A hierarchical model for estimating response time distributions

Age-dependent changes in the anger superiority effect: Evidence from a visual search task

The perception of threatening facial expressions is a critical skill necessary for detecting the emotional states of others and responding appropriately. The anger superiority effect hypothesis suggests that individuals are better at processing and identifying angry faces compared with other nonthreatening facial expressions. In adults, the anger superiority effect is present even after controlling for the bottom-up visual saliency, and when ecologically valid stimuli are used. However, it is as yet unclear whether this effect is present in children. To fill this gap, we tested the anger superiority effect in children ages 6-14 years in a visual search task by using emotional dynamic stimuli and equating the visual salience of target and distractors. The results suggest that in childhood, the angry superiority effect consists of improved accuracy in detecting angry faces, while in adolescence, the ability to discriminate angry faces undergoes further development, enabling faster and more accurate threat detection.

A hybrid approach to dynamic cognitive psychometrics : Dynamic cognitive psychometrics

Dynamic cognitive psychometrics measures mental capacities based on the way behavior unfolds over time. It does so using models of psychological processes whose validity is grounded in research from experimental psychology and the neurosciences. However, these models can sometimes have undesirable measurement properties. We propose a "hybrid" modeling approach that achieves good measurement by blending process-based and descriptive components. We demonstrate the utility of this approach in the stop-signal paradigm, in which participants make a series of speeded choices, but occasionally are required to withhold their response when a "stop signal" occurs. The stop-signal paradigm is widely used to measure response inhibition based on a modeling framework that assumes a race between processes triggered by the choice and the stop stimuli. However, the key index of inhibition, the latency of the stop process (i.e., stop-signal reaction time), is not directly observable, and is poorly estimated when the choice and the stop runners are both modeled by psychologically realistic evidence-accumulation processes. We show that using a descriptive account of the stop process, while retaining a realistic account of the choice process, simultaneously enables good measurement of both stop-signal reaction time and the psychological factors that determine choice behavior. We show that this approach, when combined with hierarchical Bayesian estimation, is effective even in a complex choice task that requires participants to perform only a relatively modest number of test trials.

Why many studies of individual differences with inhibition tasks may not localize correlations

Individual difference exploration of cognitive domains is predicated on being able to ascertain how well performance on tasks covary. Yet, establishing correlations among common inhibition tasks such as Stroop or flanker tasks has proven quite difficult. It remains unclear whether this difficulty occurs because there truly is a lack of correlation or whether analytic techniques to localize correlations perform poorly real-world contexts because of excessive measurement error from trial noise. In this paper, we explore how well correlations may localized in large data sets with many people, tasks, and replicate trials. Using hierarchical models to separate trial noise from true individual variability, we show that trial noise in 24 extant tasks is about 8 times greater than individual variability. This degree of trial noise results in massive attenuation in correlations and instability in Spearman corrections. We then develop hierarchical models that account for variation across trials, variation across individuals, and covariation across individuals and tasks. These hierarchical models also perform poorly in localizing correlations. The advantage of these models is not in estimation efficiency, but in providing a sense of uncertainty so that researchers are less likely to misinterpret variability in their data. We discuss possible improvements to study designs to help localize correlations.

Bayesian hierarchical modeling: an introduction and reassessment

With the recent development of easy-to-use tools for Bayesian analysis, psychologists have started to embrace Bayesian hierarchical modeling. Bayesian hierarchical models provide an intuitive account of inter- and intraindividual variability and are particularly suited for the evaluation of repeated-measures designs. Here, we provide guidance for model specification and interpretation in Bayesian hierarchical modeling and describe common pitfalls that can arise in the process of model fitting and evaluation. Our introduction gives particular emphasis to prior specification and prior sensitivity, as well as to the calculation of Bayes factors for model comparisons. We illustrate the use of state-of-the-art software programs Stan and brms. The result is an overview of best practices in Bayesian hierarchical modeling that we hope will aid psychologists in making the best use of Bayesian hierarchical modeling.

Quantifying Entropy in Response Times (RT) Distributions Using the Cumulative Residual Entropy (CRE) Function

Response times (RT) distributions are routinely used by psychologists and neuroscientists in the assessment and modeling of human behavior and cognition. The statistical properties of RT distributions are valuable in uncovering unobservable psychological mechanisms. A potentially important statistical aspect of RT distributions is their entropy. However, to date, no valid measure of entropy on RT distributions has been developed, mainly because available extensions of discrete entropy measures to continuous distributions were fraught with problems and inconsistencies. The present work takes advantage of the cumulative residual entropy (CRE) function-a well-known differential entropy measure that can circumvent those problems. Applications of the CRE to RT distributions are presented along with concrete examples and simulations. In addition, a novel measure of instantaneous CRE is developed that captures the rate of entropy reduction (or information gain) from a stimulus as a function of processing time. Taken together, the new measures of entropy in RT distributions proposed here allow for stronger statistical inferences, as well as motivated theoretical interpretations of psychological constructs such as mental effort and processing efficiency.

Both the domain-general and the mentalising processes affect visual perspective taking

People's attention cannot help being affected by what others are looking at. The dot-perspective task has been often employed to investigate this visual attentional shift. In this task, participants are presented with virtual scenes with a cue facing some targets and must judge how many targets are visible from their own or the cue perspective. Typically, this task shows an interference pattern: Participants record slower reaction times (RTs) and more errors when the cue is facing away from the targets. Interestingly, this occurs also when participants take their own perspective. Two accounts contend the explanation of this interference. The mentalising account focuses on the social relevance of the cue, while the domain-general account focuses on the directional features of the cue. To investigate the relative contribution of the two accounts, we developed a Social_Only cue, a cue having only social features and compared its effects with a Social+Directional cue, which had both social and directional features. Results show that while the Social+Directional cue generates the typical interference pattern, the Social_Only cue does not generate interference in the RTs, only in the error rate. We advance an integration between the mentalising and the domain-general accounts. We suggest that the dot-perspective task requires two processes: an orienting process, elicited by the directional features of the cue and measured by the RTs, and a decisional process elicited by the social features of the cue and measured also by the error rate.

A Bayesian Mixture Modelling of Stop Signal Reaction Time Distributions: The Second Contextual Solution for the Problem of Aftereffects of Inhibition on SSRT Estimations

The distribution of single Stop Signal Reaction Times (SSRT) in the stop signal task (SST) has been modelled with two general methods: a nonparametric method by Hans Colonius (1990) and a Bayesian parametric method by Dora Matzke, Gordon Logan and colleagues (2013). These methods assume an equal impact of the preceding trial type (go/stop) in the SST trials on the SSRT distributional estimation without addressing the relaxed assumption. This study presents the required model by considering a two-state mixture model for the SSRT distribution. It then compares the Bayesian parametric single SSRT and mixture SSRT distributions in the usual stochastic order at the individual and the population level under ex-Gaussian (ExG) distributional format. It shows that compared to a single SSRT distribution, the mixture SSRT distribution is more varied, more positively skewed, more leptokurtic and larger in stochastic order. The size of the results' disparities also depends on the choice of weights in the mixture SSRT distribution. This study confirms that mixture SSRT indices as a constant or distribution are significantly larger than their single SSRT counterparts in the related order. This result offers a vital improvement in the SSRT estimations.

Sensing and seeing associated with overlapping occipitoparietal activation in simultaneous EEG-fMRI

The presence of a change in a visual scene can influence brain activity and behavior, even in the absence of full conscious report. It may be possible for us to sense that such a change has occurred, even if we cannot specify exactly where or what it was. Despite existing evidence from electroencephalogram (EEG) and eye-tracking data, it is still unclear how this partial level of awareness relates to functional magnetic resonance imaging (fMRI) blood oxygen level dependent (BOLD) activation. Using EEG, fMRI, and a change blindness paradigm, we found multi-modal evidence to suggest that sensing a change is distinguishable from being blind to it. Specifically, trials during which participants could detect the presence of a colour change but not identify the location of the change (sense trials), were compared to those where participants could both detect and localise the change (localise or see trials), as well as change blind trials. In EEG, late parietal positivity and N2 amplitudes were larger for localised changes only, when compared to change blindness. However, ERP-informed fMRI analysis found no voxels with activation that significantly co-varied with fluctuations in single-trial late positivity amplitudes. In fMRI, a range of visual (BA17,18), parietal (BA7,40), and mid-brain (anterior cingulate, BA24) areas showed increased fMRI BOLD activation when a change was sensed, compared to change blindness. These visual and parietal areas are commonly implicated as the storage sites of visual working memory, and we therefore argue that sensing may not be explained by a lack of stored representation of the visual display. Both seeing and sensing a change were associated with an overlapping occipitoparietal network of activation when compared to blind trials, suggesting that the quality of the visual representation, rather than the lack of one, may result in partial awareness during the change blindness paradigm.

Visual search under physical effort is faster but more vulnerable to distractor interference

Cognition and action are often intertwined in everyday life. It is thus pivotal to understand how cognitive processes operate with concurrent actions. The present study aims to assess how simple physical effort operationalized as isometric muscle contractions affects visual attention and inhibitory control. In a dual-task paradigm, participants performed a singleton search task and a handgrip task concurrently. In the search task, the target was a shape singleton among distractors with a homogeneous but different shape. A salient-but-irrelevant distractor with a unique color (i.e., color singleton) appeared on half of the trials (Singleton distractor present condition), and its presence often captures spatial attention. Critically, the visual search task was performed by the participants with concurrent hand grip exertion, at 5% or 40% of their maximum strength (low vs. high physical load), on a hand dynamometer. We found that visual search under physical effort is faster, but more vulnerable to distractor interference, potentially due to arousal and reduced inhibitory control, respectively. The two effects further manifest in different aspects of RT distributions that can be captured by different components of the ex-Gaussian model using hierarchical Bayesian method. Together, these results provide behavioral evidence and a novel model for two dissociable cognitive mechanisms underlying the effects of simple muscle exertion on the ongoing visual search process on a moment-by-moment basis.

Factors Influencing Saccadic Reaction Time: Effect of Task Modality, Stimulus Saliency, Spatial Congruency of Stimuli, and Pupil Size

It is often assumed that the reaction time of a saccade toward visual and/or auditory stimuli reflects the sensitivities of our oculomotor-orienting system to stimulus saliency. Endogenous factors, as well as stimulus-related factors, would also affect the saccadic reaction time (SRT). However, it was not clear how these factors interact and to what extent visual and auditory-targeting saccades are accounted for by common mechanisms. The present study examined the effect of, and the interaction between, stimulus saliency and audiovisual spatial congruency on the SRT for visual- and for auditory-target conditions. We also analyzed pre-target pupil size to examine the relationship between saccade preparation and pupil size. Pupil size is considered to reflect arousal states coupling with locus-coeruleus (LC) activity during a cognitive task. The main findings were that (1) the pattern of the examined effects on the SRT varied between visual- and auditory-auditory target conditions, (2) the effect of stimulus saliency was significant for the visual-target condition, but not significant for the auditory-target condition, (3) Pupil velocity, not absolute pupil size, was sensitive to task set (i.e., visual-targeting saccade vs. auditory-targeting saccade), and (4) there was a significant correlation between the pre-saccade absolute pupil size and the SRTs for the visual-target condition but not for the auditory-target condition. The discrepancy between target modalities for the effect of pupil velocity and between the absolute pupil size and pupil velocity for the correlation with SRT may imply that the pupil effect for the visual-target condition was caused by a modality-specific link between pupil size modulation and the SC rather than by the LC-NE (locus coeruleus-norepinephrine) system. These results support the idea that different threshold mechanisms in the SC may be involved in the initiation of saccades toward visual and auditory targets.

Can hypnotic suggestibility be measured online?

Hypnosis and hypnotic suggestions are gradually gaining popularity within the consciousness community as established tools for the experimental manipulation of illusions of involuntariness, hallucinations and delusions. However, hypnosis is still far from being a widespread instrument; a crucial hindrance to taking it up is the amount of time needed to invest in identifying people high and low in responsiveness to suggestion. In this study, we introduced an online assessment of hypnotic response and estimated the extent to which the scores and psychometric properties of an online screening differ from an offline one. We propose that the online screening of hypnotic response is viable as it reduces the level of responsiveness only by a slight extent. The application of online screening may prompt researchers to run large-scale studies with more heterogeneous samples, which would help researchers to overcome some of the issues underlying the current replication crisis in psychology.

Are divergence point analyses suitable for response time data?

Estimating the time course of the influence of different factors in human performance is one of the major topics of research in cognitive psychology/neuroscience. Over the past decades, researchers have proposed several methods to tackle this question using latency data. Here we examine a recently proposed procedure that employs survival analyses on latency data to provide precise estimates of the timing of the first discernible influence of a given factor (e.g., word frequency on lexical access) on performance (e.g., fixation durations or response times). A number of articles have used this method in recent years, and hence an exploration of its strengths and its potential weaknesses is in order. Unfortunately, our analysis revealed that the technique has conceptual flaws, and it might lead researchers into believing that they are obtaining a measurement of processing components when, in fact, they are obtaining an uninterpretable measurement.

Spontaneous attribution of false beliefs in adults examined using a signal detection approach

Understanding other people have beliefs different from ours or different from reality is critical to social interaction. Previous studies suggest that healthy adults possess an implicit mentalising system, but alternative explanations for data from reaction time false belief tasks have also been given. In this study, we combined signal detection theory (SDT) with a false belief task. As application of SDT allows us to separate perceptual sensitivity from criteria, we are able to investigate how another person's beliefs change the participant's perception of near-threshold stimuli. Participants (n = 55) watched four different videos in which an actor saw (or did not see) a Gabor cube hidden (or not hidden) behind an occluder. At the end of each video, the occluder vanished revealing a cube either with or without Gabor pattern, and participants needed to report whether they saw the Gabor pattern or not. A pre-registered analysis with classical statistics weakly suggests an effect of the actor's belief on participant's perceptions. An exploratory Bayesian analysis supports the idea that when the actor believed the cube was present, participants made slower and more liberal judgements. Although these data are not definitive, these current results indicate the value of new measures for understanding implicit false belief processing.

Validity of Attention Bias Variability Indices for Posttraumatic Stress Disorder Research: Evidence From Patient Data

Although initial findings indicated that threat-related attention bias variability (ABV), an index designed to capture dynamic shifts in threat-related attention over time, was positively correlated with the severity of posttraumatic stress disorder (PTSD) symptoms, a recent study relying on simulated data has raised questions regarding the validity and empirical utility of ABV. Specifically, the simulations suggested that core features of reaction time data distinct from threat-related attention bias, such as the reaction time standard deviation and mean, could explicate the reported elevated ABV among samples with PTSD. In the present study, we evaluated these suggestions in 95 PTSD-diagnosed participants. The results showed that ABV significantly and uniquely predicted PTSD symptom severity beyond the predictive value of core reaction time features, ΔR² = .05-.23. Some of the predictions stemming from the simulated results were replicated, whereas others were not. Contrary to the conclusion drawn from the simulated data, the results from the current study suggest that ABV is a valid and replicable correlate of PTSD symptom severity.

Dynamic models of choice

Parameter estimation in evidence-accumulation models of choice response times is demanding of both the data and the user. We outline how to fit evidence-accumulation models using the flexible, open-source, R-based Dynamic Models of Choice (DMC) software. DMC provides a hands-on introduction to the Bayesian implementation of two popular evidence-accumulation models: the diffusion decision model (DDM) and the linear ballistic accumulator (LBA). It enables individual and hierarchical estimation, as well as assessment of the quality of a model's parameter estimates and descriptive accuracy. First, we introduce the basic concepts of Bayesian parameter estimation, guiding the reader through a simple DDM analysis. We then illustrate the challenges of fitting evidence-accumulation models using a set of LBA analyses. We emphasize best practices in modeling and discuss the importance of parameter- and model-recovery simulations, exploring the strengths and weaknesses of models in different experimental designs and parameter regions. We also demonstrate how DMC can be used to model complex cognitive processes, using as an example a race model of the stop-signal paradigm, which is used to measure inhibitory ability. We illustrate the flexibility of DMC by extending this model to account for mixtures of cognitive processes resulting from attention failures. We then guide the reader through the practical details of a Bayesian hierarchical analysis, from specifying priors to obtaining posterior distributions that encapsulate what has been learned from the data. Finally, we illustrate how the Bayesian approach leads to a quantitatively cumulative science, showing how to use posterior distributions to specify priors that can be used to inform the analysis of future experiments.

Multi-factor analysis in language production: Sequential sampling models mimic and extend regression results

For multi-factor analyses of response times, descriptive models (e.g., linear regression) arguably constitute the dominant approach in psycholinguistics. In contrast empirical cognitive models (e.g., sequential sampling models, SSMs) may fit fewer factors simultaneously, but decompose the data into several dependent variables (a multivariate result), offering more information to analyze. While SSMs are notably popular in the behavioural sciences, they are not significantly developed in language production research. To contribute to the development of this modelling in language, we (i) examine SSMs as a measurement modelling approach for spoken word activation dynamics, and (ii) formally compare SSMs to the default method, regression. SSMs model response activation or selection mechanisms in time, and calculate how they are affected by conditions, persons, and items. While regression procedures also model condition effects, it is only in respect to the mean RT, and little work has been previously done to compare these approaches. Through analyses of two language production experiments, we show that SSMs reproduce regression predictors, and further extend these effects through a multivariate decomposition (cognitive parameters). We also examine a combined regression-SSM approach that is hierarchical Bayesian, which can jointly model more conditions than classic SSMs, and importantly, achieve by-item modelling with other conditions. In this analysis, we found that spoken words principally differed from one another by their activation rates and production times, but not their thresholds to be activated.

Item repetition and retrieval processes in cued recall: Analysis of recall-latency distributions

The SAM (search of associative memory) model provides a unified account of accuracy effects, assuming that retrieval is a cue-dependent two-stage process of sampling and recovery, which depends on the strength of items relative to all others and on that item associated with the sampling trace, respectively. On the other hand, the relative strength model uniquely provides latency predictions, assuming that recall latency is determined solely by relative strength (similar to the sampling rule in SAM): Latency should remain unchanged for strong and weak items in pure lists, but will be shorter for strong items than for weak items in mixed lists. To test the predictions, the present study examined accuracy and latency distributions, which were fit with the ex-Gaussian, using item repetition as a means of strengthening. Massed versus spaced repetitions were used where repetitions were either cue-target pairs or cue alone. When repetitions were spaced in mixed lists, accuracy and latency both increased with cue-target repetitions, relative to cue-only repetitions, and slow recall for cue-target repetitions was due to initially nonretrievable items. However, even after successful recall on a pretest, cue-target repetitions led to an increase in latency in pure lists. These findings are difficult to reconcile with relative-strength explanations of latency. They indeed suggest that (1) separate traces are created for each repetition, (2) memory traces are updated if the item is retrieved (otherwise, new traces are stored), and (3) recovery plays a role in latency, which are discussed with the distinction between sampling and recovery of SAM.

The Role of Dorsal Premotor Cortex in Resolving Abstract Motor Rules: Converging Evidence From Transcranial Magnetic Stimulation and Cognitive Modeling

In this study, repetitive transcranial magnetic stimulation (rTMS) was applied over left dorsal premotor cortex (PMd) while participants performed a novel task paradigm that required planning of responses in accordance with both instructed rules and present stimuli. rTMS is a noninvasive form of neurostimulation that can interfere with ongoing processing of a targeted cortical region, resulting in a transient "virtual lesion" that can reveal the contribution of the region to ongoing behavior. Increased response times (RTs) were observed specifically when rTMS was applied over PMd while participants were preparing to execute a complex response to an uninstructed stimulus. To further delineate the effect of stimulation, condition-specific RT distributions were modeled as three-parameter Weibull distributions through hierarchical Bayesian modeling (HBM). Comparison of the estimated parameters to those of a paired control demonstrated that while PMd-rTMS slightly decreased nondecision time, it also greatly increased the variability in the RT distribution. This increased variability resulted in an overall increase in predicted mean RT and is consistent with a delay in cognitive processes. In conjunction, an ACT-R cognitive model of the task was developed in order to systematically test alternative hypotheses on the potential cognitive functions that may be affected by stimulation of PMd. ACT-R simulations suggested that participant's behavior was due to an effect of TMS on a "re-planning" process, indicating that PMd may be specifically involved in planning of complex motor responses to specific visual stimuli. In conjunction with the HBM modeling effort, these results suggest that PMd-rTMS is capable of pausing or slowing the execution of a motor response-planning process.

Approximating Bayesian Inference through Model Simulation

The ultimate test of the validity of a cognitive theory is its ability to predict patterns of empirical data. Cognitive models formalize this test by making specific processing assumptions that yield mathematical predictions, and the mathematics allow the models to be fitted to data. As the field of cognitive science has grown to address increasingly complex problems, so too has the complexity of models increased. Some models have become so complex that the mathematics detailing their predictions are intractable, meaning that the model can only be simulated. Recently, new Bayesian techniques have made it possible to fit these simulation-based models to data. These techniques have even allowed simulation-based models to transition into neuroscience, where tests of cognitive theories can be biologically substantiated.

Bayesian techniques for analyzing group differences in the Iowa Gambling Task: A case study of intuitive and deliberate decision-makers

The Iowa Gambling Task (IGT) is one of the most popular experimental paradigms for comparing complex decision-making across groups. Most commonly, IGT behavior is analyzed using frequentist tests to compare performance across groups, and to compare inferred parameters of cognitive models developed for the IGT. Here, we present a Bayesian alternative based on Bayesian repeated-measures ANOVA for comparing performance, and a suite of three complementary model-based methods for assessing the cognitive processes underlying IGT performance. The three model-based methods involve Bayesian hierarchical parameter estimation, Bayes factor model comparison, and Bayesian latent-mixture modeling. We illustrate these Bayesian methods by applying them to test the extent to which differences in intuitive versus deliberate decision style are associated with differences in IGT performance. The results show that intuitive and deliberate decision-makers behave similarly on the IGT, and the modeling analyses consistently suggest that both groups of decision-makers rely on similar cognitive processes. Our results challenge the notion that individual differences in intuitive and deliberate decision styles have a broad impact on decision-making. They also highlight the advantages of Bayesian methods, especially their ability to quantify evidence in favor of the null hypothesis, and that they allow model-based analyses to incorporate hierarchical and latent-mixture structures.

Symbolic Number Comparison Is Not Processed by the Analog Number System: Different Symbolic and Non-symbolic Numerical Distance and Size Effects

HIGHLIGHTS

We test whether symbolic number comparison is handled by an analog noisy system.

Analog system model has systematic biases in describing symbolic number comparison.

This suggests that symbolic and non-symbolic numbers are processed by different systems.

Dominant numerical cognition models suppose that both symbolic and non-symbolic numbers are processed by the Analog Number System (ANS) working according to Weber's law. It was proposed that in a number comparison task the numerical distance and size effects reflect a ratio-based performance which is the sign of the ANS activation. However, increasing number of findings and alternative models propose that symbolic and non-symbolic numbers might be processed by different representations. Importantly, alternative explanations may offer similar predictions to the ANS prediction, therefore, former evidence usually utilizing only the goodness of fit of the ANS prediction is not sufficient to support the ANS account. To test the ANS model more rigorously, a more extensive test is offered here. Several properties of the ANS predictions for the error rates, reaction times, and diffusion model drift rates were systematically analyzed in both non-symbolic dot comparison and symbolic Indo-Arabic comparison tasks. It was consistently found that while the ANS model's prediction is relatively good for the non-symbolic dot comparison, its prediction is poorer and systematically biased for the symbolic Indo-Arabic comparison. We conclude that only non-symbolic comparison is supported by the ANS, and symbolic number comparisons are processed by other representation.

Bayesian statistical approaches to evaluating cognitive models

Cognitive models aim to explain complex human behavior in terms of hypothesized mechanisms of the mind. These mechanisms can be formalized in terms of mathematical structures containing parameters that are theoretically meaningful. For example, in the case of perceptual decision making, model parameters might correspond to theoretical constructs like response bias, evidence quality, response caution, and the like. Formal cognitive models go beyond verbal models in that cognitive mechanisms are instantiated in terms of mathematics and they go beyond statistical models in that cognitive model parameters are psychologically interpretable. We explore three key elements used to formally evaluate cognitive models: parameter estimation, model prediction, and model selection. We compare and contrast traditional approaches with Bayesian statistical approaches to performing each of these three elements. Traditional approaches rely on an array of seemingly ad hoc techniques, whereas Bayesian statistical approaches rely on a single, principled, internally consistent system. We illustrate the Bayesian statistical approach to evaluating cognitive models using a running example of the Linear Ballistic Accumulator model of decision making (Brown SD, Heathcote A. The simplest complete model of choice response time: linear ballistic accumulation. Cogn Psychol 2008, 57:153-178). WIREs Cogn Sci 2018, 9:e1458. doi: 10.1002/wcs.1458 This article is categorized under: Neuroscience > Computation Psychology > Reasoning and Decision Making Psychology > Theory and Methods.

Bayesian inference for psychology. Part I: Theoretical advantages and practical ramifications

Bayesian parameter estimation and Bayesian hypothesis testing present attractive alternatives to classical inference using confidence intervals and p values. In part I of this series we outline ten prominent advantages of the Bayesian approach. Many of these advantages translate to concrete opportunities for pragmatic researchers. For instance, Bayesian hypothesis testing allows researchers to quantify evidence and monitor its progression as data come in, without needing to know the intention with which the data were collected. We end by countering several objections to Bayesian hypothesis testing. Part II of this series discusses JASP, a free and open source software program that makes it easy to conduct Bayesian estimation and testing for a range of popular statistical scenarios (Wagenmakers et al. this issue).

The determinants of response time in a repeated constant-sum game: A robust Bayesian hierarchical dual-process model

The investigation of response time and behavior has a long tradition in cognitive psychology, particularly for non-strategic decision-making. Recently, experimental economists have also studied response time in strategic interactions, but with an emphasis on either one-shot games or repeated social-dilemmas. I investigate the determinants of response time in a repeated (pure-conflict) game, admitting a unique mixed strategy Nash equilibrium, with fixed partner matching. Response times depend upon the interaction of two decision models embedded in a dual-process framework (Achtziger and Alós-Ferrer, 2014; Alós-Ferrer, 2016). The first decision model is the commonly used win-stay/lose-shift heuristic and the second the pattern-detecting reinforcement learning model in Spiliopoulos (2013b). The former is less complex and can be executed more quickly than the latter. As predicted, conflict between these two models (i.e., each one recommending a different course of action) led to longer response times than cases without conflict. The dual-process framework makes other qualitative response time predictions arising from the interaction between the existence (or not) of conflict and which one of the two decision models the chosen action is consistent with-these were broadly verified by the data. Other determinants of RT were hypothesized on the basis of existing theory and tested empirically. Response times were strongly dependent on the actions chosen by both players in the previous rounds and the resulting outcomes. Specifically, response time was shortest after a win in the previous round where the maximum possible payoff was obtained; response time after losses was significantly longer. Strongly auto-correlated behavior (regardless of its sign) was also associated with longer response times. I conclude that, similar to other tasks, there is a strong coupling in repeated games between behavior and RT, which can be exploited to further our understanding of decision making.

A tutorial on bridge sampling

The marginal likelihood plays an important role in many areas of Bayesian statistics such as parameter estimation, model comparison, and model averaging. In most applications, however, the marginal likelihood is not analytically tractable and must be approximated using numerical methods. Here we provide a tutorial on bridge sampling (Bennett, 1976; Meng & Wong, 1996), a reliable and relatively straightforward sampling method that allows researchers to obtain the marginal likelihood for models of varying complexity. First, we introduce bridge sampling and three related sampling methods using the beta-binomial model as a running example. We then apply bridge sampling to estimate the marginal likelihood for the Expectancy Valence (EV) model-a popular model for reinforcement learning. Our results indicate that bridge sampling provides accurate estimates for both a single participant and a hierarchical version of the EV model. We conclude that bridge sampling is an attractive method for mathematical psychologists who typically aim to approximate the marginal likelihood for a limited set of possibly high-dimensional models.

Modelling the effects of phylogeny and body size on within-host pathogen replication and immune response

Understanding how quickly pathogens replicate and how quickly the immune system responds is important for predicting the epidemic spread of emerging pathogens. Host body size, through its correlation with metabolic rates, is theoretically predicted to impact pathogen replication rates and immune system response rates. Here, we use mathematical models of viral time courses from multiple species of birds infected by a generalist pathogen (West Nile Virus; WNV) to test more thoroughly how disease progression and immune response depend on mass and host phylogeny. We use hierarchical Bayesian models coupled with nonlinear dynamical models of disease dynamics to incorporate the hierarchical nature of host phylogeny. Our analysis suggests an important role for both host phylogeny and species mass in determining factors important for viral spread such as the basic reproductive number, WNV production rate, peak viraemia in blood and competency of a host to infect mosquitoes. Our model is based on a principled analysis and gives a quantitative prediction for key epidemiological determinants and how they vary with species mass and phylogeny. This leads to new hypotheses about the mechanisms that cause certain taxonomic groups to have higher viraemia. For example, our models suggest that higher viral burst sizes cause corvids to have higher levels of viraemia and that the cellular rate of virus production is lower in larger species. We derive a metric of competency of a host to infect disease vectors and thereby sustain the disease between hosts. This suggests that smaller passerine species are highly competent at spreading the disease compared with larger non-passerine species. Our models lend mechanistic insight into why some species (smaller passerine species) are pathogen reservoirs and some (larger non-passerine species) are potentially dead-end hosts for WNV. Our techniques give insights into the role of body mass and host phylogeny in the spread of WNV and potentially other zoonotic diseases. The major contribution of this work is a computational framework for infectious disease modelling at the within-host level that leverages data from multiple species. This is likely to be of interest to modellers of infectious diseases that jump species barriers and infect multiple species. Our method can be used to computationally determine the competency of a host to infect mosquitoes that will sustain WNV and other zoonotic diseases. We find that smaller passerine species are more competent in spreading the disease than larger non-passerine species. This suggests the role of host phylogeny as an important determinant of within-host pathogen replication. Ultimately, we view our work as an important step in linking within-host viral dynamics models to between-host models that determine spread of infectious disease between different hosts.

Bayesian Inference for Correlations in the Presence of Measurement Error and Estimation Uncertainty

Whenever parameter estimates are uncertain or observations are contaminated by measurement error, the Pearson correlation coefficient can severely underestimate the true strength of an association. Various approaches exist for inferring the correlation in the presence of estimation uncertainty and measurement error, but none are routinely applied in psychological research. Here we focus on a Bayesian hierarchical model proposed by Behseta, Berdyyeva, Olson, and Kass (2009) that allows researchers to infer the underlying correlation between error-contaminated observations. We show that this approach may be also applied to obtain the underlying correlation between uncertain parameter estimates as well as the correlation between uncertain parameter estimates and noisy observations. We illustrate the Bayesian modeling of correlations with two empirical data sets; in each data set, we first infer the posterior distribution of the underlying correlation and then compute Bayes factors to quantify the evidence that the data provide for the presence of an association.

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.

A Bayesian approach for estimating the probability of trigger failures in the stop-signal paradigm

Response inhibition is frequently investigated using the stop-signal paradigm, where participants perform a two-choice response time task that is occasionally interrupted by a stop signal instructing them to withhold their response. Stop-signal performance is formalized as a race between a go and a stop process. If the go process wins, the response is executed; if the stop process wins, the response is inhibited. Successful inhibition requires fast stop responses and a high probability of triggering the stop process. Existing methods allow for the estimation of the latency of the stop response, but are unable to identify deficiencies in triggering the stop process. We introduce a Bayesian model that addresses this limitation and enables researchers to simultaneously estimate the probability of trigger failures and the entire distribution of stopping latencies. We demonstrate that trigger failures are clearly present in two previous studies, and that ignoring them distorts estimates of stopping latencies. The parameter estimation routine is implemented in the BEESTS software (Matzke et al., Front. Quantitative Psych. Measurement, 4, 918; 2013a) and is available at http://dora.erbe-matzke.com/software.html.

Parallel interactive retrieval of item and associative information from event memory

Memory contains information about individual events (items) and combinations of events (associations). Despite the fundamental importance of this distinction, it remains unclear exactly how these two kinds of information are stored and whether different processes are used to retrieve them. We use both model-independent qualitative properties of response dynamics and quantitative modeling of individuals to address these issues. Item and associative information are not independent and they are retrieved concurrently via interacting processes. During retrieval, matching item and associative information mutually facilitate one another to yield an amplified holistic signal. Modeling of individuals suggests that this kind of facilitation between item and associative retrieval is a ubiquitous feature of human memory.

Modelling individual difference in visual categorization

Recent years has seen growing interest in understanding, characterizing, and explaining individual differences in visual cognition. We focus here on individual differences in visual categorization. Categorization is the fundamental visual ability to group different objects together as the same kind of thing. Research on visual categorization and category learning has been significantly informed by computational modeling, so our review will focus both on how formal models of visual categorization have captured individual differences and how individual difference have informed the development of formal models. We first examine the potential sources of individual differences in leading models of visual categorization, providing a brief review of a range of different models. We then describe several examples of how computational models have captured individual differences in visual categorization. This review also provides a bit of an historical perspective, starting with models that predicted no individual differences, to those that captured group differences, to those that predict true individual differences, and to more recent hierarchical approaches that can simultaneously capture both group and individual differences in visual categorization. Via this selective review, we see how considerations of individual differences can lead to important theoretical insights into how people visually categorize objects in the world around them. We also consider new directions for work examining individual differences in visual categorization.

The irrational hungry judge effect revisited: Simulations reveal that the magnitude of the effect is overestimated

Danziger, Levav and Avnaim-Pesso (2011) analyzed legal rulings of Israeli parole boards concerning the effect of serial order in which cases are presented within ruling sessions. They found that the probability of a favorable decision drops from about 65% to almost 0% from the first ruling to the last ruling within each session and that the rate of favorable rulings returns to 65% in a session following a food break. The authors argue that these findings provide support for extraneous factors influencing judicial decisions and cautiously speculate that the effect might be driven by mental depletion. A simulation shows that the observed influence of order can be alternatively explained by a statistical artifact resulting from favorable rulings taking longer than unfavorable ones. An effect of similar magnitude would be produced by a (hypothetical) rational judge who plans ahead minimally and ends a session instead of starting cases that he or she assumes will take longer directly before the break. One methodological detail further increased the magnitude of the artifact and generates it even without assuming any foresight concerning the upcoming case. Implications for this article are discussed and the increased application of simulations to identify nonobvious rational explanations is recommended.

When High-Capacity Readers Slow Down and Low-Capacity Readers Speed Up: Working Memory and Locality Effects

We examined the effects of argument-head distance in SVO and SOV languages (Spanish and German), while taking into account readers' working memory capacity and controlling for expectation (Levy, 2008) and other factors. We predicted only locality effects, that is, a slowdown produced by increased dependency distance (Gibson, 2000; Lewis and Vasishth, 2005). Furthermore, we expected stronger locality effects for readers with low working memory capacity. Contrary to our predictions, low-capacity readers showed faster reading with increased distance, while high-capacity readers showed locality effects. We suggest that while the locality effects are compatible with memory-based explanations, the speedup of low-capacity readers can be explained by an increased probability of retrieval failure. We present a computational model based on ACT-R built under the previous assumptions, which is able to give a qualitative account for the present data and can be tested in future research. Our results suggest that in some cases, interpreting longer RTs as indexing increased processing difficulty and shorter RTs as facilitation may be too simplistic: The same increase in processing difficulty may lead to slowdowns in high-capacity readers and speedups in low-capacity ones. Ignoring individual level capacity differences when investigating locality effects may lead to misleading conclusions.

Why more is better: Simultaneous modeling of EEG, fMRI, and behavioral data

The need to test a growing number of theories in cognitive science has led to increased interest in inferential methods that integrate multiple data modalities. In this manuscript, we show how a method for integrating three data modalities within a single framework provides (1) more detailed descriptions of cognitive processes and (2) more accurate predictions of unobserved data than less integrative methods. Specifically, we show how combining either EEG and fMRI with a behavioral model can perform substantially better than a behavioral-data-only model in both generative and predictive modeling analyses. We then show how a trivariate model - a model including EEG, fMRI, and behavioral data - outperforms bivariate models in both generative and predictive modeling analyses. Together, these results suggest that within an appropriate modeling framework, more data can be used to better constrain cognitive theory, and to generate more accurate predictions for behavioral and neural data.

Distributional analyses in the picture–word interference paradigm: Exploring the semantic interference and the distractor frequency effects

The present study explores the distributional features of two important effects within the picture–word interference paradigm: the semantic interference and the distractor frequency effects. These two effects display different and specific distributional profiles. Semantic interference appears greatly reduced in faster response times, while it reaches its full magnitude only in slower responses. This can be interpreted as a sign of fluctuant attentional efficiency in resolving response conflict. In contrast, the distractor frequency effect is mediated mainly by a distributional shift, with low-frequency distractors uniformly shifting reaction time distribution towards a slower range of latencies. This finding fits with the idea that distractor frequency exerts its effect by modulating the point in time in which operations required to discard the distractor can start. Taken together, these results are congruent with current theoretical accounts of both the semantic interference and distractor frequency effects. Critically, distributional analyses highlight and further describe the different cognitive dynamics underlying these two effects, suggesting that this analytical tool is able to offer important insights about lexical access during speech production.

The influence of pre- and posterror responses on measures of intraindividual variability in younger and older adults

The current study examined the effects of responses on error-adjacent trials (i.e., those immediately preceding or following errors) on age differences in measures of intraindividual variability and the shape of response time (RT) distributions on a two-back task. Removing error-adjacent responses reduced variability as measured by the coefficient of variation, but did so similarly for younger and older adults. However, older adults' standard deviations (SDs) were less than those of younger adults with comparable RTs, raising questions regarding the validity of the coefficient of variation. An ex-Gaussian analysis revealed that removing the RTs on error-adjacent trials reduced the length of the tails of distributions and the skewness of the distributions. These properties were reduced more for older adults than for younger adults. These results indicate that the influence of error-adjacent trials should be considered when analyzing intraindividual variability and the shape of RT distributions to test theories of cognitive aging.

Individual differences in attention influence perceptual decision making

Sequential sampling decision-making models have been successful in accounting for reaction time (RT) and accuracy data in two-alternative forced choice tasks. These models have been used to describe the behavior of populations of participants, and explanatory structures have been proposed to account for between individual variability in model parameters. In this study we show that individual differences in behavior from a novel perceptual decision making task can be attributed to (1) differences in evidence accumulation rates, (2) differences in variability of evidence accumulation within trials, and (3) differences in non-decision times across individuals. Using electroencephalography (EEG), we demonstrate that these differences in cognitive variables, in turn, can be explained by attentional differences as measured by phase-locking of steady-state visual evoked potential (SSVEP) responses to the signal and noise components of the visual stimulus. Parameters of a cognitive model (a diffusion model) were obtained from accuracy and RT distributions and related to phase-locking indices (PLIs) of SSVEPs with a single step in a hierarchical Bayesian framework. Participants who were able to suppress the SSVEP response to visual noise in high frequency bands were able to accumulate correct evidence faster and had shorter non-decision times (preprocessing or motor response times), leading to more accurate responses and faster response times. We show that the combination of cognitive modeling and neural data in a hierarchical Bayesian framework relates physiological processes to the cognitive processes of participants, and that a model with a new (out-of-sample) participant's neural data can predict that participant's behavior more accurately than models without physiological data.

A hierarchical adaptive approach to optimal experimental design

Experimentation is at the core of research in the behavioral and neural sciences, yet observations can be expensive and time-consuming to acquire (e.g., MRI scans, responses from infant participants). A major interest of researchers is designing experiments that lead to maximal accumulation of information about the phenomenon under study with the fewest possible number of observations. In addressing this challenge, statisticians have developed adaptive design optimization methods. This letter introduces a hierarchical Bayes extension of adaptive design optimization that provides a judicious way to exploit two complementary schemes of inference (with past and future data) to achieve even greater accuracy and efficiency in information gain. We demonstrate the method in a simulation experiment in the field of visual perception.

Hierarchical approximate Bayesian computation

Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model's parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper, we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function.

Intertemporal choice as discounted value accumulation

Two separate cognitive processes are involved in choosing between rewards available at different points in time. The first is temporal discounting, which consists of combining information about the size and delay of prospective rewards to represent subjective values. The second involves a comparison of available rewards to enable an eventual choice on the basis of these subjective values. While several mathematical models of temporal discounting have been developed, the reward selection process has been largely unexplored. To address this limitation, we evaluated the applicability of the Linear Ballistic Accumulator (LBA) model as a theory of the selection process in intertemporal choice. The LBA model formalizes the selection process as a sequential sampling algorithm in which information about different choice options is integrated until a decision criterion is reached. We compared several versions of the LBA model to demonstrate that choice outcomes and response times in intertemporal choice are well captured by the LBA process. The relationship between choice outcomes and response times that derives from the LBA model cannot be explained by temporal discounting alone. Moreover, the drift rates that drive evidence accumulation in the best-fitting LBA model are related to independently estimated subjective values derived from various temporal discounting models. These findings provide a quantitative framework for predicting dynamics of choice-related activity during the reward selection process in intertemporal choice and link intertemporal choice to other classes of decisions in which the LBA model has been applied.

Release the BEESTS: Bayesian Estimation of Ex-Gaussian STop-Signal reaction time distributions

The stop-signal paradigm is frequently used to study response inhibition. In this paradigm, participants perform a two-choice response time (RT) task where the primary task is occasionally interrupted by a stop-signal that prompts participants to withhold their response. The primary goal is to estimate the latency of the unobservable stop response (stop signal reaction time or SSRT). Recently, Matzke et al. (2013) have developed a Bayesian parametric approach (BPA) that allows for the estimation of the entire distribution of SSRTs. The BPA assumes that SSRTs are ex-Gaussian distributed and uses Markov chain Monte Carlo sampling to estimate the parameters of the SSRT distribution. Here we present an efficient and user-friendly software implementation of the BPA-BEESTS-that can be applied to individual as well as hierarchical stop-signal data. BEESTS comes with an easy-to-use graphical user interface and provides users with summary statistics of the posterior distribution of the parameters as well various diagnostic tools to assess the quality of the parameter estimates. The software is open source and runs on Windows and OS X operating systems. In sum, BEESTS allows experimental and clinical psychologists to estimate entire distributions of SSRTs and hence facilitates the more rigorous analysis of stop-signal data.

A dynamic, embodied paradigm to investigate the role of serotonin in decision-making

Serotonin (5-HT) is a neuromodulator that has been attributed to cost assessment and harm aversion. In this review, we look at the role 5-HT plays in making decisions when subjects are faced with potential harmful or costly outcomes. We review approaches for examining the serotonergic system in decision-making. We introduce our group’s paradigm used to investigate how 5-HT affects decision-making. In particular, our paradigm combines techniques from computational neuroscience, socioeconomic game theory, human–robot interaction, and Bayesian statistics. We will highlight key findings from our previous studies utilizing this paradigm, which helped expand our understanding of 5-HT’s effect on decision-making in relation to cost assessment. Lastly, we propose a cyclic multidisciplinary approach that may aid in addressing the complexity of exploring 5-HT and decision-making by iteratively updating our assumptions and models of the serotonergic system through exhaustive experimentation.

Likelihood-free Bayesian analysis of memory models

Many influential memory models are computational in the sense that their predictions are derived through simulation. This means that it is difficult or impossible to write down a probability distribution or likelihood that characterizes the random behavior of the data as a function of the model's parameters. In turn, the lack of a likelihood means that these models cannot be directly fitted to data using traditional techniques. In particular, standard Bayesian analyses of such models are impossible. In this article, we examine how a new procedure called approximate Bayesian computation (ABC), a method for Bayesian analysis that circumvents the evaluation of the likelihood, can be used to fit computational models to memory data. In particular, we investigate the bind cue decide model of episodic memory (Dennis & Humphreys, 2001) and the retrieving effectively from memory model (Shiffrin & Steyvers, 1997). We fit hierarchical versions of each model to the data of Dennis, Lee, and Kinnell (2008) and Kinnell and Dennis (2012). The ABC analysis permits us to explore the relationships between the parameters in each model as well as evaluate their relative fits to data-analyses that were not previously possible.

Response Time Modeling Based on the Proportional Hazards Model

Response time data are regularly analyzed in psychology. When several response times are assessed per participant, it is common practice to use latent trait models in order to account for the dependency of the response times from the same participant. One such model is the proportional hazards model with random effects. Despite its popularity in survival analysis, this model is rarely used in psychology because of the difficulty of model estimation when latent variables are present. In this article, a new estimation method is proposed. This method is based on the rank correlation matrix containing Kendall's Tau coefficients and unweighted least squares estimation ( Kendall, 1938 ). Compared with marginal maximum likelihood estimation, the new estimation approach is simple, not computationally intensive, and almost as efficient. Additionally, the approach allows the implementation of a test for model fit. Feasibility of the estimation method and validity of the fit test is demonstrated with a simulation study. An application of the model to a real data set is provided.

Using priors to formalize theory: optimal attention and the generalized context model

Formal models in psychology are used to make theoretical ideas precise and allow them to be evaluated quantitatively against data. We focus on one important--but under-used and incorrectly maligned--method for building theoretical assumptions into formal models, offered by the Bayesian statistical approach. This method involves capturing theoretical assumptions about the psychological variables in models by placing informative prior distributions on the parameters representing those variables. We demonstrate this approach of casting basic theoretical assumptions in an informative prior by considering a case study that involves the generalized context model (GCM) of category learning. We capture existing theorizing about the optimal allocation of attention in an informative prior distribution to yield a model that is higher in psychological content and lower in complexity than the standard implementation. We also highlight that formalizing psychological theory within an informative prior distribution allows standard Bayesian model selection methods to be applied without concerns about the sensitivity of results to the prior. We then use Bayesian model selection to test the theoretical assumptions about optimal allocation formalized in the prior. We argue that the general approach of using psychological theory to guide the specification of informative prior distributions is widely applicable and should be routinely used in psychological modeling.

A method for efficiently sampling from distributions with correlated dimensions

Bayesian estimation has played a pivotal role in the understanding of individual differences. However, for many models in psychology, Bayesian estimation of model parameters can be difficult. One reason for this difficulty is that conventional sampling algorithms, such as Markov chain Monte Carlo (MCMC), can be inefficient and impractical when little is known about the target distribution--particularly the target distribution's covariance structure. In this article, we highlight some reasons for this inefficiency and advocate the use of a population MCMC algorithm, called differential evolution Markov chain Monte Carlo (DE-MCMC), as a means of efficient proposal generation. We demonstrate in a simulation study that the performance of the DE-MCMC algorithm is unaffected by the correlation of the target distribution, whereas conventional MCMC performs substantially worse as the correlation increases. We then show that the DE-MCMC algorithm can be used to efficiently fit a hierarchical version of the linear ballistic accumulator model to response time data, which has proven to be a difficult task when conventional MCMC is used.