Modeling individual differences in response time and accuracy in numeracy

Is counting a bad idea? Complex relations among children's fraction knowledge, eye movements, and performance in visual fraction comparisons

Understanding fraction magnitudes is crucial for mathematical development but is challenging for many children. Visualizations, such as tape diagrams, are thought to leverage children's early proportional reasoning skills. However, depending on children's prior knowledge, these visualizations may encourage various strategies. Children with lower fraction knowledge might rely on counting, leading to natural number bias and low performance, whereas those with higher knowledge might rely on more efficient strategies based on magnitude. This study explores the relationship between students' general fraction knowledge and their ability to visually compare fraction magnitudes represented with tape diagrams. A total of 67 children completed a fraction knowledge test and a set of comparison tasks with discretized and continuous tape diagrams while their eye movements, accuracy, and response times were recorded. Cluster analysis identified three groups. The first group, high-achieving and applying magnitude-based strategies, showed high accuracy and short response times, indicating efficiency. A second high-achieving group frequently used counting strategies, which was unexpected. This group achieved the highest accuracy but the longest response times, indicating less efficiency. The third group, low-achieving and rarely using counting strategies, had the lowest accuracy and short response times. These students tended to compare absolute sizes rather than relative sizes (i.e., showing a size bias). None of the groups exhibited a natural number bias. The study suggests that counting, although inefficient, does not necessarily lead to bias or low performance. Instead, biased reasoning with fraction visualizations can originate from reliance on absolute sizes.

When 2 become 1: Autistic simultaneity judgements about asynchronous audiovisual speech

It has been proposed that autistic people experience a temporal distortion whereby the temporal binding window of multisensory integration is extended. Research to date has focused on autistic children so whether these differences persist into adulthood remains unknown. In addition, the possibility that the previous observations have arisen from between-group differences in response bias, rather than perceptual differences, has not been addressed. Participants completed simultaneity judgements of audiovisual speech stimuli across a range of stimulus-onset asynchronies. Response times and accuracy data were fitted to a drift-diffusion model so that the drift rate (a measure of processing efficiency) and starting point (response bias) could be estimated. In Experiment 1, we tested a sample of non-autistic adults who completed the Autism Quotient questionnaire. Autism Quotient score was not correlated with either drift rate or response bias, nor were there between-group differences when splitting based on the first and third quantiles of scores. In Experiment 2, we compared the performance of autistic with a group of non-autistic adults. There were no between-group differences in either drift rate or starting point. The results of this study do not support the previous suggestion that autistic people have an extended temporal binding window for audiovisual speech. In addition, exploratory analysis revealed that operationalising the temporal binding window in different ways influenced whether a group difference was observed, which is an important consideration for future work.

Joint contributions of preview and task instructions on visual search strategy selection

People tend to employ suboptimal attention control strategies during visual search. Here we question why people are suboptimal, specifically investigating how knowledge of the optimal strategies and the time available to apply such strategies affect strategy use. We used the Adaptive Choice Visual Search (ACVS), a task designed to assess attentional control optimality. We used explicit strategy instructions to manipulate explicit strategy knowledge, and we used display previews to manipulate time to apply the strategies. In the first two experiments, the strategy instructions increased optimality. However, the preview manipulation did not significantly boost optimality for participants who did not receive strategy instruction. Finally, in Experiments 3A and 3B, we jointly manipulated preview and instruction with a larger sample size. Preview and instruction both produced significant main effects; furthermore, they interacted significantly, such that the beneficial effect of instructions emerged with greater preview time. Taken together, these results have important implications for understanding the strategic use of attentional control. Individuals with explicit knowledge of the optimal strategy are more likely to exploit relevant information in their visual environment, but only to the extent that they have the time to do so.

Developmental changes of the impact of visual cues on ANS acuity across grades 1-5: Different patterns of visual cues on numerosity processing

Numerous studies have consistently demonstrated the presence of the approximate number system (ANS) throughout development. Research has also revealed that visual cues may influence the ANS acuity, which may change with age. However, most studies have drawn conclusions based on performance differences between incongruent and congruent trials, which may be confounded by an individual's ability to inhibit interference. Therefore, to examine the developmental changes of the impact of visual cues on ANS acuity, we utilized congruent trials with varying visual cues. Our sample comprised Chinese children from grade one to grade five. We manipulated the salience of numerical cues (numerical ratio) and visual cues (dot size) in a non-symbolic numerosity comparison task. The results revealed a discernible leap in development from first to third grade and first to fifth grade; however, this upward trajectory did not persist into the transition from third to fifth grade, where no appreciable advancement was observed. Moreover, we observed different effects of visual cues on the dot-comparison task depending on the numerical cues and age. Specifically, visual cues (i.e., dot size) only facilitated ANS acuity in older school-aged children when numerical cues were weakened. The results indicate the presence of two distinct magnitude representational systems-one for the numerical dimension and another for the non-numerical dimension-during development.

Children's comparison of different-length numbers: Managing different attributes in multidigit number processing

In everyday life the comparison of numbers usually occurs between numbers with different numbers of digits. However, experimental research here is scarce. Recent research has shown that adults respond faster to congruent pairs (the initial digit in the number with more digits is larger, e.g., 2384 vs. 107) than to incongruent pairs (the initial digit is larger in the number with fewer digits, e.g., 2675 vs. 398). This has been interpreted as support for the processing of multiple attributes in parallel and against serial accounts. The current research asked whether there is a change in the relevance of these attributes as school grades increase. School-age children from the second to sixth grades (N = 206) were presented with pairs of numbers that had either the same number of digits (3 vs. 3 or 4 vs. 4) or a different number of digits (3 vs. 4). In this latter condition, the stimuli, matched by distance, could be either length/digit congruent (e.g., 2384 vs. 107) or length/digit incongruent (e.g., 2675 vs. 398). Linear mixed models showed a length/digit congruity effect from second graders. Interestingly, in the response time measure, congruity interacted with school grade and the side in which the larger number of the pair was presented. Whereas these results support a model that considers number comparison as a process that weighs different attributes in parallel, it is also argued that developmental changes are associated with differences in the level of automatization of the componential skills involved in the comparison.

Developmental Trajectory of Anticipation: Insights from Sequential Comparative Judgments

Reaction time (RT) is a critical measure of performance, and studying its distribution at the group or individual level provides useful information on the cognitive processes or strategies used to perform a task. In a previous study measuring RT in children and adults asked to compare two successive stimuli (quantities or words), we discovered that the group RT distribution was bimodal, with some subjects responding with a mean RT of around 1100 ms and others with a mean RT of around 500 ms. This bimodal distribution suggested two distinct response strategies, one reactive, the other anticipatory. In the present study, we tested whether subjects' segregation into fast and slow responders (1) extended to other sequential comparative judgments (2) evolved from age 8 to adulthood, (3) could be linked to anticipation as assessed using computer modeling (4) stemmed from individual-specific strategies amenable to instruction. To test the first three predictions, we conducted a distributional and theoretical analysis of the RT of 158 subjects tested earlier using four different sequential comparative judgment tasks (numerosity, phonological, multiplication, subtraction). Group RT distributions were bimodal in all tasks, with the two strategies differing in speed and sometimes accuracy too. The fast strategy, which was rare or absent in 8- to 9-year-olds, steadily increased through childhood. Its frequency in adolescence remained, however, lower than in adulthood. A mixture model confirmed this developmental evolution, while a diffusion model corroborated the idea that the difference between the two strategies concerns anticipatory processes preceding decision processes. To test the fourth prediction, we conducted an online experiment where 236 participants made numerosity comparisons before and after an instruction favoring either reactive or anticipatory responses. The results provide out-of-the-lab evidence of the bimodal RT distribution associated with sequential comparisons and demonstrated that the proportions of fast vs. slow responders can be modulated simply by asking subjects to anticipate or not the future result of the comparison. Although anticipation of the future is as important for cognition as memory of the past, its evolution after the first year of life is much more poorly known. The present study is a step toward meeting this challenge. It also illustrates how analyzing individual RT distributions in addition to group RT distributions and using computational models can improve the assessment of decision making cognitive processes.

Effects of Sleep Deprivation on Performance during a Change Signal Task with Adaptive Dynamics

Augmented cognition, which refers to real-time modifications to a human-system interface to improve performance and includes dynamic task environments with automated adaptations, can serve to protect against performance impairment under challenging work conditions. However, the effectiveness of augmented cognition as a countermeasure for performance impairment due to sleep loss is unknown. Here, in a controlled laboratory study, an adaptive version of a Change Signal task was administered repeatedly to healthy adults randomized to 62 h of total sleep deprivation (TSD) or a rested control condition. In the computerized task, a left- or right-facing arrow was presented to start each trial. In a subset of trials, a second arrow facing the opposite direction was presented after a delay. Subjects were to respond within 1000 ms of the trial start by pressing the arrow key corresponding to the single arrow (Go trials) or to the second arrow when present (Change trials). The Change Signal Delay (CSD)-i.e., the delay between the appearance of the first and second arrows-was shortened following incorrect responses and lengthened following correct responses so that subsequent Change trials became easier or harder, respectively. The task featured two distinct CSD dynamics, which produced relatively stable low and high error rates when subjects were rested (Low and High Error Likelihood trials, respectively). During TSD, the High Error Likelihood trials produced the same, relatively high error rate, but the Low Error Likelihood trials produced a higher error rate than in the rested condition. Thus, sleep loss altered the effectiveness of the adaptive dynamics in the Change Signal task. A principal component analysis revealed that while subjects varied in their performance of the task along a single dominant dimension when rested, a second inter-individual differences dimension emerged during TSD. These findings suggest a need for further investigation of the interaction between augmented cognition approaches and sleep deprivation in order to determine whether and how augmented cognition can be relied upon as a countermeasure to performance impairment in operational settings with sleep loss.

Uncovering the Structure of Semantic Representations Using a Computational Model of Decision-Making

According to logical theories of meaning, a meaning of an expression can be formalized and encoded in truth conditions. Vagueness of the language and individual differences between people are a challenge to incorporate into the meaning representations. In this paper, we propose a new approach to study truth-conditional representations of vague concepts. For a case study, we selected two natural language quantifiers most and more than half. We conducted two online experiments, each with 90 native English speakers. In the first experiment, we tested between-subjects variability in meaning representations. In the second experiment, we tested the stability of meaning representations over time by testing the same group of participants in two experimental sessions. In both experiments, participants performed the verification task. They verified a sentence with a quantifier (e.g., "Most of the gleerbs are feezda.") based on the numerical information provided in the second sentence, (e.g., "60% of the gleerbs are feezda"). To investigate between-subject and within-subject differences in meaning representations, we proposed an extended version of the Diffusion Decision Model with two parameters capturing truth conditions and vagueness. We fit the model to responses and reaction times data. In the first experiment, we found substantial between-subject differences in representations of most as reflected by the variability in the truth conditions. Moreover, we found that the verification of most is proportion-dependent as reflected in the reaction time effect and model parameter. In the second experiment, we showed that quantifier representations are stable over time as reflected in stable model parameters across two experimental sessions. These findings challenge semantic theories that assume the truth-conditional equivalence of most and more than half and contribute to the representational theory of vague concepts. The current study presents a promising approach to study semantic representations, which can have a wide application in experimental linguistics.

Can neuropsychological testing be improved with model-based approaches?

There has been little impact of cognitive psychology and modeling on neuropsychological testing for over 50 years. There is also a disconnect between those tests and the constructs they are said to measure. We discuss studies at the interface between testing and modeling that illustrate the opportunity for advances.

Integrated diffusion models for distance effects in number memory

I evaluated three models for the representation of numbers in memory. These were integrated with the diffusion decision model to explain accuracy and response time (RT) data from a recognition memory experiment in which the stimuli were two-digit numbers. The integrated models accounted for distance/confusability effects: when a test number was numerically close to a studied number, accuracy was lower and RTs were longer than when a test number was numerically far from a studied number. For two of the models, the representations of numbers are distributed over number (with Gaussian or exponential distributions) and the overlap between the distributions of a studied number and a test number provides the evidence (drift rate) on which a decision is made. For the third, the exponential gradient model, drift rate is an exponential function of the numerical distance between studied and test numbers. The exponential gradient model fit the data slightly better than the two overlap models. Monte Carlo simulations showed that the variability in the important parameter estimates from fitting data collected over 30-40 min is smaller than the variability among individuals, allowing differences among individuals to be studied. A second experiment compared number memory and number discrimination tasks and results showed different distance effects. Number memory had an exponential-like distance-effect and number discrimination had a linear function which shows radically different representations drive the two tasks.

Reduced choice-confidence in negative numerals

Negative numbers are central in math. However, they are abstract, hard to learn, and manipulated slower than positive numbers regardless of math ability. It suggests that confidence, namely the post-decision estimate of being correct, should be lower than positives. We asked participants to pick the larger single-digit numeral in a pair and collected their implicit confidence with button pressure (button pressure was validated with three empirical signatures of confidence). We also modeled their choices with a drift-diffusion decision model to compute the post-decision estimate of being correct. We found that participants had relatively low confidence with negative numerals. Given that participants compared with high accuracy the basic base-10 symbols (0–9), reduced confidence may be a general feature of manipulating abstract negative numerals as they produce more uncertainty than positive numerals per unit of time.

Strategy and processing speed eclipse individual differences in control ability in conflict tasks

Response control or inhibition is one of the cornerstones of modern cognitive psychology, featuring prominently in theories of executive functioning and impulsive behavior. However, repeated failures to observe correlations between commonly applied tasks have led some theorists to question whether common response conflict processes even exist. A challenge to answering this question is that behavior is multifaceted, with both conflict and nonconflict processes (e.g., strategy, processing speed) contributing to individual differences. Here, we use a cognitive model to dissociate these processes; the diffusion model for conflict tasks (Ulrich et al., 2015). In a meta-analysis of fits to seven empirical datasets containing combinations of the flanker, Simon, color-word Stroop, and spatial Stroop tasks, we observed weak (r < .05) zero-order correlations between tasks in parameters reflecting conflict processing, seemingly challenging a general control construct. However, our meta-analysis showed consistent positive correlations in parameters representing processing speed and strategy. We then use model simulations to evaluate whether correlations in behavioral costs are diagnostic of the presence or absence of common mechanisms of conflict processing. We use the model to impose known correlations for conflict mechanisms across tasks, and we compare the simulated behavior to simulations when there is no conflict correlation across tasks. We find that correlations in strategy and processing speed can produce behavioral correlations equal to, or larger than, those produced by correlated conflict mechanisms. We conclude that correlations between conflict tasks are only weakly informative about common conflict mechanisms if researchers do not control for strategy and processing speed. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Incentive motivation improves numerosity discrimination in children and adolescents

We recently showed that incentive motivation improves the precision of the Approximate Number System (ANS) in young adults. To shed light on the development of incentive motivation, the present study investigated whether this effect and its underlying mechanisms may also be observed in younger samples. Specifically, seven-year-old children (n = 23; 12 girls) and 14-year-old adolescents (n = 30; 15 girls) performed a dot comparison task with monetary reward incentives. Both age groups showed higher accuracy in a reward compared to a neutral condition and, similarly, higher processing efficiency as revealed by the drift rate parameter of the EZ-diffusion model. Furthermore, in line with the Incentive Salience Hypothesis, phasic pupil dilations—indicating the activation of the brain’s salience network—were greater in incentivized trials in both age groups. Together these finding suggest that incentive modulation improves numerosity discrimination in children and adolescents by enhancing the perceptual saliency of numerosity information. However, the observed reward anticipation effects were less pronounced in children relative to adolescents. Furthermore, unlike previous findings regarding young adults, the decision thresholds of children and adolescents were not raised by the monetary reward, which may indicate a more protracted development of incentive regulation of response caution than perceptual evidence accumulation.

Discriminating memory disordered patients from controls using diffusion model parameters from recognition memory

One hundred and five memory disordered (MD) patients and 57 controls were tested on item recognition memory and lexical decision tasks, and diffusion model analyses were conducted on accuracy and response time distributions for correct and error responses. The diffusion model fit the data well for the MD patients and control subjects, the results replicated earlier studies with young and older adults, and individual differences were consistent between the item recognition and lexical decision tasks. In the diffusion model analysis, MD patients had lower drift rates (with mild Alzheimer's [AD] patients lower than mild cognitive impairment [MCI] patients) as well as wider boundaries and longer nondecision times. These data and results were used in a series of studies to examine how well MD patients could be discriminated from controls using machine-learning techniques, linear discriminant analysis, logistic regression, and support vector machines (all of which produced similar results). There was about 83% accuracy in separating MD from controls, and within the MD group, AD patients had about 90% accuracy and MCI patients had about 68% accuracy (controls had about 90% accuracy). These methods might offer an adjunct to traditional clinical diagnosis. Limitations are noted including difficulties in obtaining a matched group of control subjects as well as the possibility of misdiagnosis of MD patients. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Not so fast! Response times in the computerized Benton Face Recognition Test may not reflect face recognition ability

Response times (RTs) are commonly used to assess cognitive abilities, though it is unclear whether face processing RTs predict recognition ability beyond accuracy. In the current study, we examined accuracy and RT on a widely used face matching assessment modified to collect meaningful RT data, the computerized Benton Facial Recognition Test (BFRT-c), and measured whether RTs predicted face recognition ability and developmental prosopagnosia (DP) vs. control group membership. 62 controls and 36 DPs performed the BFRT-c as well as validated measures of face recognition ability: the Cambridge Face Memory Test (CFMT) and a Famous Faces Memory Test (FFMT). In controls, BFRT-c accuracy robustly predicted CFMT (r = .49, p < .001), FFMT (r = .43, p < .001), and a CFMT-FFMT composite (r = .54, p < .001), whereas BFRT-c RT was not significantly associated with these measures (all r's  .21). We also found that BFRT-c accuracy significantly differed between DPs and controls, but RT failed to differentiate the groups.

The ascending arousal system promotes optimal performance through mesoscale network integration in a visuospatial attentional task

Previous research has shown that the autonomic nervous system provides essential constraints over ongoing cognitive function. However, there is currently a relative lack of direct empirical evidence for how this interaction manifests in the brain at the macroscale level. Here, we examine the role of ascending arousal and attentional load on large-scale network dynamics by combining pupillometry, functional MRI, and graph theoretical analysis to analyze data from a visual motion-tracking task with a parametric load manipulation. We found that attentional load effects were observable in measures of pupil diameter and in a set of brain regions that parametrically modulated their BOLD activity and mesoscale network-level integration. In addition, the regional patterns of network reconfiguration were correlated with the spatial distribution of the α2a adrenergic receptor. Our results further solidify the relationship between ascending noradrenergic activity, large-scale network integration, and cognitive task performance.

Peer Presence Effect on Numerosity and Phonological Comparisons in 4th Graders: When Working with a SchoolMate Makes Children More Adult-like

Simple Summary

The presence of others helps us when we are good or an expert at something and hinders us when we are bad or novice. Such social facilitation or inhibition is well-documented in adults, but much less in children despite the omnipresence of peers throughout education. To explore potential peer presence effects on children’s academic performance, fourth-graders performed basic numerical and language skills (typically mastered at their age) either alone or with a schoolmate. For comparison, the same was performed in adults. We found that a schoolmate’s presence enabled children to perform more like adults, with a better response strategy and faster and less variable response times than children tested alone. This provides research-based evidence supporting pedagogical methods promoting collective practice of individually acquired knowledge. Future studies pursuing this hitherto neglected developmental exploration of peer presence effects on academic achievements might have the potential to help educators tailor their pedagogical choices to maximize peer presence when beneficial and minimize it when harmful. The present study also paves the way towards a neuroimaging investigation of how peer presence changes the way the child brain processes cognitive tasks relevant to education.

Abstract

Little is known about how peers’ mere presence may, in itself, affect academic learning and achievement. The present study addresses this issue by exploring whether and how the presence of a familiar peer affects performance in a task assessing basic numeracy and literacy skills: numerosity and phonological comparisons. We tested 99 fourth-graders either alone or with a classmate. Ninety-seven college-aged young adults were also tested on the same task, either alone or with a familiar peer. Peer presence yielded a reaction time (RT) speedup in children, and this social facilitation was at least as important as that seen in adults. RT distribution analyses indicated that the presence of a familiar peer promotes the emergence of adult-like features in children. This included shorter and less variable reaction times (confirmed by an ex-Gaussian analysis), increased use of an optimal response strategy, and, based on Ratcliff’s diffusion model, speeded up nondecision (memory and/or motor) processes. Peer presence thus allowed children to at least narrow (for demanding phonological comparisons), and at best, virtually fill in (for unchallenging numerosity comparisons) the developmental gap separating them from adult levels of performance. These findings confirm the influence of peer presence on skills relevant to education and lay the groundwork for exploring how the brain mechanisms mediating this fundamental social influence evolve during development.

Numeral order and the operationalization of the numerical system

Recent years have witnessed an increase in research on how numeral ordering skills relate to children's and adults' mathematics achievement both cross-sectionally and longitudinally. Nonetheless, it remains unknown which core competency numeral ordering tasks measure, which cognitive mechanisms underlie performance on these tasks, and why numeral ordering skills relate to arithmetic and math achievement. In the current study, we focused on the processes underlying decision-making in the numeral order judgement task with triplets to investigate these questions. A drift-diffusion model for two-choice decisions was fit to data from 97 undergraduates. Findings aligned with the hypothesis that numeral ordering skills reflected the operationalization of the numerical system, where small numbers provide more evidence of an ordered response than large numbers. Furthermore, the pattern of findings suggested that arithmetic achievement was associated with the accuracy of the ordinal representations of numbers.

Delta plots for conflict tasks: An activation-suppression race model

We describe a mathematically simple yet precise model of activation suppression that can explain the negative-going delta plots often observed in standard Simon tasks. The model postulates a race between the identification of the relevant stimulus attribute and the suppression of irrelevant location-based activation, with the irrelevant activation only having an effect if the irrelevant activation is still present at the moment when central processing of the relevant attribute starts. The model can be fitted by maximum likelihood to observed distributions of RTs in congruent and incongruent trials, and it provides good fits to two previously-reported data sets with plausible parameter values. R and MATLAB software for use with the model is provided.

Age differences in diffusion model parameters: a meta-analysis

Older adults typically show slower response times in basic cognitive tasks than younger adults. A diffusion model analysis allows the clarification of why older adults react more slowly by estimating parameters that map distinct cognitive components of decision making. The main components of the diffusion model are the speed of information uptake (drift rate), the degree of conservatism regarding the decision criterion (boundary separation), and the time taken up by non-decisional processes (i.e., encoding and motoric response execution; non-decision time). While the literature shows consistent results regarding higher boundary separation and longer non-decision time for older adults, results are more complex when it comes to age differences in drift rates. We conducted a multi-level meta-analysis to identify possible sources of this variance. As possible moderators, we included task difficulty and task type. We found that age differences in drift rate are moderated both by task type and task difficulty. Older adults were inferior in drift rate in perceptual and memory tasks, but information accumulation was even increased in lexical decision tasks for the older participants. Additionally, in perceptual and lexical decision tasks, older individuals benefitted from high task difficulty. In the memory tasks, task difficulty did not moderate the negative impact of age on drift. The finding of higher boundary separation and longer non-decision time in older than younger adults generalized over task type and task difficulty. The results of our meta-analysis are consistent with recent findings of a more pronounced age-related decline in memory than in vocabulary performance.

Identifying relationships between cognitive processes across tasks, contexts, and time

It is commonly assumed that a specific testing occasion (task, design, procedure, etc.) provides insights that generalize beyond that occasion. This assumption is infrequently carefully tested in data. We develop a statistically principled method to directly estimate the correlation between latent components of cognitive processing across tasks, contexts, and time. This method simultaneously estimates individual-participant parameters of a cognitive model at each testing occasion, group-level parameters representing across-participant parameter averages and variances, and across-task correlations. The approach provides a natural way to "borrow" strength across testing occasions, which can increase the precision of parameter estimates across all testing occasions. Two example applications demonstrate that the method is practical in standard designs. The examples, and a simulation study, also provide evidence about the reliability and validity of parameter estimates from the linear ballistic accumulator model. We conclude by highlighting the potential of the parameter-correlation method to provide an "assumption-light" tool for estimating the relatedness of cognitive processes across tasks, contexts, and time.

Developmental Changes in ANS Precision Across Grades 1-9: Different Patterns of Accuracy and Reaction Time

The main aim of this study was to analyze the patterns of changes in Approximate Number Sense (ANS) precision from grade 1 (mean age: 7.84 years) to grade 9 (mean age: 15.82 years) in a sample of Russian schoolchildren. To fulfill this aim, the data from a longitudinal study of two cohorts of children were used. The first cohort was assessed at grades 1-5 (elementary school education plus the first year of secondary education), and the second cohort was assessed at grades 5-9 (secondary school education). ANS precision was assessed by accuracy and reaction time (RT) in a non-symbolic comparison test ("blue-yellow dots" test). The patterns of change were estimated via mixed-effect growth models. The results revealed that in the first cohort, the average accuracy increased from grade 1 to grade 5 following a non-linear pattern and that the rate of growth slowed after grade 3 (7-9 years old). The non-linear pattern of changes in the second cohort indicated that accuracy started to increase from grade 7 to grade 9 (13-15 years old), while there were no changes from grade 5 to grade 7. However, the RT in the non-symbolic comparison test decreased evenly from grade 1 to grade 7 (7-13 years old), and the rate of processing non-symbolic information tended to stabilize from grade 7 to grade 9. Moreover, the changes in the rate of processing non-symbolic information were not explained by the changes in general processing speed. The results also demonstrated that accuracy and RT were positively correlated across all grades. These results indicate that accuracy and the rate of non-symbolic processing reflect two different processes, namely, the maturation and development of a non-symbolic representation system.

Examining aging and numerosity using an integrated diffusion model

Two experiments are presented that use tasks common in research in numerical cognition with young adults and older adults as subjects. In these tasks, one or two arrays of dots are displayed, and subjects decide whether there are more or fewer dots of one kind than another. Results show that older adults, relative to young adults, tend to rely more on the perceptual feature, area, in making numerosity judgments when area is correlated with numerosity. Also, convex hull unexpectedly shows different effects depending on the task (being either correlated with numerosity or anticorrelated). Accuracy and response time (RT) data are interpreted with the integration of the diffusion decision model with models for the representation of numerosity. One model assumes that the representation of the difference depends on the difference between the numerosities and that standard deviations (SDs) increase linearly with numerosity, and the other model assumes a log representation with constant SDs. The representational models have coefficients that are applied to differences between two numerosities to produce drift rates and SDs in drift rates in the decision process. The two tasks produce qualitatively different patterns of RTs: One model fits results from one task, but the results are mixed for the other task. The effects of age on model parameters show a modest decrease in evidence driving the decision process, an increase in the duration of processes outside the decision process (nondecision time), and an increase in the amount of evidence needed to make a decision (boundary separation). (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Precision Inhibitory Stimulation of Individual-Specific Cortical Hubs Disrupts Information Processing in Humans

Noninvasive brain stimulation (NIBS) is a promising treatment for psychiatric and neurologic conditions, but outcomes are variable across treated individuals. In principle, precise targeting of individual-specific features of functional brain networks could improve the efficacy of NIBS interventions. Network theory predicts that the role of a node in a network can be inferred from its connections; as such, we hypothesized that targeting individual-specific "hub" brain areas with NIBS should impact cognition more than nonhub brain areas. Here, we first demonstrate that the spatial positioning of hubs is variable across individuals but reproducible within individuals upon repeated imaging. We then tested our hypothesis in healthy individuals using a prospective, within-subject, double-blind design. Inhibition of a hub with continuous theta burst stimulation disrupted information processing during working-memory more than inhibition of a nonhub area, despite targets being separated by only a few centimeters on the right middle frontal gyrus of each subject. Based upon these findings, we conclude that individual-specific brain network features are functionally relevant and could leveraged as stimulation sites in future NIBS interventions.

Joint modeling of the two-alternative multidimensional forced-choice personality measurement and its response time by a Thurstonian D-diffusion item response model

The two-alternative multidimensional forced-choice measurement of personality has attracted researchers' attention for its tolerance to response bias. Moreover, the response time can be collected along with the item response when personality measurement is conducted with computers. In view of this situation, the objective of this study is to propose a Thurstonian D-diffusion item response theory (IRT) model, which combines two key existing frameworks: the Thurstonian IRT model for forced-choice measurement and the D-diffusion IRT model for the response time in personality measurement. The proposed model reflects the psychological theories behind the data-generating mechanism of the item response and response time. A simulation study reveals that the proposed model can successfully recover the parameters and factor structure in typical application settings. A real data application reveals that the proposed model estimates similar but still different parameter values compared to the original Thurstonian IRT model, and this difference can be explained by the response time information. In addition, the proposed model successfully reflects the distance-difficulty relationship between the response time and the latent relative respondent position.

No calculation necessary: Accessing magnitude through decimals and fractions

Research on how humans understand the relative magnitude of symbolic fractions presents a unique case of the symbol-grounding problem with numbers. Specifically, how do people access a holistic sense of rational number magnitude from decimal fractions (e.g. 0.125) and common fractions (e.g. 1/8)? Researchers have previously suggested that people cannot directly access magnitude information from common fraction notation, but instead must use a form of calculation to access this meaning. Questions remain regarding the nature of calculation and whether a division-like conversion to decimals is a necessary process that permits access to fraction magnitudes. To test whether calculation is necessary to access fractions magnitudes, we carried out a series of six parallel experiments in which we examined how adults access the magnitude of rational numbers (decimals and common fractions) under varying task demands. We asked adult participants to indicate which of two fractions was larger in three different conditions: decimal-decimal, fraction-fraction, and mixed decimal-fraction pairs. Across experiments, we manipulated two aspects of the task demands. 1) Response windows were limited to 1, 2 or 5 s, and 2) participants either did or did not have to identify when the two stimuli were the same magnitude (catch trials). Participants were able to successfully complete the task even at a response window of 1 s and showed evidence of holistic magnitude processing. These results indicate that calculation strategies with fractions are not necessary for accessing a sense of a fractions meaning but are strategic routes to magnitude that participants may use when granted sufficient time. We suggest that rapid magnitude processing with fractions and decimals may occur by mapping symbolic components onto common amodal mental representations of rational numbers.

Decision making in numeracy tasks with spatially continuous scales

A diffusion model of decision making on continuous response scales is applied to three numeracy tasks. The goal is to explain the distributions of responses on the continuous response scale and the time taken to make decisions. In the model, information from a stimulus is spatially continuously distributed, the response is made by accumulating information to a criterion, which is a 1D line, and the noise in the accumulation process is continuous Gaussian process noise over spatial position. The model is fit to the data from three experiments. In one experiment, a one or two digit number is displayed and the task is to point to its location on a number line ranging from 1 to 100. This task is used extensively in research in education but there has been no model for it that accounts for both decision times and decision choices. In the second task, an array of dots is displayed and the task is to point to the position of the number of dots on an arc ranging from 11 to 90. In a third task, an array of dots is displayed and the task is to speak aloud the number of dots. The model we propose accounts for both accuracy and response time variables, including the full distributions of response times. It also provides estimates of the acuity of decisions (standard deviations in the evidence distributions) and it shows how representations of numeracy information are task-dependent. We discuss how our model relates to research on numeracy and the neuroscience of numeracy, and how it can produce more comprehensive measures of individual differences in numeracy skills in tasks with continuous response scales than have hitherto been available.

Automatic place-value activation in magnitude-irrelevant parity judgement

Research on multi-digit number processing suggests that, in Arabic numerals, their place-value magnitude is automatically activated, whenever a magnitude-relevant task was employed. However, so far, it is unknown, whether place-value is also activated when the target task is magnitude-irrelevant. The current study examines this question using the parity congruency effect in two-digit numbers: It describes that responding to decade-digit parity congruent numbers (e.g., 35, 46; same parity of decades and units) is faster than to decade-digit parity incongruent numbers (e.g., 25; 36; different parities of decades and units). Here we investigate the (a-) symmetry of the parity congruency effect; i.e. whether it makes a difference whether participants are assessing the parity of the unit digit or the decade digit. We elaborate, how and why such an asymmetry is related to place-value processing, because the parity of the unit digit only interferes with the parity of the decade digit, while the parity of the decade digit interferes with both the parity of the unit digit and the integrated parity of the whole two-digit number. We observed a significantly larger parity congruency effect in the decade parity decision than in the unit parity decision. This suggests that automatic place-value processing also takes place in a typical parity judgment task, in which magnitude is irrelevant. Finally, because of the cross-lingual design of the study, we can show that these results and their implications were language-independent.

Slow and steady? Strategic adjustments in response caution are moderately reliable and correlate across tasks

Speed-accuracy trade-offs are often considered a confound in speeded choice tasks, but individual differences in strategy have been linked to personality and brain structure. We ask whether strategic adjustments in response caution are reliable, and whether they correlate across tasks and with impulsivity traits. In Study 1, participants performed Eriksen flanker and Stroop tasks in two sessions four weeks apart. We manipulated response caution by emphasising speed or accuracy. We fit the diffusion model for conflict tasks and correlated the change in boundary (accuracy - speed) across session and task. We observed moderate test-retest reliability, and medium to large correlations across tasks. We replicated this between-task correlation in Study 2 using flanker and perceptual decision tasks. We found no consistent correlations with impulsivity. Though moderate reliability poses a challenge for researchers interested in stable traits, consistent correlation between tasks indicates there are meaningful individual differences in the speed-accuracy trade-off.

Implications of Change/Stability Patterns in Children's Non-symbolic and Symbolic Magnitude Judgment Abilities Over One Year: A Latent Transition Analysis

Non-symbolic magnitude abilities are often claimed to support the acquisition of symbolic magnitude abilities, which, in turn, are claimed to support emerging math abilities. However, not all studies find links between non-symbolic and symbolic magnitude abilities, or between them and math ability. To investigate possible reasons for these different findings, recent research has analyzed differences in non-symbolic/symbolic magnitude abilities using latent class modeling and has identified four different magnitude ability profiles residing within the general magnitude ability distribution that were differentially related to cognitive and math abilities. These findings may help explain the different patterns of findings observed in previous research. To further investigate this possibility, we (1) attempted to replicate earlier findings, (2) determine whether magnitude ability profiles remained stable or changed over 1 year; and (3) assessed the degree to which stability/change in profiles were related to cognitive and math abilities. We used latent transition analysis to investigate stability/changes in non-symbolic and symbolic magnitude abilities of 109 5- to 6-year olds twice in 1 year. At Time 1 and 2, non-symbolic and symbolic magnitude abilities, number transcoding and single-digit addition abilities were assessed. Visuospatial working memory (VSWM), naming numbers, non-verbal IQ, basic RT was also assessed at Time 1. Analysis showed stability in one profile and changes in the three others over 1 year. VSWM and naming numbers predicted profile membership at Time 1 and 2, and profile membership predicted math abilities at both time points. The findings confirm the existence of four different non-symbolic-symbolic magnitude ability profiles; we suggest the changes over time in them potentially reflect deficit, delay, and normal math developmental pathways.

Low and variable correlation between reaction time costs and accuracy costs explained by accumulation models: Meta-analysis and simulations

The underpinning assumption of much research on cognitive individual differences (or group differences) is that task performance indexes cognitive ability in that domain. In many tasks performance is measured by differences (costs) between conditions, which are widely assumed to index a psychological process of interest rather than extraneous factors such as speed-accuracy trade-offs (e.g., Stroop, implicit association task, lexical decision, antisaccade, Simon, Navon, flanker, and task switching). Relatedly, reaction time (RT) costs or error costs are interpreted similarly and used interchangeably in the literature. All of this assumes a strong correlation between RT-costs and error-costs from the same psychological effect. We conducted a meta-analysis to test this, with 114 effects across a range of well-known tasks. Counterintuitively, we found a general pattern of weak, and often no, association between RT and error costs (mean r = .17, range -.45 to .78). This general problem is accounted for by the theoretical framework of evidence accumulation models, which capture individual differences in (at least) 2 distinct ways. Differences affecting accumulation rate produce positive correlation. But this is cancelled out if individuals also differ in response threshold, which produces negative correlations. In the models, subtractions between conditions do not isolate processing costs from caution. To demonstrate the explanatory power of synthesizing the traditional subtraction method within a broader decision model framework, we confirm 2 predictions with new data. Thus, using error costs or RT costs is more than a pragmatic choice; the decision carries theoretical consequence that can be understood through the accumulation model framework. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Decision making on spatially continuous scales

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 1 dimensional [1D] line or a 2 dimensional [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. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Adults with Poor Reading Skills, Older Adults, and College Students: the Meanings They Understand During Reading Using a Diffusion Model Analysis

When a word is read in a text, the aspects of its meanings that are encoded should be those relevant to the text and not those that are irrelevant. We tested whether older adults, college students, and adults with poor literacy skills accomplish contextually relevant encoding. Participants read short stories, which were followed by true/false test sentences. Among these were sentences that matched the relevant meaning of a word in a story and sentences that matched a different meaning. We measured the speed and accuracy of responses to the test sentences and used a decision model to separate the information that a reader encodes from the reader's speed/accuracy tradeoff settings. We found that all three groups encoded meanings as contextually relevant. The findings illustrate how a decision-making model combined with tests of particular comprehension processes can lead to further understanding of reading skills.

More than simple facts: cross-linguistic differences in place-value processing in arithmetic fact retrieval

Linguistic specificities such as the inversion property of number words (e.g., in German 43 is spoken dreiundvierzig, literally three and  forty) moderate Arabic number processing. So far, cross-linguistic studies have mostly focused on inversion-related effects on simple (e.g., number comparison) and calculation-based (e.g., multi-digit addition) magnitude processing of numerical information. Despite the assumption that multiplication facts are represented in verbal format, not much attention has been paid to inversion-related influences on multiplication fact retrieval. Accordingly, the current study evaluated inversion-related effects on the processing of place-value information in multiplication. In a verification paradigm, the decade consistency effect (i.e., more errors when the decade of a solution probe shares the decade digit with the correct solution) was larger for English- than German-speaking participants for table-related probes. Processing of decade digits might be prioritised in English-speaking participants because the decade digit is named first in English number words, whereas in German number words the unit digit is named first. Our results indicate that (1) the influence of specificities of a verbal number word formation on place-value processing generalise to arithmetic fact retrieval and (2) inversion of number words might even be advantageous in specific cases.

A threshold-free model of numerosity comparisons

A dominant mechanism in the Judgment and Decision Making literature states that information is accumulated about each choice option until a decision threshold is met. Only after that threshold does a subject start to execute a motor response to indicate their choice. However, recent research has revealed spatial gradients in motor responses as a function of comparison difficulty as well as changes-of-mind in the middle of an action, both suggesting continued accumulation and processing of decision-related signals after the decision boundary. Here we present a formal model and supporting data from a number comparison task that a continuous motor planner, combined with a simple statistical inference scheme, can model detailed behavioral effects without assuming a threshold. This threshold-free model reproduces subjects’ sensitivity to numerical distance in reaching, accuracy, reaction time, and changes of mind. We argue that the motor system positions the effectors using an optimal biomechanical feedback controller, and continuous statistical inference on outputs from cognitive processes.

Modeling numerosity representation with an integrated diffusion model

Models of the representation of numerosity information used in discrimination tasks are integrated with a diffusion decision model. The representation models assume distributions of numerosity either with means and SD that increase linearly with numerosity or with means that increase logarithmically with constant SD. The models produce coefficients that are applied to differences between two numerosities to produce drift rates and these drive the decision process. The linear and log models make differential predictions about how response time (RT) distributions and accuracy change with numerosity and which model is successful depends on the task. When the task is to decide which of two side-by-side arrays of dots has more dots, the log model fits decreasing accuracy and increasing RT as numerosity increases. When the task is to decide, for dots of two colors mixed in a single array, which color has more dots, the linear model fits decreasing accuracy and decreasing RT as numerosity increases. For both tasks, variables such as the areas covered by the dots affect performance, but if the task is changed to one in which the subject has to decide whether the number of dots in a single array is more or less than a standard, the variables have little effect on performance. Model parameters correlate across tasks suggesting commonalities in the abilities to perform them. Overall, results show that the representation used depends on the task and no single representation can account for the data from all the paradigms. (PsycINFO Database Record

A Diffusion Model Analysis of Magnitude Comparison in Children with and without Dyscalculia: Care of Response and Ability Are Related to Both Mathematical Achievement and Stimuli

The respective roles of the approximate number system (ANS) and an access deficit (AD) in developmental dyscalculia (DD) are not well-known. Most studies rely on response times (RTs) or accuracy (error rates) separately. We analyzed the results of two samples of elementary school children in symbolic magnitude comparison (MC) and non-symbolic MC using a diffusion model. This approach uses the joint distribution of both RTs and accuracy in order to synthesize measures closer to ability and response caution or response conservatism. The latter can be understood in the context of the speed-accuracy tradeoff: It expresses how much a subject trades in speed for improved accuracy. We found significant effects of DD on both ability (negative) and response caution (positive) in MC tasks and a negative interaction of DD with symbolic task material on ability. These results support that DD subjects suffer from both an impaired ANS and an AD and in particular support that slower RTs of children with DD are indeed related to impaired processing of numerical information. An interaction effect of symbolic task material and DD (low mathematical ability) on response caution could not be refuted. However, in a sample more representative of the general population we found a negative association of mathematical ability and response caution in symbolic but not in non-symbolic task material. The observed differences in response behavior highlight the importance of accounting for response caution in the analysis of MC tasks. The results as a whole present a good example of the benefits of a diffusion model analysis.

Internal and external sources of variability in perceptual decision-making

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. (PsycINFO Database Record

Improved information pooling for hierarchical cognitive models through multiple and covaried regression

Cognitive process models are fit to observed data to infer how experimental manipulations modify the assumed underlying cognitive process. They are alternatives to descriptive models, which only capture differences on the observed data level, and do not make assumptions about the underlying cognitive process. Process models may require more observations than descriptive models however, and as a consequence, usually fewer conditions can be simultaneously modeled with them. Unfortunately, it is known that the predictive validity of a model may be compromised when fewer experimental conditions are jointly accounted for (e.g., overestimation of predictor effects, or their incorrect assignment). We develop a hierarchical and covaried multiple regression approach to address this problem. Specifically, we show how to map the recurrences of all conditions, participants, items, and/or traits across experimental design cells to the process model parameters. This systematic pooling of information can facilitate parameter estimation. The proposed approach is particularly relevant for multi-factor experimental designs, and for mixture models that parameterize per cell to assess predictor effects. This hierarchical framework provides the capacity to model more conditions jointly to improve parameter recovery at low observation numbers (e.g., using only 1/6 of trials, recovering as well as standard hierarchical Bayesian methods), and to directly model predictor and covariate effects on the process parameters, without the need for post hoc analyses (e.g., ANOVA). An example application to real data is also provided.

How numbers mean: Comparing random walk models of numerical cognition varying both encoding processes and underlying quantity representations

How do people derive meaning from numbers? Here, we instantiate the primary theories of numerical representation in computational models and compare simulated performance to human data. Specifically, we fit simulated data to the distributions for correct and incorrect responses, as well as the pattern of errors made, in a traditional "relative quantity" task. The results reveal that no current theory of numerical representation can adequately account for the data without additional assumptions. However, when we introduce repeated, error-prone sampling of the stimulus (e.g., Cohen, 2009) superior fits are achieved when the underlying representation of integers reflects linear spacing with constant variance. These results provide new insights into (i) the detailed nature of mental numerical representation, and, (ii) general perceptual processes implemented by the human visual system.

The Dynamics of Functional Brain Networks: Integrated Network States during Cognitive Task Performance

Higher brain function relies upon the ability to flexibly integrate information across specialized communities of brain regions; however, it is unclear how this mechanism manifests over time. In this study, we used time-resolved network analysis of fMRI data to demonstrate that the human brain traverses between functional states that maximize either segregation into tight-knit communities or integration across otherwise disparate neural regions. Integrated states enable faster and more accurate performance on a cognitive task, and are associated with dilations in pupil diameter, suggesting that ascending neuromodulatory systems may govern the transition between these alternative modes of brain function. Together, our results confirm a direct link between cognitive performance and the dynamic reorganization of the network structure of the brain.

A Systematic Investigation of Accuracy and Response Time Based Measures Used to Index ANS Acuity

The approximate number system (ANS) was proposed to be a building block for later mathematical abilities. Several measures have been used interchangeably to assess ANS acuity. Some of these measures were based on accuracy data, whereas others relied on response time (RT) data or combined accuracy and RT data. Previous studies challenged the view that all these measures can be used interchangeably, because low correlations between some of the measures had been observed. These low correlations might be due to poor reliability of some of the measures, since the majority of these measures are mathematically related. Here we systematically investigated the relationship between common ANS measures while avoiding the potential confound of poor reliability. Our first experiment revealed high correlations between all accuracy based measures supporting the assumption that all of them can be used interchangeably. In contrast, not all RT based measures were highly correlated. Additionally, our results revealed a speed-accuracy trade-off. Thus, accuracy and RT based measures provided conflicting conclusions regarding ANS acuity. Therefore, we investigated in two further experiments which type of measure (accuracy or RT) is more informative about the underlying ANS acuity, depending on participants’ preferences for accuracy or speed. To this end, we manipulated participants’ preferences for accuracy or speed both explicitly using different task instructions and implicitly varying presentation duration. Accuracy based measures were more informative about the underlying ANS acuity than RT based measures. Moreover, the influence of the underlying representations on accuracy data was more pronounced when participants preferred accuracy over speed after the accuracy instruction as well as for long or unlimited presentation durations. Implications regarding the diffusion model as a theoretical framework of dot comparison as well as regarding the relationship between ANS acuity and math performance are discussed.

Cognitive factors affecting children's nonsymbolic and symbolic magnitude judgment abilities: A latent profile analysis

Early math abilities are claimed to be linked to magnitude representation ability. Some claim that nonsymbolic magnitude abilities scaffold the acquisition of symbolic (Arabic number) magnitude abilities and influence math ability. Others claim that symbolic magnitude abilities, and ipso facto math abilities, are independent of nonsymbolic abilities and instead depend on the ability to process number symbols (e.g., 2, 7). Currently, the issue of whether symbolic abilities are or are not related to nonsymbolic abilities, and the cognitive factors associated with nonsymbolic-symbolic relationships, remains unresolved. We suggest that different nonsymbolic-symbolic relationships reside within the general magnitude ability distribution and that different cognitive abilities are likely associated with these different relationships. We further suggest that the different nonsymbolic-symbolic relationships and cognitive abilities in combination differentially predict math abilities. To test these claims, we used latent profile analysis to identify nonsymbolic-symbolic judgment patterns of 124, 5- to 7-year-olds. We also assessed four cognitive factors (visuospatial working memory [VSWM], naming numbers, nonverbal IQ, and basic reaction time [RT]) and two math abilities (number transcoding and single-digit addition abilities). Four nonsymbolic-symbolic ability profiles were identified. Naming numbers, VSWM, and basic RT abilities were differentially associated with the different ability profiles and in combination differentially predicted math abilities. Findings show that different patterns of nonsymbolic-symbolic magnitude abilities can be identified and suggest that an adequate account of math development should specify the inter-relationship between cognitive factors and nonsymbolic-symbolic ability patterns.

Modeling Individual Differences in the Go/No-go Task with a Diffusion Model

The go/no-go task is one in which there are two choices, but the subject responds only to one of them, waiting out a time-out for the other choice. The task has a long history in psychology and modern applications in the clinical/neuropsychological domain. In this article we fit a diffusion model to both experimental and simulated data. The model is the same as the two-choice model and assumes that there are two decision boundaries and termination at one of them produces a response and at the other, the subject waits out the trial. In prior modeling, both two-choice and go/no-go data were fit simultaneously and only group data were fit. Here the model is fit to just go/no-go data for individual subjects. This allows analyses of individual differences which is important for clinical applications. First, we fit the standard two-choice model to two-choice data and fit the go/no-go model to RTs from one of the choices and accuracy from the two-choice data. Parameter values were similar between the models and had high correlations. The go/no-go model was also fit to data from a go/no-go version of the task with the same subjects as the two-choice task. A simulation study with ranges of parameter values that are obtained in practice showed similar parameter recovery between the two-choice and go/no-go models. Results show that a diffusion model with an implicit (no response) boundary can be fit to data with almost the same accuracy as fitting the two-choice model to two-choice data.