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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Parallel identification processes

Most models of reaction time based on the formation of mental codes assume not only that separate mental codes are formed for relevant and irrelevant stimulus features, but that the codes are formed in parallel by separate processes. Whenever a stimulus is characterized by more than one dimension (i.e. whenever there is more than one stimulus set), each stimulus dimension can be understood as a separate functional stimulus (Miller, 1988), from the point of view of the perceptual system.

Thus, instead of there being a single stimulus identification process, each dimension of the stimulus is identified by its own separate process, or separate “channel.” These processes can operate completely concurrently, and they do not depend on one another for information. (There is debate, however, as to whether there is “cross-talk” between different stimulus identification processes that are going on at the same time; see, e.g., Egeth, 1977; Estes, 1972, 1982; Mordkoff, 1991; Morton, 1969).

The assumption of multiple identification processes was developed by Eriksen and colleagues (Eriksen, 1966; Eriksen & Lappin, 1965, 1967; Eriksen & Spencer, 1969) for displays with multiple elements, such as flanker stimuli. They suggested that display items that are presented in different spatial locations are identified through separate and independent processes that act in parallel. The idea that the stimulus dimensions of color and word are processed by separate “perceptual analyzers” has also been assumed in even the earliest accounts of performance in the Stroop task (e.g. Morton & Chambers, 1973; Posner & Snyder, 1975). These assumptions were brought together to form the general assumption of separate stimulus identification processes or “channels” (see Egeth, 1977; Miller, 1988): when a stimulus consists of multiple dimensions, they form separate functional stimuli, and are processed by separate stimulus identification processes.


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Stimulus codes form automatically

One of the assumptions shared by all coding models of reaction time is that mental codes for irrelevant stimuli are formed automatically, even though they are not necessary to carry out a task. Coding models explain consistency effects in terms of a match or a mismatch between this irrelevant stimulus code and one of the mental codes required to perform the task.

This kind of explanation is very general, because mental codes can be about anything. As a result, any kind of irrelevant stimulus can give rise to a consistency effect: letters, words, locations, colors, and so on.  What these models must specify is exactly when and how irrelevant stimulus codes influence the formation of one or more of the mental codes that are required to carry out a task.

Wallace (1971, 1972) first suggested that the S-R consistency effect in a Simon task appears because people automatically, involuntarily form a spatial code, even though the stimulus position is irrelevant. Eriksen and Eriksen (1974; see also Eriksen & Schultz, 1979) similarly suggested that flanker letters in a Flanker task are identified (forming their own letter codes) even though they are known to be irrelevant to the task. This view has been generalized since then to apply to any irrelevant stimulus characteristic, and is an assumption made by all coding models of consistency effects.

Irrelevant stimulus codes form automatically, and influence the formation of other mental codes.  Many coding models assume that mental codes form gradually, and that selective attention will eventually suppress the formation of the irrelevant stimulus code once it is identified as irrelevant. This mechanism of attention produces a rising-then-falling, or inverted U-shaped activation of the irrelevant stimulus code.

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What are mental codes?

Consider what has to go on in your mind in order for you to carry out the instructions for a typical Choice Reaction Time task, such as: “press the left key when you see the color green and the right key when you see the color blue.”

When a stimulus appears, at least three things have to happen: 1) you have to figure out the color of the stimulus, 2) you have to decide which key to press, and 3) you have to actually press the key. These are usually considered the three most basic, broadly-defined processes involved in carrying out a task, and are usually called stimulus identification, response selection, and motor programming, respectively (although they can be broken down into more specific sub-processes, as well; see Sanders, 1980, 1990).

These processes can be described more concretely in terms of information and mental codes. Your senses give you signals that contain information about what is going on in the world around you. In order to understand and react to the world, you use that information to create a mental picture of your environment. In other words, you form a stimulus code: a mental representation of what properties are in the stimulus environment that produced the sensory signals that you received.

Stimulus identification can be thought of as the process of forming stimulus codes based on sensory information. Those stimulus codes, in turn, contain information that can be used to decide on a response. In order to act on the world, you form a response code: a mental representation of what actions you want to carry out. Response selection can be thought of as the process of forming response codes based on information from stimulus codes. Finally, motor programming is the process of using information from response codes t prepare specific muscular movements that carry out your response. This can be thought of as the formation of motor codes, which are the programs your muscles use to make a response.

The idea that thought and action in the world consists of mental codes (representations of stimulus properties and response actions) is called the information processing approach, and models of performance based on this framework are called information processing models (see Anderson 1995; Bower 1975; Miller, 1988). Performing a task requires transforming information from the world into a stimulus code, a response code, and then a motor code, through a sequence of mental processes.

These processes clearly depend on one another. In the example above, what key you press depends on what side (left or right) you decide is correct, and what side you decide is correct depends on what you think the color of the stimulus is. In the language of information processing models, the output of stimulus identification, which contains information about the stimulus code, is used as the input for response selection. Similarly, the output of response selection, which contains information about the response code, is used as input for motor execution. Information processing models use terms like “input” and “output” a lot, because they were originally motivated by the idea that mental processes are like computer programs, and mental codes are like computer data (see Newell, Rosenbleem, & Laird, 1989; Simon, 1981; Simon & Kaplan, 1989).

Psychologists want to know exactly what is going on in these processes; that is, how information is represented in these codes, and how they are actually formed. One way to approach this question is to measure people’s performance, their speed and accuracy when carrying out a task, under different kinds of task conditions. The amount of time it takes for you to make a response is related to how difficult each of these processes is: when something about the task makes your response faster or slower, it is because one (or more) of these processes has been helped or hindered. By examining how different kinds of task conditions influence performance, psychologists are able to get an idea about what is actually going on in the formation of these different mental codes. This approach is called mental chronometry (see Meyer et al., 1988; Sanders, 1993).

There are a number of specific questions one can ask about the formation of mental codes during choice reaction time tasks. Is input information compared to items in memory one by one, until a match is found? Or is the input information compared to all possible items in memory at once? Does input information for a process cause mental codes to form gradually, or do mental codes form in chunks, like “yes” and “no” decisions? Does incomplete information get used by later processes, or do they have to wait until the previous process is completed?

Even more questions can be asked about consistency effects in classification tasks. How does irrelevant information affect the formation of mental codes? Does it influence the formation of stimulus codes, response codes, or motor codes? Does irrelevant information always have the same kind of influence on mental codes, or does it depend on task conditions?

Today, most models of consistency effects share a few basic assumptions about mental codes and how they behave during classification tasks (see, e.g., Barber & O’Leary, 1997; Kornblum et al., 1990; O’Leary & Barber, 1993; Lu & Procter, 1995; Prinz, 1990; Proctor, Reeve, & van Zandt, 1992; Umilta & Nicoletti, 1990; Wallace, 1971). For example, they assume that irrelevant stimulus codes form automatically, that different stimulus features are formed by multiple parallel identification processes, that mental codes are abstract representations, and that mental codes form gradually over time.

However, they also disagree on a few very key assumptions about mental processing. For example, different models often disagree about where selective inhibition happens. They also can disagree about whether the formation of response codes from stimulus information is continuous or happens only in discrete stage-like chunks. Finally, they can disagree about whether irrelevant stimulus information influences the formation of stimulus codes, the formation of response codes, or both.

This last question is the key issue that differentiates the Dimensional Overlap Model from other models of consistency effects. Most models of consistency effects assume that irrelevant stimulus information influences the formation of response codes, whereas the Dimensional Overlap Model assumes that influence of the irrelevant stimulus depends on what the irrelevant stimulus dimension overlaps with.

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Debate: What is the locus of the S-S Overlap Effect?


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