The Representational Model

One of the core assumptions of the dimensional overlap model is that different types of consistency influence mental processing in different ways. As a result, the different task ensembles in the dimensional overlap taxonomy each have different underlying representation and processing assumptions; however, when two tasks are of the same task type in the taxonomy, then the same representation and processing mechanisms generate the effect–regardless of the specific stimuli and responses that are involved in the task (more info: What is consistency?, Taxonomy of DO Ensembles).

Dimensional Overlap Representational Boxology

The basic representational assumptions of the dimensional overlap model were originally presented by Kornblum, S., Hasbroucq, T., & Osman, A., (1990).  The most recent version of that model was presented by  Kornblum & Lee (1995), where the above figure first appeared.

Processing occurs in two modules, separated by a cut-point:  the Stimulus Vector (SV).  These modules have additive effects.  The first module is the input, or stimulus encoding & identification module. The second is the response production module, which has two branches: 1. the upper branch, Automatic Response Identity & Verification; and 2. the lower branch, Response Identification.  These two branches come together in the response-execution area, which consists of response-execution, response-abort, response program-retrieval and response execution.

When a stimulus is first presented, the input module generates a stimulus vector (SV) which consists of all the attributes or features encoded by the stimulus identification module, including the relevant and the irrelevant stimulus attributes. The relevant stimulus attribute is identified in the vector by a tag.

Whether or not the stimulus set and the response set overlap, the relevant stimulus in the stimulus vector activates the response identification process, which identifies the response that was specified by the mapping, i.e. the correct response.

Response identification (lower branch of the response production module) may be performed in one of three ways: by use of the identity rule, by use of a different rule but a rule nevertheless, or by search.  By assumption (supported by much evidence) the identity rule is the fastest; search in the longest; and “other rules”, depending on their complexity,  is usually in between.

When a stimulus has more than one dimension that can be varied (e.g. the shape of a stimulus and its location in space), one or both stimuli may be correlated with the response.  If both stimuli are correlated, they are called redundant  in the sense that the response can be identified on the basis of either.  However, if only one stimulus is correlated (and it is usually r = 1), it is called the relevant stimulus, and the other the irrelevant stimulus (usually r = 0), in the sense that it cannot be used to identify the response at a better than chance level.  Yet, when the irrelevant stimulus overlaps with the response and is consistent with it, it produces results that are qualitatively similar to the mapping effect that would have been obtained had that stimulus been relevant; i.e. RT is faster than if it had been inconsistent.

This representational model can be used to describe the underlying cognitive processing mechanisms behind the effects of dimeansional overlap  in each of the tasks in the dimensional overlap taxonomy (more info: Taxonomy of DO Ensembles).

Type 1 Tasks

When there is no S-R overlap in an ensemble, the only process triggered by the stimulus presentation is response identification, which is activated by the relevant (so tagged) attribute.  In the absence of DO, response identification proceeds by search.  After the correct response has been identified, the appropriate motor program is retrieved, and the response is then executed.

Type 2 Tasks

The model postulates that if a stimulus is presented that comes from a stimulus set that overlaps with the response set (e.g. Type 2 ensemble), it automatically activates its corresponding element in the response set.  This process is represented by the upper branch of the response-production stage.

Before being activated, the correctness of the automatically activated response is verified If the automatically activated response and the correct response are one and the same, then the automatically activated response is said to be congruent, and is executed without further ado. If the two differ, the automatically activated response is said to be incongruent, and: a) is aborted, b) the program for the correct response is retrieved, and c) that response is then executed.  Note that by being executed immediately after having been verified as correct, in contrast to the incongruent response which has to be aborted first and then have the appropriate program retrieved, both of which take time, the time to execute the congruent response will be shorter than for the incongruent response.  Automatic activation is said to have had a facilitative effect in the congruent case, and an interfering effect in the incongruent case.

If he S-R ensemble has no dimensional overlap (Type1), the response has not been activated automatically so that execution requires neither aborting the response, nor retrieving a new program.  The time to execute that response (the neutral case) will, therefore, be faster the incongruent case, but longer than the congruent.  Thus, the model predicts that the fastest response will be for the congruent mapping, the slowest for the incongruent mapping, and the time for the neutral response will fall between the two.

Type 3 Tasks

When the irrelevant stimulus set and the response set overlap, presentation of the stimulus element triggers automatic response activation as well as the response identification process.  However, each is activated by a different feature in the stimulus vector:

a. automatic response activation will be triggered by the stimulus feature that represents a value on the irrelevant stimulus dimension that overlaps with the response;

b. the response identification process will be triggered by the tagged, relevant feature that does not overlap with the response, and will necessarily use search in identifying the correct response.

Type 4 Tasks

If the relevant and the irrelevant stimulus set overlap (e.g. Type 4), then the presentation of a stimulus element automatically activates two stimulus identification codes ( “i” and “j” ) as potential candidates for the relevant stimulus.  If the two codes or features do not differ, then it matters little which is tagged as “i” or “j”, and one of them is passed on to the response production stage  If the two codes do differ, than one of them is tagged as relevant before being passed on to the response production stage.  It is on the basis of the tagged attribute that the correct response is subsequently identified.

Type 5 Tasks

Because the Hedge and Marsh task, a type 5 task, exhibits both relevant S-R overlap and irrelevant S-R overlap, both of the mechanisms at work for relevant and irrelevant S-R consistency come into play in this task. Essentially, this is a combination of a Type 2 and Type 3 task (more info: The Hedge and Marsh task).

This representational model, however, cannot explain the highly-debated reverse-Simon effect (more info: Debate: Explaining the reverse-Simon effect).

Kornblum and Stevens (1997, November) were able to show that the computational dimensional overlap model could explain the reverse-Simon effect, while still preserving key assumptions of the represntational model, if the activation of the irrelevant stimulus is suppressed below zero for long reaction times. More recently, a large volume of experimental data, both behavioral and neurological, has supported this suppression-below-zero hypothesis (e.g. van den Wildenberg et al., 2010) (more info:  The Computational Model).

Type 7 Tasks

The SS x SR Task, a type 7 task, is a straight-forward factorial combination of S-S overlap and irrelevant S-R overlap. The processing in this task is therefore simply a combination of the processing mechanisms in Type 3 and Type 4 tasks. Moreover, because S-S and S-R effects arise during different processing stages, the model predicts that the effects will be additive and will not necessarily exhibit the same time-course characteristics. These assumptions were tested by Kornblum (1994) (more info: The SS x SR Task).

Type 8 Tasks

According to the dimensional overlap process model, the Stroop task, a type 8 task, should exhibit all three consistency effects: relevant S-R, irrelevant S-R, and S-S. In most variations of the Stroop task, these effects are confounded so that it is impossible to determine whether all three types of consistency really produce an effect on performance. Zhang and Kornblum (1998) used a four-choice Stroop task with both compatible and incompatible mapping instructions to verify this prediction of the dimensional overlap process model: all three types of dimensional overlap in the task produced independent consistency effects (more info: The Stroop task).



This qualitative version of the model has enabled us to make ordinal predictions about consistency effects in various tasks that have been experimentally verified in our own labs, as well as others. A number of experiments that have been performed that have tested the predictions of the dimensional overlap model (more info: The Experiments).

One of the drawbacks of this simple box-and-arrow process model is that it is only able to make ordinal predictions, i.e. predict which conditions should be faster than others. In order to make quantitative predictions about both reaction time and errors in compatibility tasks, the basic assumptions of the dimensional overlap model were implemented as a computational model (more info: The Computational Model).

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