Performance-contingent reward increases the use of congruent distracting information.

In conflict tasks like the Simon task, participants are instructed to respond to a task-relevant target dimension while ignoring additional distracting information. In the Simon task the distracting spatial information can be congruent or incongruent with the task-relevant target information, causing a congruency effect. As seen in the proportion congruency effect and the congruency sequence effect, this congruency effect is larger in mostly congruent blocks and following congruent trials, respectively. Common theories suggest that when the proportion of incongruent trials is high or after an incongruent trial, focus on the task-relevant target information is increased and distracting information is inhibited. In two experiments, we investigated how reward modulates these phenomena. Specifically, performance-contingent reward - but not non-contingent reward - increased the usage of the distracting information in mostly congruent blocks or following congruent trials, while the adaptation to incongruency (i.e., mostly incongruent blocks or preceding incongruent trials) was the same in all conditions. Additional diffusion model analyses found that this effect of performance-contingent reward was captured by the drift rate parameter. These results suggest an increased focus on the target information by incongruent trials independent from reward, while the adaptation to (mostly) congruent trials characterized by increased usage of distracting information can be motivationally boosted. That is, performance-contingent reward increases the use of congruent distracting information beyond a mere relaxation of the increased target-focus following (mostly) congruent trials.

On the difficulty to think in ratios: a methodological bias in Stevens' magnitude estimation procedure.

In the field of new psychophysics, the magnitude estimation procedure is one of the most frequently used methods. It requires participants to assess the intensity of a stimulus in relation to a reference. In three studies, we examined whether difficulties of thinking in ratios influence participants' intensity perceptions. In Study 1, a standard magnitude estimation procedure was compared to an adapted procedure in which the numerical response dimension was reversed so that smaller (larger) numbers indicated brighter (darker) stimuli. In Study 2, participants first had to indicate whether a stimulus was brighter or darker compared to the reference, and only afterwards they estimated the magnitude of this difference, always using ratings above the reference to indicate their perception. In Study 3, we applied the same procedure as in Study 2 to a different physical dimension (red saturation). Results from Study 1 (N = 20) showed that participants in the reversal condition used more (less) extreme ratings for brighter (darker) stimuli compared to the standard condition. Data from the unidirectional method applied in Study 2 (N = 34) suggested a linear psychophysical function for brightness perception. Similar results were found for red saturation in Study 3 (N = 36) with a less curved power function describing the association between objective red saturation and perceived redness perception. We conclude that the typical power functions that emerge when using a standard magnitude estimation procedure might be biased due to difficulties experienced by participants to think in ratios.

Age differences in diffusion model parameters: a meta-analysis.

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

Processing emotional expressions under fear of rejection: Findings from diffusion model analyses.

In the mood-of-the-crowd task, participants have to classify crowds of emotional faces according to the predominant emotions. We examined 2 possible moderators of a previously found positivity bias in this task: fear of rejection and threat of social exclusion. Participants (Study 1: N = 84, Study 2: N = 126) received bogus feedback on their future social relationships that was either negative (frustration group) or positive (satisfaction group). By means of diffusion model analyses (Ratcliff, 1978), we examined the cognitive processes involved in the task. Our main findings are that more fearful individuals accumulated negative facial information more quickly than their less fearful counterparts (drift rate of the diffusion model; dynamic bias). Furthermore, individuals with a lower fear of rejection who were frustrated showed a prior bias (i.e., shifted starting point of the diffusion model) for positive rather than negative faces in contrast to the more fearful individuals. This suggests that the less fearful individuals tried to restore the thwarted motive by shifting a criterion, so that ambiguous situations are perceived more positively. The present studies demonstrate that diffusion modeling supplies important information about underlying cognitive processes in the domain of the affiliation motive. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Do Non-Decision Times Mediate the Association between Age and Intelligence across Different Content and Process Domains?

In comparison to young adults, middle-aged and old people show lower scores in intelligence tests and slower response times in elementary cognitive tasks. Whether these well-documented findings can both be attributed to a general cognitive slow-down across the life-span has become subject to debate in the last years. The drift diffusion model can disentangle three main process components of binary decisions, namely the speed of information processing, the conservatism of the decision criterion and the non-decision time (i.e., time needed for processes such as encoding and motor response execution). All three components provide possible explanations for the association between response times and age. We present data from a broad study using 18 different response time tasks from three different content domains (figural, numeric, verbal). Our sample included people between 18 to 62 years of age, thus allowing us to study age differences across young-adulthood and mid-adulthood. Older adults generally showed longer non-decision times and more conservative decision criteria. For speed of information processing, we found a more complex pattern that differed between tasks. We estimated mediation models to investigate whether age differences in diffusion model parameters account for the negative relation between age and intelligence, across different intelligence process domains (processing capacity, memory, psychometric speed) and different intelligence content domains (figural, numeric, verbal). In most cases, age differences in intelligence were accounted for by age differences in non-decision time. Content domain-general, but not content domain-specific aspects of non-decision time were related to age. We discuss the implications of these findings on how cognitive decline and age differences in mental speed might be related.

Diffusion modeling and intelligence: Drift rates show both domain-general and domain-specific relations with intelligence.

Several previous studies reported relationships between speed of information processing as measured with the drift parameter of the diffusion model (Ratcliff, 1978) and general intelligence. Most of these studies utilized only few tasks and none of them used more complex tasks. In contrast, our study (N = 125) was based on a large battery of 18 different response time tasks that varied both in content (numeric, figural, and verbal) and complexity (fast tasks with mean RTs of ca. 600 ms vs. more complex tasks with mean RTs of ca. 3,000 ms). Structural equation models indicated a strong relationship between a domain-general drift factor and general intelligence. Beyond that, domain-specific speed of information processing factors were closely related to the respective domain scores of the intelligence test. Furthermore, speed of information processing in the more complex tasks explained additional variance in general intelligence. In addition to these theoretically relevant findings, our study also makes methodological contributions showing that there are meaningful interindividual differences in content specific drift rates and that not only fast tasks, but also more complex tasks can be modeled with the diffusion model. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Sequential sampling models with variable boundaries and non-normal noise: A comparison of six models.

One of the most prominent response-time models in cognitive psychology is the diffusion model, which assumes that decision-making is based on a continuous evidence accumulation described by a Wiener diffusion process. In the present paper, we examine two basic assumptions of standard diffusion model analyses. Firstly, we address the question of whether participants adjust their decision thresholds during the decision process. Secondly, we investigate whether so-called Lévy-flights that allow for random jumps in the decision process account better for experimental data than do diffusion models. Specifically, we compare the fit of six different versions of accumulator models to data from four conditions of a number-letter classification task. The experiment comprised a simple single-stimulus task and a more difficult multiple-stimulus task that were both administered under speed versus accuracy conditions. Across the four experimental conditions, we found little evidence for a collapsing of decision boundaries. However, our results suggest that the Lévy-flight model with heavy-tailed noise distributions (i.e., allowing for jumps in the accumulation process) fits data better than the Wiener diffusion model.

Experimental validation of the diffusion model based on a slow response time paradigm.

The diffusion model (Ratcliff, Psychol Rev 85(2):59-108, 1978) is a stochastic model that is applied to response time (RT) data from binary decision tasks. The model is often used to disentangle different cognitive processes. The validity of the diffusion model parameters has, however, rarely been examined. Only few experimental paradigms have been analyzed with those being restricted to fast response time paradigms. This is attributable to a recommendation stated repeatedly in the diffusion model literature to restrict applications to fast RT paradigms (more specifically, to tasks with mean RTs below 1.5 s per trial). We conducted experimental validation studies in which we challenged the necessity of this restriction. We used a binary task that features RTs of several seconds per trial and experimentally examined the convergent and discriminant validity of the four main diffusion model parameters. More precisely, in three experiments, we selectively manipulated these parameters, using a difficulty manipulation (drift rate), speed-accuracy instructions (threshold separation), a more complex motoric task (non-decision time), and an asymmetric payoff matrix (starting point). The results were similar to the findings from experimental validation studies based on fast RT paradigms. Thus, our experiments support the validity of the parameters of the diffusion model and speak in favor of an extension of the model to paradigms based on slower RTs.

The Quality of Response Time Data Inference: A Blinded, Collaborative Assessment of the Validity of Cognitive Models.

Most data analyses rely on models. To complement statistical models, psychologists have developed cognitive models, which translate observed variables into psychologically interesting constructs. Response time models, in particular, assume that response time and accuracy are the observed expression of latent variables including 1) ease of processing, 2) response caution, 3) response bias, and 4) non-decision time. Inferences about these psychological factors, hinge upon the validity of the models' parameters. Here, we use a blinded, collaborative approach to assess the validity of such model-based inferences. Seventeen teams of researchers analyzed the same 14 data sets. In each of these two-condition data sets, we manipulated properties of participants' behavior in a two-alternative forced choice task. The contributing teams were blind to the manipulations, and had to infer what aspect of behavior was changed using their method of choice. The contributors chose to employ a variety of models, estimation methods, and inference procedures. Our results show that, although conclusions were similar across different methods, these "modeler's degrees of freedom" did affect their inferences. Interestingly, many of the simpler approaches yielded as robust and accurate inferences as the more complex methods. We recommend that, in general, cognitive models become a typical analysis tool for response time data. In particular, we argue that the simpler models and procedures are sufficient for standard experimental designs. We finish by outlining situations in which more complicated models and methods may be necessary, and discuss potential pitfalls when interpreting the output from response time models.

A diffusion model analysis of the response-effect compatibility effect.

Humans act goal-oriented, and this idea is at the core of ideomotor theory (IT), which claims that actions are selected by mentally anticipating the sensory consequences brought about by the respective bodily movement (i.e., their action effects). Evidence for this effect anticipation mainly derives from the response-effect (R-E) compatibility (REC) paradigm: In the spatial domain, for example, a left response is produced faster (and sometimes less error-prone) if followed by a compatible left rather than an incompatible right action effect. In the present study, we employed the diffusion model to elucidate the reasons for this observation. To this end, we reanalyzed data from the seminal study by Kunde (2001) and from a new experiment. The overall results suggest that REC affects drift rate. This result fits well with conceptualizing REC as an endogenously created case of stimulus-response compatibility (SRC). Several consequences of this view are discussed against the background of available empirical results. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Speed-accuracy manipulations and diffusion modeling: Lack of discriminant validity of the manipulation or of the parameter estimates?

The diffusion model (Ratcliff, 1978) is a mathematical model theorized to untangle different cognitive processes involved in binary decision tasks. To test the validity of the diffusion model parameters, several experimental validation studies have been conducted. In these studies, the validity of the threshold separation parameter was tested with speed-accuracy manipulations. Typically, this manipulation not only results in the expected effect on the threshold separation parameter but it also impacts nondecision time: Nondecision time is longer in the accuracy than in the speed condition. There are two possible interpretations of the finding: On the one hand, it could indicate that speed versus accuracy instructions really have an impact on the duration of extradecisional processes. On the other hand, the effect on the measure for nondecision time could be spurious-that is, based on a problem in the parameter estimation procedures. In simulation studies-with the parameter sets based on typical values from experimental validation studies-we checked for possible biases in the parameter estimation. Our analyses strongly suggest that the observed pattern (i.e., slower nondecision processes under accuracy instructions) is attributable to a lack of discriminant validity of the manipulation rather than to trade-offs in the parameter estimations.

Interindividual differences in the intraindividual association of competence and well-being: Combining experimental and intensive longitudinal designs.

OBJECTIVE: The aim of the present study is to assess whether people differ in the degree to which their well-being is affected by fulfillment of the need for competence. Specifically, we want to examine (a) whether interindividual differences in the within-person coupling of competence satisfaction and well-being (competence satisfaction effect) and of competence dissatisfaction and well-being (competence dissatisfaction effect) exist, and (b) whether these differences moderate the effects of an experimentally induced frustration of the need for competence. METHOD: A daily diary study (N = 89) and a laboratory based experiment (N = 150) were conducted to investigate interindividual differences in need effects. In a third study, participants of an additional daily diary study (N = 129) were subsequently subjected to an experimental frustration of the need for competence. RESULTS: Including interindividual differences in the within-person coupling of need fulfillment and well-being improved model fit significantly, indicating that there were statistically meaningful interindividual differences in need effects. The interaction of competence satisfaction effect and competence dissatisfaction effect moderated the effect of an experimental competence frustration on negative affect. CONCLUSION: Results show that interindividual differences in the association of competence fulfillment and well-being are a matter of degree, but not quality. They also support the claim that need satisfaction and dissatisfaction are more than psychometric opposites.

Impact of Context Information on Metaphor Elaboration.

In experiments by Gibbs, Kushner, and Mills (1991) , sentences were supposedly either authored by poets or by a computer. Gibbs et al. (1991) concluded from their results that the assumed source of the text influences speed of processing, with a higher speed for metaphorical sentences in the Poet condition. However, the dependent variables used (e.g., mean RTs) do not allow clear conclusions regarding processing speed. It is also possible that participants had prior biases before the presentation of the stimuli. We conducted a conceptual replication and applied the diffusion model ( Ratcliff, 1978 ) to disentangle a possible effect on processing speed from a prior bias. Our results are in accordance with the interpretation by Gibbs et al. (1991) : The context information affected processing speed, not a priori decision settings. Additionally, analyses of model fit revealed that the diffusion model provided a good account of the data of this complex verbal task.

How many trials are required for parameter estimation in diffusion modeling? A comparison of different optimization criteria.

Diffusion models (Ratcliff, 1978) make it possible to identify and separate different cognitive processes underlying responses in binary decision tasks (e.g., the speed of information accumulation vs. the degree of response conservatism). This becomes possible because of the high degree of information utilization involved. Not only mean response times or error rates are used for the parameter estimation, but also the response time distributions of both correct and error responses. In a series of simulation studies, the efficiency and robustness of parameter recovery were compared for models differing in complexity (i.e., in numbers of free parameters) and trial numbers (ranging from 24 to 5,000) using three different optimization criteria (maximum likelihood, Kolmogorov-Smirnov, and chi-square) that are all implemented in the latest version of fast-dm (Voss, Voss, & Lerche, 2015). The results revealed that maximum likelihood is superior for uncontaminated data, but in the presence of fast contaminants, Kolmogorov-Smirnov outperforms the other two methods. For most conditions, chi-square-based parameter estimations lead to less precise results than the other optimization criteria. The performance of the fast-dm methods was compared to the EZ approach (Wagenmakers, van der Maas, & Grasman, 2007) and to a Bayesian implementation (Wiecki, Sofer, & Frank, 2013). Recommendations for trial numbers are derived from the results for models of different complexities. Interestingly, under certain conditions even small numbers of trials (N < 100) are sufficient for robust parameter estimation.

Retest reliability of the parameters of the Ratcliff diffusion model.

In the recent years, there is a growing interest to use the Ratcliff Diffusion Model (1978) for diagnostic purposes as the parameters of the model capture interindividual differences in specific cognitive processes. The parameters are estimated using reaction time data from binary classification tasks. For a potential diagnostic application of parameter values sufficient reliability is a necessary precondition. In two studies, each with two sessions separated by 1 week, the retest reliability of the diffusion model parameters was assessed. In Study 1, 105 participants completed a lexical decision task and a recognition memory task. In Study 2, 128 participants worked on an associative priming task. Results show that the reliability of the main parameters of the Ratcliff Diffusion Model (in particular of the speed of information accumulation and the threshold separation with rs > 0.70 for all three tasks) is satisfying. Besides, we analyzed the influence of the number of trials on the retest reliability using different estimation methods (Kolmogorov-Smirnov, Maximum Likelihood, Chi-square and EZ) and both empirical and simulated datasets.

Model Complexity in Diffusion Modeling: Benefits of Making the Model More Parsimonious.

The diffusion model (Ratcliff, 1978) takes into account the reaction time distributions of both correct and erroneous responses from binary decision tasks. This high degree of information usage allows the estimation of different parameters mapping cognitive components such as speed of information accumulation or decision bias. For three of the four main parameters (drift rate, starting point, and non-decision time) trial-to-trial variability is allowed. We investigated the influence of these variability parameters both drawing on simulation studies and on data from an empirical test-retest study using different optimization criteria and different trial numbers. Our results suggest that less complex models (fixing intertrial variabilities of the drift rate and the starting point at zero) can improve the estimation of the psychologically most interesting parameters (drift rate, threshold separation, starting point, and non-decision time).

Assessing cognitive processes with diffusion model analyses: a tutorial based on fast-dm-30.

Diffusion models can be used to infer cognitive processes involved in fast binary decision tasks. The model assumes that information is accumulated continuously until one of two thresholds is hit. In the analysis, response time distributions from numerous trials of the decision task are used to estimate a set of parameters mapping distinct cognitive processes. In recent years, diffusion model analyses have become more and more popular in different fields of psychology. This increased popularity is based on the recent development of several software solutions for the parameter estimation. Although these programs make the application of the model relatively easy, there is a shortage of knowledge about different steps of a state-of-the-art diffusion model study. In this paper, we give a concise tutorial on diffusion modeling, and we present fast-dm-30, a thoroughly revised and extended version of the fast-dm software (Voss and Voss, 2007) for diffusion model data analysis. The most important improvement of the fast-dm version is the possibility to choose between different optimization criteria (i.e., Maximum Likelihood, Chi-Square, and Kolmogorov-Smirnov), which differ in applicability for different data sets.

Diffusion models in experimental psychology: a practical introduction.

Stochastic diffusion models (Ratcliff, 1978) can be used to analyze response time data from binary decision tasks. They provide detailed information about cognitive processes underlying the performance in such tasks. Most importantly, different parameters are estimated from the response time distributions of correct responses and errors that map (1) the speed of information uptake, (2) the amount of information used to make a decision, (3) possible decision biases, and (4) the duration of nondecisional processes. Although this kind of model can be applied to many experimental paradigms and provides much more insight than the analysis of mean response times can, it is still rarely used in cognitive psychology. In the present paper, we provide comprehensive information on the theory of the diffusion model, as well as on practical issues that have to be considered for implementing the model.