided estimates of how much of this total variability was systematic and dependent on the stimulus. These results provide the first behavioral evidence independent of model fits for trial-to-trial variability in drift rate in tasks used in examining perceptual decision-making.

We examined the effects of aging on performance in an item-recognition experiment with confidence judgments. A model for confidence judgments and response time (RTs; Ratcliff & Starns, 2013) was used to fit a large amount of data from a new sample of older adults and a previously reported sample of younger adults. This model of confidence judgments allows us to distinguish between changes evidence from memory and changes in decision-related components and it accounts for both RT distributions and response proportions. Older adults took longer to respond than younger adults, older adults exhibited a small decrease in the strength of evidence from memory compared with younger adults and a slight bias toward judging items as "old." The difference in RTs between the 2 age groups was primarily explained by the difference in the nondecision component. Although our small sample size makes the general conclusions about aging tentative, the results are consistent with other research examining the effects of aging in two-choice RT tasks and response-signal tasks, and the study demonstrates that confidence judgment choice proportion and RT distribution data from older adults can be fit with the response time and confidence 2 (RTCON2) model. (PsycINFO Database Record

Theories of memory have typically focused on the representation of information in memory and relied on signal detection theory to describe how this information is translated into a decision. This approach fails to account for the amount of time taken to make a decision and the relationship between response time (RT) and response proportions. Modeling the RTs as well as the response proportions in various memory tasks can produce new explanations for behaviors and distinguish between changes in memory strength and changes in the decision-making process. In this chapter, we describe several applications of sequential sampling models.

Optimality studies and studies of decision-making in monkeys have been used to support a model in which the decision boundaries used to evaluate evidence collapse over time. This article investigates whether a diffusion model with collapsing boundaries provides a better account of human data than a model with fixed boundaries. We compared the models using data from four new numerosity discrimination experiments and two previously published motion discrimination experiments. When model selection was based on BIC values, the fixed boundary model was preferred over the collapsing boundary model for all of the experiments. When model selection was carried out using a parametric bootstrap cross-fitting method (PBCM), which takes into account the flexibility of the alternative models and the ability of one model to account for data from another model, data from 5 of 6 experiments favored either fixed boundaries or boundaries with only negligible collapse. We found that the collapsing boundary model produces response times distributions with the same shape as those produced by the fixed boundary model and that its parameters were not well-identified and were difficult to recover from data. Furthermore, the estimated boundaries of the best-fitting collapsing boundary model were relatively flat and very similar to those of the fixed-boundary model. Overall, a diffusion model with decision boundaries that converge over time does not provide an improvement over the standard diffusion model for our tasks with human data.

Research examining models of memory has focused on differences in the shapes of ROC curves across tasks and has used these differences to argue for and against the existence of multiple memory processes. ROC functions are usually obtained from confidence judgments, but the reaction times associated with these judgments are rarely considered. The RTCON2 diffusion model for confidence judgments has previously been applied to data from an item recognition paradigm. It provided an alternative explanation for the shape of the z-ROC function based on how subjects set their response boundaries and these settings are also constrained by reaction times. In our experiments, we apply the RTCON2 model to data from associative recognition tasks to further test the model's ability to accommodate non-linear z-ROC functions. The model is able to fit and explain a variety of z-ROC shapes as well as individual differences in these shapes while simultaneously fitting reaction time distributions. The model is able to distinguish between differences in the information feeding into a decision process and differences in how subjects make responses (i.e., set decision boundaries and confidence criteria). However, the model is unable to fit data from a subset of subjects in these tasks and this has implications for models of memory.