Differences in Ex-Gaussian Parameters from Response Time Distributions Between Individuals with and Without Attention Deficit/Hyperactivity Disorder: A Meta-analysis.

Attention Deficit Hyperactivity Disorder (ADHD) is one of the most prevalent neurodevelopmental disorders in childhood and adolescence. Differences in reaction times (RT) in cognitive tasks have been consistently observed between ADHD and typical participants. Instead of estimating means and standard deviations, fitting non-symmetrical distributions like the ex-Gaussian, characterized by three parameters (µ, σ, and τ), account for the whole RT distributions. A meta-analysis is performed with all the available literature using ex-Gaussian distributions for comparisons between individuals with ADHD and controls. Results show that τ and σ are generally greater for ADHD samples, while µ tends to be larger for typical groups but only for younger ages. Differences in τ are also moderated by ADHD subtypes. τ and σ show, respectively, quadratic and linear relationships with inter-stimulus intervals from Continuous Performance Test and Go/No Go tasks. Furthermore, tasks and cognitive domains influence the three parameters. Interpretations of ex-Gaussian parameters and clinical implications of these findings are also discussed. Fitting ex-Gaussian distributions to RT data is a useful way to explore differences between individuals with ADHD and healthy controls.

Cardiac timing and threatening stimuli influence response inhibition and ex-Gaussian parameters of reaction time in a Go/No-go task.

Sensorimotor responses vary as a function of the cardiac cycle phase. These effects, known as cardiac cycle time effects, have been explained by the inhibition of cardiac afferent signals on information processing. However, the validity of cardiac cycle time effects is challenged by mixed findings. Factors such as current information processing and affective context may modulate cardiac cycle time effects and account for inconsistencies in the literature. The current study examines the influence of cardiac cycle time and threatening stimuli on two aspects of sensorimotor processing, response speed and inhibition. Thirty-four participants (Mage  = 19.35 years; 29 female) completed an auditory Go/No-go task in no face, neutral face, and fearful face conditions. Faces were presented at either cardiac diastole or systole. Participants' reaction times (RTs) during Go trials and failures in response inhibition during No-go trials were recorded. The ex-Gaussian model was fit to RT data in each condition deriving the parameters, mu (µ) and tau (τ), that indicate response speed and attentional lapses, respectively. Repeated measures ANOVA were used to analyze behavioral data. Results showed that cardiac systole prolonged µ but decreased τ, and that cardiac diastole reduced inhibition errors in the fearful face condition but not in other conditions. These findings indicate that cardiac timing differentially modulates sensory-perceptual and top-down attentional processes and cardiac timing interacts with threatening contexts to influence response inhibition. These results highlight the specificity of cardiac cycle time effects on sensorimotor processing.

Examining reaction time variability on the stop-signal task in the ABCD study.

OBJECTIVE: Reaction time variability (RTV) has been estimated using Gaussian, ex-Gaussian, and diffusion model (DM) indices. Rarely have studies examined interrelationships among these performance indices in childhood, and the use of reaction time (RT) computational models has been slow to take hold in the developmental psychopathology literature. Here, we extend prior work in adults by examining the interrelationships among different model parameters in the ABCD sample and demonstrate how computational models of RT can clarify mechanisms of time-on-task effects and sex differences in RTs. METHOD: This study utilized trial-level data from the stop signal task from 8916 children (9-10 years old) to examine Gaussian, ex-Gaussian, and DM indicators of RTV. In addition to describing RTV patterns, we examined interrelations among these indicators, temporal patterns, and sex differences. RESULTS: There was no one-to-one correspondence between DM and ex-Gaussian parameters. Nonetheless, drift rate was most strongly associated with standard deviation of RT and tau, while nondecisional processes were most strongly associated with RT, mu, and sigma. Performance worsened across time with changes driven primarily by decreasing drift rate. Boys were faster and less variable than girls, likely attributable to girls' wide boundary separation. CONCLUSIONS: Intercorrelations among model parameters are similar in children as has been observed in adults. Computational approaches play a crucial role in understanding performance changes over time and can also clarify mechanisms of group differences. For example, standard RT models may incorrectly suggest slowed processing speed in girls that is actually attributable to other factors.

Event-related brain-oscillatory and ex-Gaussian markers of remission and persistence of ADHD.

BACKGROUND: Attention-deficit/hyperactivity disorder (ADHD) often persists into adolescence and adulthood, but the processes underlying persistence and remission remain poorly understood. We previously found that reaction time variability and event-related potentials of preparation-vigilance processes were impaired in ADHD persisters and represented markers of remission, as ADHD remitters were indistinguishable from controls but differed from persisters. Here, we aimed to further clarify the nature of the cognitive-neurophysiological impairments in ADHD and of markers of remission by examining the finer-grained ex-Gaussian reaction-time distribution and electroencephalographic (EEG) brain-oscillatory measures in ADHD persisters, remitters and controls. METHODS: A total of 110 adolescents and young adults with childhood ADHD (87 persisters, 23 remitters) and 169 age-matched controls were compared on ex-Gaussian (mu, sigma, tau) indices and time-frequency EEG measures of power and phase consistency from a reaction-time task with slow-unrewarded baseline and fast-incentive conditions ('Fast task'). RESULTS: Compared to controls, ADHD persisters showed significantly greater mu, sigma, tau, and lower theta power and phase consistency across conditions. Relative to ADHD persisters, remitters showed significantly lower tau and theta power and phase consistency across conditions, as well as lower mu in the fast-incentive condition, with no difference in the baseline condition. Remitters did not significantly differ from controls on any measure. CONCLUSIONS: We found widespread impairments in ADHD persisters in reaction-time distribution and brain-oscillatory measures. Event-related theta power, theta phase consistency and tau across conditions, as well as mu in the more engaging fast-incentive condition, emerged as novel markers of ADHD remission, potentially representing compensatory mechanisms in individuals with remitted ADHD.

No need to collect more data: ex-Gaussian modelling of existing data (Craig & Lipp, 2018) reveals an interactive effect of face race and face sex on speeded expression recognition.

The results of a previous study (Craig & Lipp, 2018) into the effects of multiple social category cues (face race and face sex) on facial emotion recognition indicate that face sex dominates face race, and moreover, participant sex differences contribute little to the observed effects. Here, I modelled the same dataset (https://osf.io/rsmxb/) using the ex-Gaussian, a distribution that is 1) well suited to RT data and 2) separates slow from relatively fast influences. Corroborating recent results (Tipples, 2022) current results show larger effects of face sex (for the faces of White individuals) for female participants. Further novel interaction effects were revealed. For example, results support a different time course for the influence of face sex on expression for the faces of Black compared to White individuals.

Neural substrates underpinning intra-individual variability in children with ADHD: A voxel-based morphometry study.

BACKGROUND/PURPOSE: Increased intra-individual variability (IIV) in reaction time (RT) is a key feature of attention-deficit/hyperactivity disorder (ADHD). However, little is known about neurobiology underpinnings of IIV in ADHD. METHODS: We assessed 55 youths with ADHD, and 55 individually-matched typically developing control (TDC) with the MRI and Conners' Continuous Performance Test. The ex-Gaussian distribution of RT was estimated to capture IIV with the parameters σ (sigma) and τ (tau). The regional brain volumes, analyzed by voxel-based morphometry, were correlated with IIV parameters. RESULTS: We found both distinct and shared correlations among ADHD and TDC. For grey matter, there were significant σ-by-group interactions in the cingulate cortex and thalamus and also a τ-by-group interaction in the right inferior frontal gyrus. There was also shared negative associations between σ and regional volumes of the right posterior cerebellum and a positive association between τ and the right anterior insula. For white matter, there was a significant σ-by-group interaction in the genu of the corpus callosum and significant τ-by-group interactions in the right anterior corona radiata, the left splenium of the corpus callosum, and bilateral posterior cerebellum. There were also shared patterns that increased τ was associated with increased regional volumes of the right anterior corona radiata and decreased regional volumes of the right posterior limb of the internal capsule. CONCLUSION: This study highlights that brain regions responsible for the motor, salience processing and multimodal information integration are associated with increased IIV in youths with ADHD.

Changes in BOLD variability are linked to the development of variable response inhibition.

Research on the development of response inhibition in humans has focused almost exclusively on average stopping performance. The development of intra-individual variability in stopping performance and its underlying neural circuitry has remained largely unstudied, even though understanding variability is of core importance for understanding development. In a total sample of 45 participants (19 children aged 10-12 years and 26 adults aged 18-26 years) of either sex we aimed to identify age-related changes in intra-individual response inhibition performance and its underlying brain signal variability. While there was no difference in average stopping performance between children and adults, stop signal latencies for the children were more variable. Further, brain signal variability during successful stopping was significantly higher in adults compared to children, especially in bilateral thalamus, but also across regions of the inhibition network. Finally, brain signal variability was significantly associated with stopping performance behavioral variability in adults. Together these results indicate that variability in stopping performance decreases, whereas neural variability in the inhibition network increases, from childhood to adulthood. Future work will need to assess whether developmental changes in neural variability drive those in behavioral variability. In sum, both, neural and behavioral variability indices might be a more sensitive measure of developmental differences in response inhibition compared to the standard average-based measurements.

Word and Face Recognition Processing Based on Response Times and Ex-Gaussian Components.

The face is a fundamental feature of our identity. In humans, the existence of specialized processing modules for faces is now widely accepted. However, identifying the processes involved for proper names is more problematic. The aim of the present study is to examine which of the two treatments is produced earlier and whether the social abilities are influent. We selected 100 university students divided into two groups: Spanish and USA students. They had to recognize famous faces or names by using a masked priming task. An analysis of variance about the reaction times (RT) was used to determine whether significant differences could be observed in word or face recognition and between the Spanish or USA group. Additionally, and to examine the role of outliers, the Gaussian distribution has been modified exponentially. Famous faces were recognized faster than names, and differences were observed between Spanish and North American participants, but not for unknown distracting faces. The current results suggest that response times to face processing might be faster than name recognition, which supports the idea of differences in processing nature.

The location-based Simon effect: Reliability of ex-Gaussian analysis.

Task-irrelevant stimulus location can influence the response performance to task-relevant attributes, generating the location-based Simon effect. Using a Monte Carlo study and other methods, we examined whether the ex-Gaussian distribution provides a good fit to empirical reaction time (RT) distributions in the Simon task and whether reliable Simon effects occur on the ex-Gaussian parameters: (a) the mean (µ), (b) the standard deviation (σ) of the normal distribution, and (c) the tail (τ). Results showed that the ex-Gaussian function fits well to empirical RT distributions, and that these ex-Gaussian parameters are reliable between two trial blocks at the group level. At the individual level, correlation analysis showed that the Simon effect was reliable on the µ parameter but not on σ and τ. Moreover, a partial correlation analysis, with µs of the two blocks as controlling variables, showed that the Simon effect on τ was reliable. These results provide evidence that the ex-Gaussian function is a valuable tool for analyzing the Simon effect and can be considered as an alternative for analyzing RT distributions in Simon-type tasks.

Distinct and similar patterns of emotional development in adolescents and young adults.

Adolescence is a developmental period of increased sensitivity to social emotional cues, but it is less known whether young adults demonstrate similar social emotional sensitivity. The current study tested variation in reaction times to emotional face cues during different phases of emotional development. Ex-Gaussian parameters mu, sigma, and tau were computed, in addition to mean, median and standard deviation (SD) in reaction times (RT) during an emotional go/nogo-paradigm with fearful, happy, and calm facial expressions in 377 participants, 6-30 years of age. Across development, mean RT showed slowing to fearful facial expressions relative to both calm and happy facial cues, but mu revealed that this pattern was specific to adolescence. In young adulthood, increased variability to fearful expressions relative to both happy and calm ones was captured by SD and tau. The findings that adolescents had longer response latencies to fearful faces, whereas young adults demonstrated greater response variability to fearful faces, together reflect how social emotional processing continues to evolve from adolescence into early adulthood. The findings suggest that young adulthood is also a vulnerable period for processing social emotional cues that ultimately may be important to better understand why different psychopathologies emerge in early adulthood.

Non-Gaussian Distributional Analyses of Reaction Times (RT): Improvements that Increase Efficacy of RT Tasks for Describing Cognitive Processes.

This didactic aims of this review are to demonstrate the advantages of examining the entire reaction time (RT) distribution to better realize the efficacy of mental speed assessment in clinical neuropsychology. RT distributions are typically non-normal, requiring consideration of a host of statistical issues. Specifically, the appropriate model of the mental speed task's distribution (e.g., ex-Gaussian, Weibull, Normal-Gaussian, etc.) must be determined to know what parameters can be used to characterize test performance. While RT mean and standard deviation are typically used to characterize clinical performance, these parameters are usually inappropriate because RT performance rarely conforms to a normal-Gaussian distribution. For illustrative purposes, a tutorial for examining the entire RT distribution is provided that demonstrates differences between an Attention Deficit/Hyperactivity and a neurotypical group of college students. While such analyses are descriptive, it is important to characterize test performance in the context of a theoretical model of RT performance. Therefore, the tutorial includes interpretation that uses the Diffusion model (Ratcliff Psychological Review, 85, 59-108, 1978), which assumes an ex-Gaussian distribution. It is concluded that current results conform to a large literature demonstrating a more nuanced understanding of cognition afforded by non-Gaussian analysis of RT. This literature is compelling neuropsychology to enlarge assessment technology beyond the limitations of paper-and-pencil instruments.

Response Time Consistency Is an Indicator of Executive Control Rather than Global Cognitive Ability.

OBJECTIVES: Intraindividual variability increases with age, but the relative strength of association with cognitive domains is still unclear. The objective of this study was to examine the relation between cognitive domains and the shape and spread of response time (RT) distributions as indexed by intraindividual standard deviation (ISD), and ex-Gaussian parameters (µ, σ, τ). METHODS: Healthy adults (40 young [aged 18-30 years], 40 young-old [aged 65-74 years], and 41 old-old [aged 75-85 years]) completed neuropsychological testing and a touch-screen attention task from which ISD and ex-Gaussian parameters were derived. The relation between RT performance and cognitive domains (memory, processing speed, executive functioning) was examined with structural equation modeling (SEM), and the predictive power of RT distribution indices over age was investigated with linear regression. RESULTS: ISD, µ, and τ, but not σ, showed a linear increase with age group. An SEM showed that independent of age, τ was most strongly associated with executive functioning, while µ exhibited less critical associations. Linear regression indicated that µ and τ explained a significant portion of variance in processing speed and executive ability in addition to age group. Memory was more parsimoniously predicted by age, without any significant contribution of ex-Gaussian parameters. CONCLUSIONS: The findings suggest that exceptionally slow responses convey attention lapses through wavering of cognitive control, which strongly correspond to executive functioning tests. General slowing and extremely slow responses predicted processing speed and executive performance beyond age group, indicating that RT metrics are sensitive to differences in cognitive ability. (JINS, 2018, 24, 456-465).

Effects of saccade training on express saccade proportions, saccade latencies, and peak velocities: an investigation of nasal/temporal differences.

Express saccades have very short latencies and are often considered a special population of saccadic eye movements. Recent evidence suggests that express saccade generation in humans increases with training, and that this training is independent of the actual saccade vector being trained. We assessed the time course of these training-induced increases in express saccade generation and how they differ between the nasal and temporal hemifields, and second whether they transfer from the trained to the untrained eye. We also measured the effects of training on saccade latencies more generally, and upon peak velocities. The training effect transferred between the nasal and temporal hemifields and between the trained and untrained eyes. More surprisingly, we found an asymmetric effect of training on express saccade proportions: Before training, express saccade proportions were higher for saccades made into the nasal hemifield but with training this reversed. This training-induced asymmetry was also observed in overall saccade latencies, showing how training can unmask nasal/temporal asymmetries in saccade latencies. Finally, we report for the first time that saccadic peak velocities increased with training, independently of changes in amplitude.

The location-, word-, and arrow-based Simon effects: An ex-Gaussian analysis.

Task-irrelevant spatial information, conveyed by stimulus location, location word, or arrow direction, can influence the response to task-relevant attributes, generating the location-, word-, and arrow-based Simon effects. We examined whether different mechanisms are involved in the generation of these Simon effects by fitting a mathematical ex-Gaussian function to empirical response time (RT) distributions. Specifically, we tested whether which ex-Gaussian parameters (µ, σ, and τ) show Simon effects and whether the location-, word, and arrow-based effects are on different parameters. Results show that the location-based Simon effect occurred on mean RT and µ but not on τ, and a reverse Simon effect occurred on σ. In contrast, a positive word-based Simon effect was obtained on all these measures (including σ), and a positive arrow-based Simon effect was evident on mean RT, σ, and τ but not µ. The arrow-based Simon effect was not different from the word-based Simon effect on τ or σ but was on µ and mean RT. These distinct results on mean RT and ex-Gaussian parameters provide evidence that spatial information conveyed by the various location modes are different in the time-course of activation.

Multisensory integration is independent of perceived simultaneity.

The importance of multisensory integration for perception and action has long been recognised. Integrating information from individual senses increases the chance of survival by reducing the variability in the incoming signals, thus allowing us to respond more rapidly. Reaction times (RTs) are fastest when the components of the multisensory signals are simultaneous. This response facilitation is traditionally attributed to multisensory integration. However, it is unclear if facilitation of RTs occurs when stimuli are perceived as synchronous or are actually physically synchronous. Repeated exposure to audiovisual asynchrony can change the delay at which multisensory stimuli are perceived as simultaneous, thus changing the delay at which the stimuli are integrated-perceptually. Here we set out to determine how such changes in multisensory integration for perception affect our ability to respond to multisensory events. If stimuli perceived as simultaneous were reacted to most rapidly, it would suggest a common system for multisensory integration for perception and action. If not, it would suggest separate systems. We measured RTs to auditory, visual, and audiovisual stimuli following exposure to audiovisual asynchrony. Exposure affected the variability of the unisensory RT distributions; in particular, the slowest RTs were either speed up or slowed down (in the direction predicted from shifts in perceived simultaneity). Additionally, the multisensory facilitation of RTs (beyond statistical summation) only occurred when audiovisual onsets were physically synchronous, rather than when they appeared simultaneous. We conclude that the perception of synchrony is therefore independent of multisensory integration and suggest a division between multisensory processes that are fast (automatic and unaffected by temporal adaptation) and those that are slow (perceptually driven and adaptable).

Evidence of substantial development of inhibitory control and sustained attention between 6 and 8years of age on an unpredictable Go/No-Go task.

Inhibitory control and sustained attention are important cognitive abilities; however, their developmental trajectories remain unclear. In total, 35 6-year-olds, 32 8-year-olds, and 37 10-year-olds performed a Go/No-Go task; this required frequent responding to stimuli with infrequent inhibition to a target that appeared unpredictably. Children performed this task three times over 12months. Response time variability and accuracy measures, linked to inhibition and sustained attention, were assessed. Specifically, fast Fourier transform and ex-Gaussian analyses of response time data provided several measures of response time variability; these measures are thought to represent different components of sustained attention. The 6-year-olds performed less well than the older groups on most measures. The 8-year-olds exhibited greater momentary fluctuations in response time and made more long responses than the 10-year-olds; otherwise, there were few differences between the two older groups. Response inhibition and sustained attention developed significantly between 6 and 8years of age, with subtle changes in attentional control between 8 and 11years of age.

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 .

The effect of noise-induced variance on parameter recovery from reaction times.

BACKGROUND: Technical noise can compromise the precision and accuracy of the reaction times collected in psychological experiments, especially in the case of Internet-based studies. Although this noise seems to have only a small impact on traditional statistical analyses, its effects on model fit to reaction-time distributions remains unexplored. RESULTS: Across four simulations we study the impact of technical noise on parameter recovery from data generated from an ex-Gaussian distribution and from a Ratcliff Diffusion Model. Our results suggest that the impact of noise-induced variance tends to be limited to specific parameters and conditions. CONCLUSIONS: Although we encourage researchers to adopt all measures to reduce the impact of noise on reaction-time experiments, we conclude that the typical amount of noise-induced variance found in these experiments does not pose substantial problems for statistical analyses based on model fitting.

The Effect of Corrective Feedback on Performance in Basic Cognitive Tasks: An Analysis of RT Components.

The current work examines the effect of trial-by-trial feedback about correct and error responding on performance in two basic cognitive tasks: a classic Stroop task (n = 40) and a color-word matching task (n = 30). Standard measures of both RT and accuracy were examined in addition to measures obtained from fitting the ex-Gaussian distributional model to the correct RTs. For both tasks, RTs were faster in blocks of trials with feedback than in blocks without feedback, but this difference was not significant. On the other hand, with respect to the distributional analyses, providing feedback served to significantly reduce the size of the tails of the RT distributions. Such results suggest that, for conditions in which accuracy is fairly high, the effect of corrective feedback might either be to reduce the tendency to double-check before responding or to decrease the amount of attentional lapsing.

Neurocognitive intra-individual variability in mood disorders: effects on attentional response time distributions.

BACKGROUND: Attentional impairment is a core cognitive feature of major depressive disorder (MDD) and bipolar disorder (BD). However, little is known of the characteristics of response time (RT) distributions from attentional tasks. This is crucial to furthering our understanding of the profile and extent of cognitive intra-individual variability (IIV) in mood disorders. METHOD: A computerized sustained attention task was administered to 138 healthy controls and 158 patients with a mood disorder: 86 euthymic BD, 33 depressed BD and 39 medication-free MDD patients. Measures of IIV, including individual standard deviation (iSD) and coefficient of variation (CoV), were derived for each participant. Ex-Gaussian (and Vincentile) analyses were used to characterize the RT distributions into three components: mu and sigma (mean and standard deviation of the Gaussian portion of the distribution) and tau (the 'slow tail' of the distribution). RESULTS: Compared with healthy controls, iSD was increased significantly in all patient samples. Due to minimal changes in average RT, CoV was only increased significantly in BD depressed patients. Ex-Gaussian modelling indicated a significant increase in tau in euthymic BD [Cohen's d = 0.39, 95% confidence interval (CI) 0.09-0.69, p = 0.011], and both sigma (d = 0.57, 95% CI 0.07-1.05, p = 0.025) and tau (d = 1.14, 95% CI 0.60-1.64, p < 0.0001) in depressed BD. The mu parameter did not differ from controls. CONCLUSIONS: Increased cognitive variability may be a core feature of mood disorders. This is the first demonstration of differences in attentional RT distribution parameters between MDD and BD, and BD depression and euthymia. These data highlight the utility of applying measures of IIV to characterize neurocognitive variability and the great potential for future application.