Mechanisms of Training-Related Change in Processing Speed: A Drift-Diffusion Model Approach

Measuring Performance in Speeded Decision Tasks

A common finding during cognitive training is that people improve in the trained tasks (e.g., von Bastian, Belleville, et al., 2022; Simons et al., 2016). These improvements are referred to as training effects, while improvements in tasks different from the trained tasks are called transfer effects. Processing speed can be assessed with simple tasks that require people to perceptually locate, classify, compare or merely detect stimuli presented to them. In a two-choice RT task, for example, participants are presented with one or more stimuli and two response options to choose from, such as viewing a face and categorizing it as familiar or not. Often, the presentation time of the stimuli is limited and participants are asked to respond both quickly and accurately. Performance on these speeded tasks is then measured by RTs and error rates with decreases in mean RT and error rate used as indicators for training effects.

However, the use of RTs and error rates as performance measures for training-related improvements in processing speed tasks has several limitations. First, RT distributions are often skewed (e.g., Micceri, 1989). Therefore, commonly used metrics such as the mean do not capture the RT distribution well. Second, processing speed tasks are designed so that the task itself is easy and can be performed well by most people. Therefore, error rates typically show ceiling effects, resulting in limited variance and, thus, interpretability. Third, the theoretical interpretation of improvements in RTs and error rates is not informative with regards to the specific cognitive mechanisms affected by training. For example, RTs can be reduced not only by improving the efficiency in stimulus information processing, but also by enhancing the speed of motor responses and perceptual encoding (Pashler & Baylis, 1991; Strobach et al., 2013). Finally, changes in RT can indicate improved task performance but also reflect strategic changes in speed-accuracy trade-offs. Whereas slow RTs can be the result of a more cautious response strategy favoring accuracy over speed, fast RTs can reflect favoring speed over accuracy (e.g., Schouten & Bekker, 1967; Wood & Jennings, 1976). Overall, while improved RTs and error rates are often used to measure training effects, these measures provide only limited information about the mechanisms underlying training-related change (see also von Bastian, Reinhartz, et al., 2022).

Estimating Decision Components with the Drift-Diffusion Model

Cognitive models can provide more insight into response strategies and training-related mechanisms underlying changes in behavioral performance. A widely used cognitive computational model applicable to speeded decision tasks is the drift-diffusion model. The model is fit to the RT distribution and error rates simultaneously, thereby accounting for the speed-accuracy trade-off (Stafford et al., 2020), to estimate interpretable decision parameters (Ratcliff, 1978; Ratcliff & McKoon, 2008). Figure 1 illustrates the components of the decision-making process in Ratcliff’s (1978) diffusion model. The model distinguishes the rate of a noisy evidence accumulation process from response strategies and processes unrelated to the decision itself, such as stimulus encoding and motor response (Ratcliff, 1978; Ratcliff & McKoon, 2008).

Figure 1

In Ratcliff’s (1978) diffusion model, the evidence accumulation begins after the encoding of a presented stimulus, for example, a familiar or an unfamiliar face. The starting point of the evidence accumulation process reflects possible a priori biases towards either response option. In Figure 1, the starting point is located in the middle between the two response options reflecting no bias, while a bias would be indicated by a starting point shifted to one of the response options. The slope of the evidence accumulation process indicates how efficiently stimulus information is processed and is quantified as the drift rate (v). Reaching the threshold for either response option (e.g., that the presented face is familiar or unfamiliar) indicates that sufficient evidence has been accumulated to execute the decision. The distance between the two response thresholds is the boundary separation (a). The boundary separation reflects response caution and, thus, is an indicator for the speed-accuracy trade-off. The boundary separation can be wide, indicating high response caution, thus favoring accuracy and accumulating more evidence prior to a decision, or narrow, indicating low response caution, favoring speed and accumulating less evidence prior to a decision. Ultimately, when a decision has been made, a corresponding response has to be executed by, for example, pressing a response key. The non-decision time (t₀) captures the time for any other processes not directly related to the decision itself, for example, encoding the stimulus and executing the motor response.

Training-Related Changes in Decision Parameters

Previous studies have shown that repeatedly performing a task can affect evidence accumulation, response caution and, occasionally, non-decision processes. Several studies found that, when repeatedly performing the same speeded task for up to six sessions, the speed of evidence accumulation increases (Dutilh et al., 2011; Dutilh et al., 2009; Liu & Watanabe, 2012; Petrov et al., 2011; Ratcliff et al., 2006; van Ravenzwaaij et al., 2014; Zhang & Rowe, 2014). This indicates that training may improve the efficiency of information processing and suggests that increased drift rates are one factor underlying the decrease in response times that is consistently observed when repeatedly performing a task (Heathcote et al., 2000; Logan, 1992; Newell & Rosenbloom, 1981). Another factor that contributes to the decrease in response times is a shift in response strategy after repeated task practice. While drift rates increase during brief periods of training, the boundary separation indeed often decreases (Dutilh et al., 2011; Dutilh et al., 2009; Liu & Watanabe, 2012; Petrov et al., 2011; Ratcliff et al., 2006; Zhang & Rowe, 2014). Therefore, training can elicit a shift in response caution leading people to focus more on speed rather than accuracy. Training-related changes elicited in non-decision time are less consistent. Some studies have shown a decrease in this decision parameter (Dutilh et al., 2011; Dutilh et al., 2009; Petrov et al., 2011), while other studies suggest that repeatedly performing a task does not substantially affect perceptual and motor processing (Pashler & Baylis, 1991; Strobach et al., 2013).

Training-related improvements in evidence accumulation combined with an increased focus on speed, as opposed to accuracy, can explain why decreased RTs after training are still often accompanied by increased accuracy (Liu & Watanabe, 2012; Petrov et al., 2011; Ratcliff et al., 2006; Zhang & Rowe, 2014). More efficient information processing has been argued to counteract the decrease in response caution, thus, allowing for error rates to remain low. However, whether error rates decrease also depends on the type of feedback provided during task performance. For example, Dutilh and colleagues (2009) provided accuracy-related feedback to one half of their participants and speed-related feedback to the other half. The group focusing on accuracy made less errors already at the start of training and mainly improved in their RTs. The group focusing on speed showed the opposite pattern, with faster responses already at the start of training and mainly improving in accuracy. This demonstrates that the type of feedback provided when repeatedly performing a task influences not only the initial task performance but also the pattern of change during training. However, the type of feedback provided during training of speeded decision tasks has varied greatly in previous studies. While some studies have experimentally varied accuracy versus speed-related feedback (Dutilh et al., 2009; Zhang & Rowe, 2014), others have provided feedback either only for slow responses (Liu & Watanabe, 2012, van Ravenzwaaij et al., 2014), for slow, fast, and incorrect responses (Dutilh et al., 2011; Ratcliff et al., 2006) or instead given bonus points for correct responses (Petrov et al., 2011). Therefore, it remains unclear how training affects drift-diffusion parameters when consistent feedback is given on all responses throughout training.

Moreover, previous studies investigating changes during training used only a single training task during their training. This might be problematic, because it remains unclear whether changes observed are task-specific or task-general (Shipstead et al., 2012; von Bastian et al., 2019). In addition, these studies mainly used only one of two types of perceptual discrimination tasks, that is, either dot-motion detection tasks (Liu & Watanabe, 2012; Petrov et al., 2011; van Ravenzwaaij et al., 2014; Zhang & Rowe, 2014) or verbal discrimination tasks (Dutilh et al., 2011; Dutilh et al., 2009; Ratcliff et al., 2006). The limited variability in speeded decision tasks limits the generalizability of previously reported training-related changes in decision parameters and raises the question whether the same effects emerge in a wider variety of decision tasks. A recent paper by Schmiedek and colleagues (2022) addressed this concern by analyzing the difference in performance on three different choice-RT tasks before and after an extensive 100-session training intervention. The results showed pre- to post-training increases in drift rate and decreases in boundary separation and non-decision time across these different tasks. However, Schmiedek et al. (2022) did not report on changes occurring during training.

Further limitations of the previous studies investigating changes during training concern the duration of training and the number of participants included in the studies. While cognitive training interventions typically consist of 10 to 20 sessions performed over several weeks (von Bastian, Belleville, et al., 2022) and even up to 100 sessions (e.g., Schmiedek et al., 2010, 2022), the training-related changes in decision parameters have only been investigated for six training sessions or less (Dutilh et al., 2011; Dutilh et al., 2009; Liu & Watanabe, 2012; Petrov et al., 2011; Ratcliff et al., 2006; van Ravenzwaaij et al., 2014; Zhang & Rowe, 2014). Also, in most previous studies, sample sizes were small, ranging from 4 to 14 participants (Dutilh et al., 2011; Dutilh et al., 2009; Liu & Watanabe, 2012; Zhang & Rowe, 2014), increasing the risk of false-positive findings (Button et al., 2013). Changes in the drift-diffusion model parameters studied with accuracy-versus-speed group manipulations need to be interpreted with caution when, for example, groups consisted of only two participants each (Dutilh et al., 2009). Taken together, although the previous studies provide tentative evidence supporting changes in drift-diffusion parameters when repeatedly performing a single task, it remains unclear how these decision-making components change during an extensive, prolonged training regime with varied decision tasks and performance-based, trial-by-trial feedback.

Present Study

In the present study, we fit the drift-diffusion model to existing data of a previously published, multi-session processing speed training intervention (von Bastian & Oberauer, 2013). During this training intervention, 30 participants performed 20 training sessions over the course of four weeks, completing three different choice-RT tasks each session: a face-matching, a pattern-matching, and a digit-matching task. These tasks require evidence accumulation regarding whether two stimuli that are presented simultaneously are the same. Therefore, in our application, the diffusion model does not describe the processing of a single stimulus as in the original model by Ratcliff (1978). However, this model instead describes the decision-making process on a more general level, which is similar to previous studies that used tasks with similar (e.g., dot-motion detection tasks; Liu & Watanabe, 2012; Petrov et al., 2011; van Ravenzwaaij et al., 2014; Zhang & Rowe, 2014; verbal discrimination tasks; Dutilh et al., 2011; Dutilh et al., 2009; Ratcliff et al., 2006; and other choice-RT tasks; Schmiedek et al., 2022) or even higher complexity, such as judging the correctness of mathematical equations (Lerche et al., 2020).

The use of three different tasks enables the comparison of training-related changes in different perceptual contexts and task difficulties. Each task consisted of 500 trials per session, thereby providing 30,000 trials per participant over the course of training and, thus, a considerably higher trial count compared to previous studies. Unlike previous studies, no specific speed- or accuracy-related manipulations were applied in the present study; participants were instructed to perform both accurately and quickly during all trials when deciding whether the two presented stimuli portrayed the same face, same pattern, or same series of digits. After each trial, feedback on the correctness of the participant’s response was provided. The presentation time of the stimuli was adjusted adaptively based on the participant’s performance. Therefore, by providing variability in tasks, consistent feedback, and adaptive training, this study’s training regime made use of components that are crucial to successful training (Schmidt & Bjork, 1992) and offers an ideal dataset to investigate the changes in training-related mechanisms during an extensive processing speed training.

With this study, we examined whether decision parameters estimated by the drift-diffusion model show similar patterns during extensive training as previously found during brief training periods. Therefore, throughout the course of the 20 training sessions, we expected participants to increase in their efficiency of evidence accumulation, that is, their drift rate (Hypothesis 1). Furthermore, we expected a decrease in boundary separation over time, thereby indicating that participants decrease their response caution and increasingly emphasize speed over accuracy as their training progresses (Hypothesis 2). We did not expect to see such training-related changes in non-decision time and assumed perceptual and motor processing to remain unaffected by extensive training (Hypothesis 3). Additionally, we aimed to understand whether training-related changes differed for the different choice-RT tasks included (speeded face-, digit-, and pattern-matching tasks). Therefore, we tested our hypotheses using the type of task as a predictive factor in our analyses.

Participants

Participants of von Bastian and Oberauer (2013) were recruited for a “cognitive training study” at the University of Zurich via the university’s subject pool and using flyers. They were randomly assigned to 1 of 4 training groups practicing either different facets of working memory or practicing processing speed as an active control training compared to the working memory training groups. In the current study, we focus only on the active control group, which included 30 young adults (21 female, 9 male, M age = 23.77 years, SD = 4.73 years). All participants gave informed written consent for participation prior to testing. After completion of the study, participants received monetary compensation (CHF 150) or course credits.

Design

Study participation consisted of 4 weeks of training, in which participants were asked to perform 20 training sessions. Each session took about 30–40 minutes. Participants performed their training on their home computer via Tatool (von Bastian, Locher, & Ruflin, 2013). Therefore, participants could decide themselves when they preferred to perform their training. At the end of each training session, training data were automatically uploaded to a web server. Whereas self-administering training at home increases ecological validity, it can also lead to loss of experimental control. Several measures were taken to assure active and conscious execution of the training program, such as signing a participation agreement that training completion will be taken seriously, monitoring training data to detect irregularities, and maintaining regular email contact with the participants as well as providing technical support when needed.

Materials

Each training session consisted of three tasks with 500 trials each, in the following order: face-matching, digit-matching and pattern-matching, with breaks offered between tasks. During these tasks, participants were presented with a pair of stimuli for which they had to decide whether the pair showed the same person (face matching), the same six-digit number (digit matching), or the same fractal pattern (pattern matching). The face stimuli were 12 pictures each from 84 people (42 female, 42 male) with different facial expressions or accessories, taken from the AR face database (Martinez & Benavente, 1998). The digit stimuli were six-digit numbers presented in the same font. The pattern stimuli were 305 computer-generated squares of fractal patterns of various bright colors and shapes (see Figure 2 for some examples).

Figure 2

During all tasks, participants were asked to respond as quickly and as accurately as possible to the stimulus pair by pressing the “A” key for a matching stimulus pair, and the “L” key for a non-matching pair. After every trial, participants received feedback about the correctness of their response with a green check, indicating they correctly identified the stimulus pair as either matching or non-matching and a red cross indicating an incorrect response. The trial type (matching vs. non-matching), the matching stimulus pairs, and the combinations of non-matching pairs were selected at random. The intertrial interval was 100 ms. The stimuli were displayed until the participant’s response was registered or until the maximum stimulus presentation was exceeded. All participants started training with a maximum stimulus presentation duration of 5000 ms. During training, this maximum stimulus presentation was reduced adaptively based on the participant’s performance in the preceding 40% of trials to increase the difficulty of the tasks and to motivate participants to continuously focus on both speed and accuracy (see von Bastian & Oberauer, 2013, for more details on the adaptive level algorithm). The increase in difficulty was minor, however, with the maximum response time set to the 99th percentile of the RTs of those trials completed after the last reduction.

Data Preparation and Parameter Estimation

Model Estimation and Fit

We estimated the drift rate (v), boundary separation (a), and non-decision time (t₀) separately per task. For each task, parameters were estimated for participants and training sessions (accounting for the dependency between sessions using the “depends” fast-dm function) with a fixed starting point of 0.5 between the upper (1, correct response) and lower (0, incorrect response) threshold using the open-source fast-dm-30 software applying Kolmogorov-Smirnov as optimization criterion (Voss & Voss, 2007, 2008; Voss et al., 2015). Subsequently, using the fast-dm construct-samples tool (Voss & Voss, 2007, 2008; Voss et al., 2015), data were simulated for each task, participant, and the corresponding sessions separately, with the same number of trials as in the empirical session data. As illustrated in Figure 3, while only slightly overestimating RTs in the first quartile, the model fits the data well. Identical patterns of model fit were found for all tasks irrespective of stimuli and differences in the number of available data points post-trimming.

Figure 3

Analysis of Training- and Task-Related Effects

Linear Mixed-Effects (LME) models were used to analyze the training data with the lmer function from the lme4 package (Bates et al., 2015) in R (version 4.2.1; R Core Team, 2022). The models were specified with the dependent variable (mean RT to correct responses, error rate, drift rate, boundary separation, or non-decision time) predicted by training session (1 to 20) and training task (face, digit, and pattern matching), with a random effect of participant on the intercept.¹ Type III ANOVA test statistics were estimated for the LME models using the lmerTest package (Kuznetsova et al., 2017). Satterthwaite’s degrees of freedom were used to estimate p-values for the effects of session, task, and their interaction.

Reaction Times and Error Rates

Figure 4 illustrates performance in the training tasks over the course of 20 training sessions. For mean RT to correct responses, we found a significant main effect of session, F(19, 1440) = 72.49, p < .001, η_p² = 0.49, and of task, F(2, 1442) = 987.77, p < .001, η_p² = 0.58. Moreover, the interaction between session and task was significant, F(38, 1440) = 10.01, p < .001, η_p² = 0.21. Similarly, for error rates, the effect of session was also significant, F(19, 1440) = 5.80, p < .001, η_p² = 0.07, as was the effect of task, F(2, 1443) = 345.57, p < .001, η_p² = 0.32. However, the interaction between session and task was not significant, F(38, 1440) = 1.05, p = .391, η_p² = 0.03. For better comparability to the original analysis reported in von Bastian and Oberauer (2013), we ran the same set of analyses but including sessions with less than 4% error rates. The patterns of results were the same as for the reduced data set used in the present study, except that the interaction between session and task was then also a significant predictor of error rates, F(38, 1585) = 1.43, p = .045, η_p² = 0.03.

Figure 4

Diffusion-Model Parameters

Figure 5 illustrates the changes in drift rate, boundary separation, and non-decision time over the course of the 20 training sessions. Drift rate increased over the course of the sessions, F(19, 1440) = 12.75, p < .001, η_p² = 0.14, and differed per task, F(2, 1445) = 826.48, p < .001, η_p² = 0.53. Also, the interaction of task and session was significant, F(38, 1440) = 1.78, p = .003, η_p² = 0.04. In contrast to the drift rate, boundary separation decreased over the course of the sessions, F(19, 1440) = 82.63, p < .001, η_p² = 0.52. The effect of task on boundary separation was significant, F(2, 1443) = 300.17, p < .001, η_p² = 0.29, as well as the interaction between task and session, F(38, 1440) = 6.81, p < .001, η_p² = 0.15. Non-decision time also decreased as an effect of session, F(19, 1440) = 32.97, p < .001, η_p² = 0.30, and differed per task, F(2, 1441) = 1410.51, p < .001, η_p² = 0.66. Session and task also interacted with regards to non-decision time, F(38, 1440) = 3.73, p < .001, η_p² = 0.09. We ran the same estimation procedures while including the otherwise excluded sessions with less than 4% error rates, which also fit the data well. The patterns of results from these subsequent analyses were the same as for the estimated parameters using the reduced data set, except that the interaction between session and task was no longer a significant predictor of drift rate, F(38, 1703) = 1.23, p = .158.

Figure 5

In summary, drift rates increased with training, while boundary separation and non-decision time decreased. These changes over the course of training were found across the individual participants, as shown in Figures A1-3 in the Appendix. Drift rates were highest for pattern-matching, followed by digit-matching and face-matching. The reverse pattern emerged for boundary separation which was highest in the face-matching task and lowest in pattern-matching, although this difference was most pronounced at the beginning of training. Non-decision time remained lowest for pattern-matching throughout all training sessions.

Limitations and Outlook

The use of multiple tasks during an extensive amount of training sessions strengthens the implications of the current study and allows for conclusions about training-related changes with regards to different task stimuli beyond their initial training effects. However, direct comparisons between the three tasks must be interpreted with caution. First, the drift-diffusion parameters were generated separately per task which might limit the comparability of the exact values of the parameters between these tasks. This limitation does not, however, hold for the RT and error data which show effects equivalent to the parameters. Therefore, we can compare the parameters between tasks at least to some degree. Second, the difficulty of the training tasks was consistent with the order of the trained tasks within each training session. Thus, it is possible that there was a confounding effect between task difficulty and task order during training: the most difficult task of face-matching was performed first, while the seemingly easiest task of pattern-matching was performed last and the digit-matching task in-between. This raises the question whether participants improved within individual training sessions which led them to perform best during the final pattern-matching task. Since the difference between tasks was present in all measures and drift-diffusion parameters, we cannot completely exclude an impact of this confound between task order and task difficulty.

Given our results, we recommend that future training studies apply an extensive training regime with at least 10 training sessions and multiple training tasks in order to disentangle the differential effects of session and task. However, we also recommend accounting for differences in task difficulty and task order during training. Furthermore, it would be of great value to investigate how training-related changes relate to transfer effects on untrained tasks of similar or different cognitive domains. Few and only recent studies have applied drift-diffusion analyses to analyze transfer effects in working memory tasks (e.g., Chen et al., 2022; Schmiedek et al., 2022). Findings from these studies suggested that pre- to post-training effects in processing speed tasks (Schmiedek et al., 2022) are similar to those observed in our study during training. To study the associations between training-related change in drift-diffusion parameters and transfer effects, a certain number of trials is required, as discussed in the results section. Further, a substantial number of participants is required, as stable correlations are obtained with a minimum of 250 participants (Schönbrodt & Perugini, 2013). The present study does not include this substantial number and, therefore, we were not able to associate the parameter changes during training with transfer measures.

Due to this study’s sample size, we were also not able to investigate individual differences during training and possible differences in training curves and effects. Overall, the stated training-related changes were found across individual participants, with potential for individual variation mainly in the drift rate (see Figures A1-3 in the Appendix). Future studies with larger statistical power are required to investigate such individual variation in drift-diffusion model parameters, ideally with Bayesian hierarchical approaches (e.g., Heathcote et al., 2019; Wiecki et al., 2013) which provide more flexibility in modeling individual differences over time.