A comparison of bounded diffusion models for choice in time controlled tasks

The Wiener diffusion model (WDM) for 2-alternative tasks assumes that sensory information is integrated over time. Recent neurophysiological studies have found neural correlates of this integration process in certain neuronal populations. This paper analyses the properties of the WDM with two different boundary conditions in decision making tasks in which the time of response is indicated by a cue. A dual reflecting boundary mechanism is proposed and its performance is compared with a well-established absorbing boundary in the cases of the WDM, the WDM with extensions, and the WDM with prior probability. The two types of boundary influence the dynamics of the model and introduce differential weighting of evidence. Comparisons with Ornstein-Uhlenbeck models are also done, and it is shown that the WDM with both types of boundary achieves similar performance and produces similar fits to existing behavioural data. Further studies are proposed to distinguish which boundary mechanism is more consistent with experimental data.     

An EZ-diffusion model for response time and accuracy

The EZ-diffusion model for two-choice response time tasks takes mean response time, the variance of response time, and response accuracy as inputs. The model transforms these data via three simple equations to produce unique values for the quality of information, response conservativeness, and nondecision time. This transformation of observed data in terms of unobserved variables addresses the speed—accuracy trade-off and allows an unambiguous quantification of performance differences in two-choice response time tasks. The EZ-diffusion model can be applied to data-sparse situations to facilitate individual subject analysis. We studied the performance of the EZ-diffusion model in terms of parameter recovery and robustness against misspecification by using Monte Carlo simulations. The EZ model was also applied to a real-world data set.     

Effects of aging and IQ on item and associative memory

The effects of aging and IQ on performance were examined in 4 memory tasks: item recognition, associative recognition, cued recall, and free recall. For item and associative recognition, accuracy and the response time (RT) distributions for correct and error responses were explained by Ratcliff's (1978) diffusion model at the level of individual participants. The values of the components of processing identified by the model for the recognition tasks, as well as accuracy for cued and free recall, were compared across levels of IQ (ranging from 85 to 140) and age (college age, 60-74 years old, and 75-90 years old). IQ had large effects on drift rate in recognition and recall performance, except for the oldest participants with some measures near floor. Drift rates in the recognition tasks, accuracy in recall, and IQ all correlated strongly. However, there was a small decline in drift rates for item recognition and a large decline for associative recognition and cued recall accuracy (70%). In contrast, there were large effects of age on boundary separation and nondecision time (which correlated across tasks) but small effects of IQ. The implications of these results for single- and dual-process models of item recognition are discussed, and it is concluded that models that deal with both RTs and accuracy are subject to many more constraints than are models that deal with only one of these measures. Overall, the results of the study show a complicated but interpretable pattern of interactions that present important targets for modeling.     

Multisensory processing of redundant information in go/no-go and choice responses

In multisensory research, faster responses are commonly observed when multimodal stimuli are presented, as compared to unimodal target presentations. This so-called redundant-signals effect can be explained by several frameworks, including separate-activation and coactivation models. The redundant-signals effect has been investigated in a large number of studies; however, most of those studies have been limited to the rejection of separate-activation models. Coactivation models have been analyzed in only a few studies, primarily using simple response tasks. Here, we investigated the mechanism of multisensory integration underlying go/no-go and choice responses to redundant auditory–visual stimuli. In the present study, the mean and variance of response times, as well as the accuracy rates of go/no-go and choice responses, were used to test a coactivation model based on the linear superposition of diffusion processes (Schwarz, 1994) within two absorbing barriers. The diffusion superposition model accurately describes the means and variances of response times as well as the proportions of correct responses observed in the two tasks. Linear superposition thus seems to be a general principle in the integration of redundant information provided by different sensory channels, and is not restricted to simple responses. The results connect existing theories of multisensory integration with theories on choice behavior.     

Linking together different measures of preference: A dynamic model of matching derived from decision field theory

Two frequently used tasks for measuring preferences among gambles are choice and selling price tasks. However, the rank orders observed with these tasks do not agree, and these disagreements are called preference reversals. In this article, we propose an extension of decision field theory that was originally designed to account for choice probability and the distribution of choice response times. In this extension, we show how this same theory can be used to derive predictions for the distribution of values produced by selling price tasks. This model not only accounts for the basic preference reversal results but also can explain the effects of various information processing factors on preference reversals including time, effort, and practice. We conclude by summarizing the advantages of the decision field matching model over two earlier models of choice and selling prices—expression theory and the contingent weighting model.     

Interval bias in 2AFC detection tasks: sorting out the artifacts

Proportion correct in two-alternative forced choice (2AFC) detection tasks often varies when the stimulus is presented in the first or in the second interval. Reanalysis of published data reveals that these order effects (or interval bias) are strong and prevalent, refuting the standard difference model of signal detection theory. Order effects are commonly regarded as evidence that observers use an off-center criterion under the difference model with bias. We consider an alternative difference model with indecision whereby observers are occasionally undecided and guess with some bias toward one of the response options. Whether or not the data show order effects, the two models fit 2AFC data indistinguishably, but they yield meaningfully different estimates of sensory parameters. Under indeterminacy as to which model governs 2AFC performance, parameter estimates are suspect and potentially misleading. The indeterminacy can be circumvented by modifying the response format so that observers can express indecision when needed. Reanalysis of published data collected in this way lends support to the indecision model. We illustrate alternative approaches to fitting psychometric functions under the indecision model and discuss designs for 2AFC experiments that improve the accuracy of parameter estimates, whether or not order effects are apparent in the data.     

Heterogeneity of strategy use in the Iowa gambling task: A comparison of win-stay/lose-shift and reinforcement learning models

The Iowa gambling task (IGT) has been used in numerous studies, often to examine decision-making performance in different clinical populations. Reinforcement learning (RL) models such as the expectancy valence (EV) model have often been used to characterize choice behavior in this work, and accordingly, parameter differences from these models have been used to examine differences in decision-making processes between different populations. These RL models assume a strategy whereby participants incrementally update the expected rewards for each option and probabilistically select options with higher expected rewards. Here we show that a formal model that assumes a win-stay/lose-shift (WSLS) strategy—which is sensitive only to the outcome of the previous choice—provides the best fit to IGT data from about half of our sample of healthy young adults, and that a prospect valence learning (PVL) model that utilizes a decay reinforcement learning rule provides the best fit to the other half of the data. Further analyses suggested that the better fits of the WSLS model to many participants’ data were not due to an enhanced ability of the WSLS model to mimic the RL strategy assumed by the PVL and EV models. These results suggest that WSLS is a common strategy in the IGT and that both heuristic-based and RL-based models should be used to inform decision-making behavior in the IGT and similar choice tasks.     

The counterintuitive impact of responses and response times on parameter estimates in the drift diffusion model

Given a drift diffusion model with unknown drift and boundary parameters, we analyse the behaviour of maximum likelihood estimates with respect to changes of responses and response times. It is shown analytically that a single fast response time can dominate the estimation in that no matter how many correct answers a test taker provides, the estimate of the drift (ability) parameter decreases to zero. In addition, it is shown that although higher drift rates imply shorter response times, the reverse implication does not hold for the estimates: shorter response times can decrease the drift rate estimate. In the light of these analytical results, we illustrate the actual impact of the findings in a small simulation for a mental rotation test. The method of analysis outlined is applicable to a broader range of models, and we emphasize the need to further check currently used reaction time models within this framework.     

The Parallel Episodic Processing (PEP) model 2.0: A single computational model of stimulus-response binding,contingency learning,power curves,and mixing costs

The current paper presents an extension of the Parallel Episodic Processing model. The model is developed for simulating behaviour in performance (i.e., speeded response time) tasks and learns to anticipate both how and when to respond based on retrieval of memories of previous trials. With one fixed parameter set, the model is shown to successfully simulate a wide range of different findings. These include: practice curves in the Stroop paradigm, contingency learning effects, learning acquisition curves, stimulus-response binding effects, mixing costs, and various findings from the attentional control domain. The results demonstrate several important points. First, the same retrieval mechanism parsimoniously explains stimulus-response binding, contingency learning, and practice effects. Second, as performance improves with practice, any effects will shrink with it. Third, a model of simple learning processes is sufficient to explain phenomena that are typically (but perhaps incorrectly) interpreted in terms of higher-order control processes. More generally, we argue that computational models with a fixed parameter set and wider breadth should be preferred over those that are restricted to a narrow set of phenomena.     

Drawing conclusions from choice response time models: A tutorial using the linear ballistic accumulator

Cognitive models of choice and response times can lead to deeper insights into the processes underlying decisions than standard analyses of accuracy and response time data. The application of these models, however, has historically been reserved for the authors of the models, and their associates. Recently, choice response time models have become more accessible through the release of user-friendly software for estimating their parameters. The aim of this tutorial is to provide guidance about the process of using these parameter estimates and associated model fits to make conclusions about experimental data. We use an application of one response time model, the linear ballistic accumulator, as an example to demonstrate the steps required to select an appropriate parametric characterization of a data set. We also discuss how to evaluate the quality of the agreement between model and data, including guidelines for presenting model predictions for group-level data.     

Integration of anatomical and external response mappings explains crossing effects in tactile localization: A probabilistic modeling approach

To act upon a tactile stimulus its original skin-based, anatomical spatial code has to be transformed into an external, posture-dependent reference frame, a process known as tactile remapping. When the limbs are crossed, anatomical and external location codes are in conflict, leading to a decline in tactile localization accuracy. It is unknown whether this impairment originates from the integration of the resulting external localization response with the original, anatomical one or from a failure of tactile remapping in crossed postures. We fitted probabilistic models based on these diverging accounts to the data from three tactile localization experiments. Hand crossing disturbed tactile left–right location choices in all experiments. Furthermore, the size of these crossing effects was modulated by stimulus configuration and task instructions. The best model accounted for these results by integration of the external response mapping with the original, anatomical one, while applying identical integration weights for uncrossed and crossed postures. Thus, the model explained the data without assuming failures of remapping. Moreover, performance differences across tasks were accounted for by non-individual parameter adjustments, indicating that individual participants’ task adaptation results from one common functional mechanism. These results suggest that remapping is an automatic and accurate process, and that the observed localization impairments in touch result from a cognitively controlled integration process that combines anatomically and externally coded responses.     

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.     

Bayes factors for the linear ballistic accumulator model of decision-making

Evidence accumulation models of decision-making have led to advances in several different areas of psychology. These models provide a way to integrate response time and accuracy data, and to describe performance in terms of latent cognitive processes. Testing important psychological hypotheses using cognitive models requires a method to make inferences about different versions of the models which assume different parameters to cause observed effects. The task of model-based inference using noisy data is difficult, and has proven especially problematic with current model selection methods based on parameter estimation. We provide a method for computing Bayes factors through Monte-Carlo integration for the linear ballistic accumulator (LBA; Brown and Heathcote, 2008), a widely used evidence accumulation model. Bayes factors are used frequently for inference with simpler statistical models, and they do not require parameter estimation. In order to overcome the computational burden of estimating Bayes factors via brute force integration, we exploit general purpose graphical processing units; we provide free code for this. This approach allows estimation of Bayes factors via Monte-Carlo integration within a practical time frame. We demonstrate the method using both simulated and real data. We investigate the stability of the Monte-Carlo approximation, and the LBA’s inferential properties, in simulation studies.     

On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints

The authors show how the use of inequality constraints on parameters in structural equation models may affect the distribution of the likelihood ratio test. Inequality constraints are implicitly used in the testing of commonly applied structural equation models, such as the common factor model, the autoregressive model, and the latent growth curve model, although this is not commonly acknowledged. Such constraints are the result of the null hypothesis in which the parameter value or values are placed on the boundary of the parameter space. For instance, this occurs in testing whether the variance of a growth parameter is significantly different from 0. It is shown that in these cases, the asymptotic distribution of the chi-square difference cannot be treated as that of a central chi-square-distributed random variable with degrees of freedom equal to the number of constraints. The correct distribution for testing 1 or a few parameters at a time is inferred for the 3 structural equation models mentioned above. Subsequently, the authors describe and illustrate the steps that one should take to obtain this distribution. An important message is that using the correct distribution may lead to appreciably greater statistical power.     

Effects of fatigue induced by repetitive movements and isometric tasks on reaction time

PurposeThe understanding of fatigue of the human motor system is important in the fields of ergonomics, sport, rehabilitation and neurology. In order to understand the interactions between fatigue and reaction time, we evaluated the effects of two different fatiguing tasks on reaction time.Methods83 healthy subjects were included in a case-control study with three arms where single and double choice reaction time tasks were performed before and after 2 min fatiguing task (an isometric task, a finger tapping task and at rest).ResultsAfter an isometric task, the right-fatigued hand was slower in the choice component of a double choice reaction time task (calculated as the individual difference between single and double choice reaction times); also, the subjects that felt more fatigued had slower choice reaction time respect to the baseline assessment. Moreover, in relationship to the performance decay after two minutes, finger tapping task produces more intense fatigability perception.ConclusionsWe confirmed that two minutes of isometric or repetitive tasks are enough to produce fatigue. The fatigue perception is more intense for finger tapping tasks in relation to the performance decay. We therefore confirmed that the two fatiguing tasks produced two different kind of fatigue demonstrating that with a very simple protocol it is possible to test subjects or patients to quantify different form of fatigue.     

Fourteen-month-olds’ imitation is influenced more strongly by a model’s competence than by a model’s certainty

Research has shown that infants are more likely to learn from certain and competent models than from uncertain and incompetent models. However, it is unknown which of these cues to a model’s reliability infants consider more important. In Experiment 1, we investigated whether 14-month-old infants (n = 35) imitate and adopt tool choices selectively from an uncertain but competent compared to a certain but incompetent model. Infants watched videos in which an adult expressed either uncertainty but acted competently or expressed certainty but acted incompetently with familiar objects. In tool-choice tasks, the adult then chose one of two objects to operate an apparatus, and in imitation tasks, the adult then demonstrated a novel action. Infants did not adopt the model’s choice in the tool-choice tasks but they imitated the uncertain but competent model more often than the certain but incompetent model in the imitation tasks. In Experiment 2, 14-month-olds (n = 33) watched videos in which an adult expressed only either certainty or uncertainty in order to test whether infants at this age are sensitive to a model’s certainty. Infants imitated and adopted the tool choice from a certain model more than from an uncertain model. These results suggest that 14-month-olds acknowledge both a model’s competence and certainty when learning novel actions. However, they rely more on a model’s competence than on his certainty when both cues are in conflict. The ability to detect reliable models when learning how to handle cultural artifacts helps infants to become well-integrated members of their culture.     

Measurement of Ability in Adaptive Learning and Assessment Systems when Learners Use On-Demand Hints

Adaptive learning and assessment systems support learners in acquiring knowledge and skills in a particular domain. The learners’ progress is monitored through them solving items matching their level and aiming at specific learning goals. Scaffolding and providing learners with hints are powerful tools in helping the learning process. One way of introducing hints is to make hint use the choice of the student. When the learner is certain of their response, they answer without hints, but if the learner is not certain or does not know how to approach the item they can request a hint. We develop measurement models for applications where such on-demand hints are available. Such models take into account that hint use may be informative of ability, but at the same time may be influenced by other individual characteristics. Two modeling strategies are considered: (1) The measurement model is based on a scoring rule for ability which includes both response accuracy and hint use. (2) The choice to use hints and response accuracy conditional on this choice are modeled jointly using Item Response Tree models. The properties of different models and their implications are discussed. An application to data from Duolingo, an adaptive language learning system, is presented. Here, the best model is the scoring-rule-based model with full credit for correct responses without hints, partial credit for correct responses with hints, and no credit for all incorrect responses. The second dimension in the model accounts for the individual differences in the tendency to use hints.     

A computational model of anterior cingulate function in speeded response tasks: effects of frequency,sequence, and conflict

A growing body of evidence from functional neuroimaging and computational modeling studies indicates that the anterior cingulate cortex (ACC) detects the presence of response conflict and conveys this information to other brain regions, enabling subsequent adjustments in cognitive control. The present study examined previous empirical findings of increased ACC for low-frequency stimuli across three distinct speeded response tasks (two-alternative forced choice, go/no-go, and oddball). Simulations conducted in a neural network model incorporating sequential priming mechanisms (developed in Cho et al., 2002) confirmed that a computational measure of response conflict was higher on low-frequency trials across all three tasks. In addition, the model captured detailed aspects of behavioral reaction time and accuracy data, predicted the dynamics of ACC activity related to trial sequence effects, and provided evidence for the functional role of conflict information in performance monitoring and optimization. The results indicate that the conflict-monitoring hypothesis, augmented by mechanisms for encoding stimulus history, can explain key phenomena associated with performance in sequential speeded response tasks.     

Beyond resources: Formal models of complexity effects and age differences in working memory

We explore several alternative formal models of working memory capacity limits and of the effect of ageing on these capacity limits. Three models test variations of resource accounts, one assumes a fixed number of free slots in working memory, one is based on decay and processing speed, one attributes capacity limits to interference, and one to crosstalk between associations of content and context representations. The models are evaluated by fitting them to time–accuracy functions of 16 young and 17 old adults working on a numerical memory-updating task under varied memory-load conditions. With increasing complexity (i.e., memory load), both asymptotic accuracy and the rate of approach to the asymptote decreased. Old adults reached lower asymptotes with the more complex tasks, and had generally slower rates. The interference model and the decay model fit the individual time–accuracy functions reasonably well, whereas the other models failed to account for the data. Within the interference model, age effects could be attributed to the older adults' higher susceptibility to interference. Within the decay model, old adults differed from young adults by a higher degree of variability in the activation of working memory contents.     

Integrating Cognitive Process and Descriptive Models of Attitudes and Preferences

Discrete choice experiments—selecting the best and/or worst from a set of options—are increasingly used to provide more efficient and valid measurement of attitudes or preferences than conventional methods such as Likert scales. Discrete choice data have traditionally been analyzed with random utility models that have good measurement properties but provide limited insight into cognitive processes. We extend a well‐established cognitive model, which has successfully explained both choices and response times for simple decision tasks, to complex, multi‐attribute discrete choice data. The fits, and parameters, of the extended model for two sets of choice data (involving patient preferences for dermatology appointments, and consumer attitudes toward mobile phones) agree with those of standard choice models. The extended model also accounts for choice and response time data in a perceptual judgment task designed in a manner analogous to best–worst discrete choice experiments. We conclude that several research fields might benefit from discrete choice experiments, and that the particular accumulator‐based models of decision making used in response time research can also provide process‐level instantiations for random utility models.