Automatic and controlled stimulus processing in conflict tasks: Superimposed diffusion processes and delta functions
Introduction
In conflict tasks, the processing of task-relevant and task-irrelevant stimulus features may activate different responses that compete for execution. In order to produce a correct response in these tasks, participants have to suppress the task-irrelevant activation as much as possible. There are at least three tasks, however, which indicate that this suppression must be incomplete because a clear influence of the task-irrelevant features on performance can be observed. The most prominent example represents the Stroop task (Stroop, 1935), in which participants are asked to name the color of an inked color word (for a review, see MacLeod, 1991). Participants typically respond faster when the task-relevant ink color and the task-irrelevant color name require the same response than when they require different ones. The Simon task (Simon, 1969) represents another prominent example (for a review, see Lu & Proctor, 1995). In this task, a non-spatial stimulus attribute (e.g., color, form, tone pitch) defines the task-relevant feature whereas the spatial position of the stimulus is task-irrelevant. For example, participants are instructed to perform a left-hand response to a blue circle and a right-hand response to a red circle. Responses are typically faster when the stimulus side and the response side match than when they mismatch. Finally, the Eriksen flanker task (Eriksen & Eriksen, 1974) embodies a third example (for a review, see Eriksen, 1995). In this task, participants are asked to respond to a visual target item that is flanked by task-irrelevant items. For example, the letter S may require a left-hand response and the letter H a right-hand response. In congruent trials, the flankers match the identity of the target item (e.g., SSS S SSS), whereas in incongruent trials, the flankers match the identity of the alternative target stimulus (e.g., HHH S HHH). Responses typically are faster in congruent than in incongruent trials.
Although the same effect pattern is observed in these conflict tasks at the level of mean reaction time (RT), a distinct pattern emerges at a more fine-grained distributional level (e.g., Balota and Yap, 2011, Heathcote et al., 1991) suggesting that different mechanisms may operate across these tasks (Pratte, Rouder, Morey, & Feng, 2010). Often the size of a congruency effect differs between fast and slow responses. For some tasks, like the Stroop task, the congruency effect usually grows with increasing RT (e.g., Pratte et al., 2010, Spieler et al., 1996), whereas for other tasks, like the visual Simon task, the effect usually declines (e.g., Burle et al., 2005, Pratte et al., 2010). These different patterns have been considered to reflect different underlying mechanisms across conflict tasks. Delta functions – often also called delta plots – introduced by De Jong, Liang, and Lauber (1994) provide an intuitively accessible way to reveal different time-courses of congruency effects. These functions depict the quantile difference for the RT distributions in incongruent and congruent conditions on the y-axis and the average of these two quantiles on the x-axis. Increasing congruency effects are associated with positive-going delta functions, whereas decreasing effects are associated with negative-going delta functions (for a detailed characterization of delta functions, see Speckman, Rouder, Morey, & Pratte, 2008).
Following the seminal paper by De Jong et al. (1994), delta functions have been frequently applied to examine the mechanism underlying conflict tasks. Specifically, Ridderinkhof (2002a) promoted this method to examine his activation–suppression model. According to this dual-process model, automatic response activation by task-irrelevant stimulus attributes is held in check by an active (top-down) suppression process of executive control. Critically, selective suppression is assumed to gradually build up, varying in its onset, build-up rate, or strength as a function of both task and person factors. Thus, in accord with these assumptions, suppression has been taken to be more efficient for slower responses. More specifically, this is often indicated by negative-going delta functions in the visual Simon task and by initially positive-going and subsequently flat delta functions in the Eriksen flanker task (for a review, see van den Wildenberg et al., 2010). Sometimes, even inverted U-shaped delta functions have been reported for these tasks (e.g., Bratzke et al., 2012, Davranche and McMorris, 2009, Mattler, 2003, Wiegand and Wascher, 2005).
In addition, the analysis of delta functions has proved to be a very useful tool to examine potentially deficient executive control processes in developmental and clinical populations. For example, less-negative going delta functions were taken to indicate a deficiency of suppression in advanced age groups and persons suffering from ADHD and Parkinson disease (cf. van den Wildenberg et al., 2010). However, the interpretation of negative-going delta functions as a marker of selective suppression has not gone unchallenged. In particular, the Stroop task and the Eriksen flanker task commonly show positive-going delta functions, and even in the Simon task negative-going delta functions are found to be restricted to specific visual task variants (cf. Proctor, Miles, & Baroni, 2011). Given the impact of delta functions as an inferential tool, it is therefore essential to develop a better understanding of the processes as well as conditions that lead to different slopes in delta functions.
Positive-going delta functions are consistent with many processing models that predict a positive relationship between the mean and the standard deviation of RT, a relationship that is typically observed (Wagenmakers and Brown, 2007). By contrast, negative-going delta functions violate this commonly observed principle, because in this case larger RT variability is observed in congruent trials instead of incongruent ones. Therefore, negative-going delta functions pose a particular theoretical challenge to RT modelers. Schwarz and Miller (2012) elaborated this issue and provided five classes of cognitive architectures that can account for such plots. For example, the class of exhausting models assumes that the processing mechanisms differ between congruent and incongruent trials. In congruent trials, processing proceeds serially starting with stimulus encoding A, followed by response activation , and finishing with response execution C. Therefore, in congruent trials the total RT is the sum of the corresponding three stage durations. In incongruent trials, however, it is assumed that the encoding stage A detects a mismatch between relevant and irrelevant stimulus attributes. According to these authors, this mismatch leads not only to the activation of the correct response but also to the inhibition of the incorrect response. These two processes proceed in parallel and activation of the correct response requires time units whereas inhibition of the wrong response requires time units. As a result, response execution cannot begin before these two processes are completed (i.e., after time units). Because the mean of is usually larger than the mean of , this model can account for longer RTs in incongruent than in congruent trials. Most crucially, however, under specific distributional assumptions about and , this model even predicts a smaller variance in incongruent than in congruent trials, thereby violating the principle of a positive relationship between the mean and the standard deviation of RT, and thus accounting for negative-going delta functions. Schwarz and Miller (2012) put forward similar elaborations for traditional stage models (Sternberg, 1969), mixture models (Yantis, Meyer, & Smith, 1991), cascade models (McClelland, 1979), and parallel channels models (Townsend & Ashby, 1983).
Interestingly, current diffusion models fail in explaining negative-going delta functions (Pratte et al., 2010, Schwarz and Miller, 2012, Servant et al., 2014), although these models usually provide plausible and successful accounts of RT data (Hübner et al., 2010, Ratcliff and Smith, 2004, Ratcliff and McKoon, 2008, Schwarz, 2006). The prominent diffusion model (Ratcliff, 1978, Ratcliff and Smith, 2004, Stone, 1960) assumes that noisy task-relevant information is accumulated over time until one of two decision boundaries is reached at which the corresponding response is launched. One boundary is associated with the correct response and the other boundary is associated with the incorrect response. Accumulation of evidence starts somewhere between the two boundaries. As shown by Wagenmakers and Brown (2007) this class of RT models predicts that the mean and the standard deviation of RT are positively related and thus do not allow for negative-going delta functions.
A modified version of the diffusion process model, the premature sampling model (Rouder, 1996), cannot account for such negative-going delta functions either (see also Pratte et al., 2010). This modified version assumes that the accumulation process in the incongruent conditions initially drifts at a constant rate towards the decision boundary associated with the incorrect response. After some time, the process abruptly shifts its direction and then drifts with the same rate towards the decision boundary associated with the correct response. As discussed in Pratte et al. (2010), this premature sampling model mimics a standard accumulation model with a shifted starting point of the task-relevant process. Consequently, as stressed by these authors (Pratte et al., 2010, p. 2023), this modified model would also not predict negative-going delta functions.
Another sophistication of the standard diffusion model was suggested by Schwarz and Miller (2012, p. 567). They proposed two simultaneous accumulation processes, respectively, for processing of relevant and irrelevant stimulus features. In congruent trials, the two processes activate the same response, whereas in incongruent trials they activate opposite responses. More specifically, in congruent trials the two activations add whereas they subtract in incongruent trials (compare also Schwarz & Ischebeck, 2003). On the basis of the additional assumptions regarding the diffusion process for irrelevant stimulus features, the authors concluded that this sophisticated diffusion model cannot account for negative-going delta functions. Nevertheless, the authors did not rule out the possibility that more complex variants of the diffusion model may produce such functions.
Moreover, further elaborations of the standard diffusion model have recently been developed to account for RT effects in the flanker task. First, the shrinking spotlight (SSP) model explains the flanker effect by an attentional zoom-lens metaphor with a time-dependent drift rate (White et al., 2012, White et al., 2011). The SSP model assumes that visual attention is widely distributed at the beginning of the trial and zooms into the target stimulus with increasing time. Thereby the effect of the flankers diminish over the time-course of a single trial. White et al. (2011) and White et al. (2012) have successfully applied this elaboration of the standard diffusion model to data from the flanker task. Second, the dual-stage two-phase (DSTP) model of selective attention by Hübner and colleagues (Dambacher and Hübner, 2015, Hübner et al., 2010, Hübner and Töbel, 2014) assumes an early and late stage of response selection. Each phase is governed by a separate diffusion process. In an early phase, stimulus information is passed through a perceptual filter which corresponds to an early selection stage. However, the filtering in the first stage is imperfect and flankers can hence influence the processing within this stage. The second phase corresponds to a late selection stage and operates on the stimulus information that has been selected by the first stage. Both elaborations have been successfully applied to data from the flanker task. According to Servant et al. (2014), however, neither elaboration can explain processing in the Simon task, because they are not capable to account for negative-going delta functions.
Therefore, it is the main goal of the present article to introduce an elaboration of the standard diffusion model that can provide a general model framework for different conflict tasks. Specifically, in this article we suggest a Diffusion Model for Conflict tasks (DMC) that takes into account the widespread idea of two simultaneous processes, where one process (i.e., controlled processes) operates on task-relevant information and the other (i.e., automatic processes) on task-irrelevant information (e.g., Botvinick et al., 2001, Cohen et al., 1990, Hommel, 1993, Kornblum et al., 1990, Lindsay and Jacoby, 1994, Logan, 1980, Logan and Zbrodoff, 1979, Posner and Snyder, 1975, Ridderinkhof, 2002b, Wiegand and Wascher, 2005). We demonstrate that DMC can account for empirical findings concerning delta functions. In particular, DMC is capable to predict virtually all observed shapes of delta functions, including negative-going ones. By that means, DMC provides a less-intuitive interpretation of delta functions that is suited to advance our conceptual understanding of prominent dual-process architectures by providing a specific modus operandi (e.g., see Ulrich, 2009) how automatic and controlled processes interact. It must be kept in mind, however, that in contrast to previous elaborations (Hübner et al., 2010, Schwarz and Miller, 2012, White et al., 2011) of the standard diffusion model, DMC is certainly not specific enough to capture the processing specificities of the various conflict tasks. Nevertheless, DMC can address the general principle of automatic and controlled processing that may underlie conflict tasks in choice RT tasks.
Section snippets
The assumptions of DMC
As mentioned above, several theoretical accounts of congruency effects proceed from the notion that different processes act simultaneously on the stimulus’ input. According to these accounts, task-relevant information is processed by controlled processes whereas task-irrelevant information is mediated by automatic processes in a separate, parallel processing pathway (e.g., Cohen et al., 1990, Coles et al., 1985, Hommel, 1993, Logan, 1980, Logan and Zbrodoff, 1979, Ridderinkhof, 2002a). Within
Experiment
In Section 2 it was shown that DMC can qualitatively account for major benchmark effects observed in conflict tasks. In order to also provide a quantitative test of the model, we fitted DMC to experimental data from both standard Simon and Eriksen (flanker) tasks that were run in a single experiment. Participants performed both tasks and the experimental procedures for the two tasks were as similar as possible in order to facilitate a proper comparison of results from these two tasks. We
Discussion
There is an increasing trend to move beyond the analysis of mean RT in studies of cognitive processes (Balota and Yap, 2011, Heathcote et al., 1991). Specifically, it is now widely recognized that the characteristics of RT distributions provide useful insights into the cognitive mechanisms during information processing. Especially delta functions have been suggested as being a valuable data-analytic tool to capture distributional differences among experimental conditions (e.g., De Jong et al.,
Acknowledgments
This work was supported by the German Research Foundation (DFG), Collaborative Research Centre 833, Projects B4 and B7. We thank an anonymous reviewer, Jeff Miller, Andrew Heathcote, and especially Ronald Hübner for helpful comments on a previous draft of the manuscript. Part of this work was presented at the 55th Annual Meeting of the Psychonomic Society, November 20–22, 2014, Long Beach, USA.
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