The DSTP model (H¨ubner et al., 2010) is a sequential sampling approach that has been developed in the context of selective attention. An impor-tant advantage of the DSTP model is its ability to account for data from tasks involving response conflicts (e.g., the flanker task), a characteristic
Introduction 53 that increasingly gains importance in the field of sequential sampling model-ing (Servant, Montagnini, & Burle, 2014; van Maanen, Turner, & Forstmann, 2015). In particular, the DSTP model makes the assumption of two staggered selection processes, stimulus selection and response selection. The model fo-cuses mainly on the dynamics of response selection, which are assumed to be strongly affected by stimulus selection.
Figure 5. An example of stimulus and response selection in the Dual-Stage Two-Phase (DSTP) model. An early stage of stimulus selection (i.e., sensory filtering/weighting) provides the drift rateµRS1 for Phase 1 of response selection.
In parallel, a late stage of stimulus selection runs with rate µSS until it reaches one of two boundaries C and −D that reflect the selection of either the target or a flanker for selective processing. On completion of the late stimulus selection SS, response selection enters Phase 2, which is characterized by a transition of the drift rate fromµRS1 toµRS2. A decision is completed as soon as the response selection process (either during Phase 1 or Phase 2) hits one of two response boundaries A and −B reflecting the choice alternatives. The duration of the non-decision time (e.g., sensory encoding, sensory filtering, motor commands) is captured in parameter ter.
Figure 5 illustrates that response selection is divided into Phase 1 and Phase 2, represented by the diffusion processes RS1 and RS2, respectively (Ratcliff, 1978). These diffusion processes are characterized by two drift rates (parametersµRS1 and µRS2) reflecting the evidence available for responses A
54 Research Paper II: If-then Planning Enhances Selective Attention versus B. Noisy samples of evidence are accumulated over time, until one of the corresponding boundaries (parameters A and−B) is reached and the associated response is triggered. Similar to other sequential sampling models, higher drift rates are indicative of faster evidence accumulation and hence reflect enhanced processing efficiency.
In Phase 1 of response selection, the efficiency of information processing (i.e.,µRS1) is determined by an early stage of stimulus selection, representing a sensory filter that enhances or attenuates the impact of stimulus compo-nents. In the domain of visual perception, for example, this filter is often described as a spotlight that can be allocated to a certain location in space.
Items at that location are then processed more intensively than items at other positions (Posner, 1980; Posner et al., 1980). For instance, in the flanker tasks used in the present study the central stimulus component is always the target and therefore receives higher attentional weights than non-central flanker components. The product of sensory bottom-up processes and the attentional weights provides the drift rates indexing the processing efficiency of the response-relevant target (parameter µta) and the irrelevant flanker (parameter µfl). Both rates sum up to the total drift rate µRS1 for Phase 1 of response selection (i.e., µRS1 = µta + µfl). In classical flanker tasks, the value ofµfl is positive if the flankers are response-compatible (i.e., congruent stimuli) and it is negative if they are response-incompatible (i.e., incongruent stimuli). Thus, the overall drift rate for Phase 1 of response selection is reduced for incongruent compared to congruent stimuli, and can even be negative.
If response selection relied only on this early phase there would be no qual-itative improvement over time, and accuracy for incongruent stimuli would remain at a relatively low level. Empirical data show, however, that such a simple mechanism is insufficient to account for response distributions in flanker tasks. Therefore, H¨ubner et al. (2010) proposed that a more so-phisticated late stage of stimulus selection runs in parallel with Phase 1 of response selection. The late stage has the function to select only response-relevant items for processing and is implemented as an independent diffusion process SS. When stimulus selection (parameter µSS) hits one of its bound-aries (parameters C and –D), either the target or a flanker item of a stimulus is selected for further processing, whereas unselected stimulus components are henceforth ignored. Thus, once the late stimulus selection process is fin-ished, and given that no response has been selected yet, response selection enters Phase 2, in which only the selected item drives response selection at a new drift rate for late response selection (parameterµRS2). As a consequence, the rate of response selection changes from Phase 1 to Phase 2 according to two possible scenarios: First, when late stimulus selection correctly selected
Introduction 55 the target, the drift rate in Phase 2 of response selection is usually higher than in Phase 1 (i.e., µRS2> µRS1), especially for incongruent stimuli. Sec-ond, when late stimulus selection erroneously selects the flanker, the drift rate in Phase 2 of response selection depends on the response-compatibility of the flanker. If it is incongruent, the drift rate is negative (i.e., µRS2< 0) and leads with high probability to an error. If the flanker is congruent, the drift rate is positive (i.e.,µRS2>0). Response selection usually enters Phase 2 in a substantial proportion of trials, which explains why accuracy is higher for slow than for fast responses.
Finally, while Phases 1 and 2 of response selection reflect the duration of the central decision process, the DSTP model also captures non-decisional phases (parameter ter), which comprise the duration of pre-decisional pro-cesses, such as stimulus encoding or sensory filtering (i.e., the early stage of stimulus selection), as well as of post-decisional processes, such as motor planning or response execution.