Choice Reaction Time (CRT) Tasks

One of the ways that cognitive psychologists study decision-making is by studying simplified versions of real-world tasks called choice reaction time (CRT) tasks (see Luce, 1986). A basic CRT task can be defined in terms of three components: 1) a relevant stimulus set, which is the set of stimulus properties that you have to discriminate in order to determine what you should do, 2) a response set, which is the set of actions that you may have to perform, and 3) the mapping instructions, which associate each element in the stimulus set with an element in the response set. The relevant stimulus set and the response set are often not just a haphazard collection of elements, but are described by dimensions (called the relevant stimulus dimension and response dimension, respectively), with the elements within the set defined in terms of values of that dimension.

For example, the following would be a typical CRT task: the relevant stimulus dimension is pitch, with a 750 Hz tone and a 250 Hz tone as the elements in the relevant stimulus set; the response dimension is spatial direction, with a pressing of a left or right key as the response set; and the mapping instructions are “press the left key when you hear a high pitch and press the right key when you hear a low pitch.” By manipulating the various stimulus conditions and measuring how they affect the speed and accuracy of responses, psychologists can learn about the underlying process of decision-making.

Choice Reaction Time tasks can also be used to study selective attention, or the ability to filter out irrelevant information. In order to do this, there also has to be a collection of stimulus properties that appear in the task, but that are completely unrelated to what you should do. These are elements of the irrelevant stimulus set, and, like the elements in the relevant stimulus and response sets, they are usually defined in terms of values along an irrelevant stimulus dimension. In the above task, for example, the high- and low-pitched tones could also be presented either loud or soft, where the volume of the tone is completely random, unrelated to pitch or to anything that you should do. A CRT task with an irrelevant stimulus set is called a classification task (Garner, 1978b) or a filtering task (Posner, 1964).

Sometimes there is no relationship between any of the dimensions that define a Choice Reaction Time task. For example, suppose you are presented with a letter in the center of the screen: the letter can be either “H” or “S”, and can be either blue or green, combining to make total of four possible stimuli that can appear. You are told to press a left key whenever you see the letter “H” and a right key whenever you see the letter “S”. In this task, the response dimension is position (left, right), the relevant stimulus dimension is letter (H, S), and the irrelevant stimulus dimension is color (blue, green). All of these dimensions are completely unrelated. As a result, there will be no compatibility effects in this task.

The dimensional overlap model was devised to provide a basic framework for talking about compatibility effects, and rests on the idea of “dimensional overlap” between stimulus and response dimensions. By outlining different ways in which stimulus and response dimensions may overlap, the model is able to define a taxonomy of different types of compatibility tasks, and goes on to provide a theory about how these types of overlap influence cognitive processing.


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Online Simulation Model (DO2000)

This is a live, functioning version of the connectionist network model created by Greg Stevens to implement Sylvan Kornblum’s Dimensional Overlap model. The application below is based on the most recent and complete version of the model, presented in Greg Stevens’s doctoral dissertation, The locus of consistency effects in Simon, Eriksen, and Stroop tasks: New data and a comparison of models, published in 2000. As a result, this version of the model is nicknamed DO2000.

If you are not familiar with the dimensional overlap model, you may first want to check out the brief history of the model, to see how it came into being, or start reading the introductory overview of the basic concepts underlying the theory (more info: A brief history of the model, What is Dimensional Overlap?).

On the other hand, if you are ready to begin playing around with the simulation model, scroll down to view all of the parameters below.  You can select the type of task that you want to simulate, and adjust various parameters to see how they impact the performance of the model and the predicted effects of the conditions in the task. The default parameters are largely for illustration purposes only, but are designed to give results that are in the ballpark of the expected reaction times for these sorts of tasks.

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The Experiments

This is an annotated list of the published papers and meeting presentations that have played a key role in the development and experimental verification of the dimensional overlap model.  All the  experiments were performed in Dr. Kornblum’s  lab with the exception of the experiment reported in Kornblum et al (1999), which was performed in Dr. Jean Requin’s lab. at the CNRS in Marseille, France.  Each paper in the list below gives you the full citation of the article, a link to a summary of the article, and a quick set of key-word notes to let you know what issues are addressed by the paper. In some cases, clicking to view the summary of the article will also give you access to download the full PDF of the original manuscript.

The papers are presented in chronological order.

Kornblum, S., Hasbroucq, T., & Osman, A. (1990). Dimensional overlap: Cognitive basis for stimulus-response compatibility – A model and taxonomy. Psychological Review, 97, 253-270.


Key topics: Definition of Dimensional Overlap;  first appearance of the Process Model; first version of the Taxonomy; discussion of the Fitts Task.

Kornblum, S., & Zhang, H. (1991). The Time Course of Automatic Response Activation Process in Stimulus-Response Compatibility. Paper presented at the Meeting on “Analytic Approaches to Human Cognition”, in Brussels, June 1991.


Key topics: Testing the Process Model using the Fitts Task (Type 2).

Oliver, L., & Kornblum, S. (1991). Dimensional overlap and population stereotype as joint predictors of stimulus-response compatibility. Presented at the Psychonomic Society meeting in San Francisco, November, 1991.


Key topics: Testing the basic Dimensional Overlap assumption using the Fitts Task (Type 2).

Kornblum, S. (1992). Dimensional overlap and dimensional relevance in stimulus-response and stimulus-stimulus compatibility. Tutorials in Motor Behavior II, G.E. Stelmach & J. Requin (editors), Elsevier Science Publishers B.V.


Key topics: Discuss the process model; the final version of the Taxonomy; test the model using the Fitts Task (Type 2), manipulating number of alternatives.

Kornblum, S. (1994). The way irrelevant dimensions are processed depends on what they overlap with: The case of Stroop- and Simon-like stimuli. Psychological Research, 56, 130-135.


Key topics: explores the assumption of the process model that S-S and S-R consistency effects arise in different stages; examines performance in Simon tasks (Type 3), Stroop-like tasks (Type 4), and their factorial combination SS x SR tasks (Type 7).

Kornblum, S., & Lee, J.-W., (1995). Stimulus-response compatibility with relevant and irrelevant stimulus dimensions that do and do not overlap with the response. Journal of Experimental Psychology: Human Perception and Performance, 21, 855-875.


Key topics: refines the process model; explores predictions of the model in four-choice CRT tasks (Type 1), Fitts tasks (Type 2), and Simon tasks (Type 3).

Stevens, G. T., Whipple, A., Requin, J., & Kornblum, S. (1996, November). The time-course of S-S and S-R consistency effects: Data and model. Poster presented at the 37th annual meeting of the Psychonomic Society, Chicago.


Key topics: The first appearance of the computational model; simulation of results in a SS x SR Task (Type 7).

Kornblum, S., & Stevens, G. T. (1997, November). Reverse consistency effects and logical recoding: Insights from four-choice tasks. Paper presented at the 38th annual meeting of the Psychonomic Society, Philadelphia.


Key topics: Debate over the reverse-Simon effect in Hedge and Marsh tasks (Type 5); an explanation using the computational dimensional overlap model and below-zero suppression of irrelevant activation.

Zhang, H., & Kornblum, S. (1998).The effects of S-R mapping, and irrelevant S-R and S‑S overlap in four-choice Stroop tasks with single carrier stimuli. Journal of Experimental Psychology: Human perception and Performance, 24, 3-29.


Key topics: demonstration of independent S-S and S-R effects in a four-choice Stroop task (Type 8).

Zhang H., Zhang, J., & Kornblum, S. (1999). A Parallel Distributed Parallel Processing Model of Stimulus- Stimulus and Stimulus-Response Compatibility, Cognitive Psychology, 1999, 38, 386 – 432.


Key topics: pre-cursor version of the computational model.

Kornblum, S., Stevens, G. T., Whipple, A., & Requin, J. (1999). The effects of irrelevant stimuli: The time course of S-S and S-R consistency effects with Stroop-like stimuli, Simon-like tasks, and their factorial combinations, The Journal of Experimental Psychology: Human Perception and Performance, 25, 688-714.


Key topics: description of the computational model; simulation of the time-course of consistency effects in an SSxSR Task (Type 7).

Stevens, G. T. (2000). The locus of consistency effects in Simon, Eriksen, and Stroop tasks: New data and a comparison of models. Doctoral Dissertation, University of Michigan, Ann Arbor, MI. (Advisor: Sylvan Kornblum, Ph.D.)


Key topics: the final and most complete description of the computational model; testing the dimensional overlap model’s hypothesis about the locus of S-S consistency effects; experiments looked at variations of Flanker tasks (Type 4), Stroop-like tasks (Type 4) and Stroop tasks (Type 8).

Kornblum, S., & Stevens, G. T. (2002). Sequential effects of dimensional overlap: Findings and issues. In W. Prinz & B. Hommel (Eds.), Common mechanisms in perception and action. Attention and Performance XIX. (pp. 9-54). Cambridge, MA: MIT Press.


Key topics: the relationship between dimensional overlap and sequential effects in compatibility tasks.

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The Computational Model

The computational dimensional overlap model was first published in detail in Kornblum, Stevens, Whipple and Requin (1999) and explored in its most generalized and complete form in Stevens (2000).  The model is a localist connectionist network model (Grainger & Jacobs, 1998; Quinlan, 1991; Rumelhart, McClelland, et al., 1986) that implements most of the major assumptions of the original dimensional overlap representational model, as well as adding some new assumptions that allow the model to make precise quantitative predictions and account for the time-courses of consistency effects.

Like all connectionist models, the computational dimensional overlap model consists of a network of interconnected processing units, where each unit is very simple, characterized by a single variable (called the unit’s “activation”) that changes over time as a function of input to the unit and determines the output of the unit to be transferred to other connected units. Each unit represents a discrete stimulus or response feature, such as the stimulus color, the stimulus location, or the response word. In connectionist models of performance, activation in a stimulus feature unit increases when that feature is present in the environment, and the feature is identified as present in the environment when the activation reaches a critical identification threshold. Correspondingly, activation in a response feature unit increases as evidence for the correct response increases, and when the activation reaches a critical response threshold that response has been selected.

The overall structure of the original dimensional overlap process model is preserved: the units in the network are organized into two layers: the stimulus processing units are in the first layer (functionally equivalent to the “stimulus encoding” stage of the process model) and a response processing units are in a second layer (functionally equivalent  to the “response production and execution” stage of the process model). Activation of the units in the stimulus layer is not allowed to trigger activation in the response layer until the activation reaches the stimulus identification threshold: this allows the network model to implement the basic assumption of stage-like processing from the original model.

Like the original representational model, the computational model also provides two pathways for activation to pass from the stimulus to the response: a set of controlled connections that associate each stimulus unit to the unit for the response that it is assigned to by the mapping instructions (this corresponds to the “response identification” path in the original representational  model); and a set of automatic connections, if there is dimensional overlap between the stimulus and the response, that associate each stimulus unit to the corresponding unit in the response as determined by the dimensional overlap between the sets (this corresponds to the “automatic response identity and verification” path in the original process model).

Finally, the computational model preserves the fundamental assumption of the dimensional overlap model about the locus of consistency effects. Specifically, S-S overlap is modeled using automatic connections between units within the stimulus layer that represent different (but corresponding) stimulus features, while S-R overlap is modeled using automatic connections between stimulus units and response units that represent corresponding stimulus and response features.


Computational Dimensional Overlap Architecture: Stroop Task

Although the architecture of the model depends on the task being represented, the model of a Stroop task (Type 8) illustrates all three types of overlap: irrelevant S-R, relevant S-R and S-S.  This is represented in the network using three distinct sets of automatic lines: automatic lines between pairs of corresponding stimulus units, automatic lines between relevant stimulus units and response units, and automatic lines between irrelevant stimulus units and response units.  In the illustration here, the network is modeling a congruent mapping: the automatic lines from the relevant stimulus units to the response units run parallel to the controlled lines from the relevant stimulus units to the response units.

(Note: in addition to the corresponding automatic lines, there are also inhibitory non-corresponding automatic lines between units that represent features that do not align. These connections have a negative weight, so that activation in a stimulus unit will decrease the activation in a non-corresponding response unit when they are connected by automatic connections. These inhibitory connections are not shown in the diagram simply for the sake of simplicity.)

To understand exactly how the model works, consider what happens in these units when a stimulus is presented.

When the stimulus is presented, activation begins to accumulate in units of the stimulus layer that correspond to features of the stimulus.  At that point all the response units are clamped to zero, and are immune to any and all attempts at activation.

When there is S-S overlap, activation will be  accumulating in two of the stimulus units: one corresponding to the relevant stimulus feature and one corresponding to the irrelevant stimulus feature. If the stimulus is S-S consistent, then the activation in the irrelevant stimulus unit will be connected with a positive automatic line to the relevant stimulus unit, enhancing its overall input and making its activation grow faster. On the other hand, if the stimulus is S-S inconsistent, then the activation in the irrelevant stimulus unit will be connected with a negative automatic line to the relevant stimulus unit, inhibiting its overall input and making its activation grow more slowly.  As a result, the stimulus identification process is slower when the stimulus is S-S inconsistent than when it is S-S consistent.

When the level of activation in a relevant stimulus unit reaches the stimulus threshold, the stimulus has been identified. This triggers a control process that unclamps the response units and initiates the accumulation of activation in the response layer.  When there is irrelevant S-R overlap, activation of the irrelevant stimulus unit may also begin feeding its output to the response units at this time.

The model postulates that the inputs to both the relevant and the irrelevant stimulus units start at the same value – say 1.  The input to the relevant unit stays at that level, whereas the input to the irrelevant stimulus unit decays shortly after its onset. Moreover, there is increasing evidence that it may decrease below zero for longer processing times, leading to negative activation of the irrelevant stimulus and the reverse-Simon effect in the Hedge and Marsh task (see Kornblum & Stevens, 1997, November).

Relevant and Irrelevant Stimulus Activation

As the input to the irrelevant unit start to decay, the activation level of that unit levels off and starts to decrease as well, and ends up in an inverted U shape.  In the meantime, the activation level of the relevant unit increases until it reaches threshold.

When there is irrelevant S-R consistency in a task, the response units are being given input from both the relevant stimulus unit (via the controlled connections) and the irrelevant stimulus units (via the automatic connections). When the irrelevant stimulus is S-R consistent, activation of the irrelevant stimulus unit would lead to the automatic activation of the corresponding response unit which is also being activated by the controlled line.   This additional activation would interact with the accumulated activation in that response unit, thus being facilitative. On the other hand, when the irrelevant stimulus is S-R inconsistent, the irrelevant stimulus unit activates the incorrect response unit, but feeds negative input to the response unit that is being activated by the controlled line. As a result, activation in the correct response unit accumulates faster for the S-R consistent condition than the S-R inconsistent condition.

Activation in the response units continues until the activation level in a response unit reaches the response threshold, and a response is selected and executed.

The shape of the irrelevant stimulus activation curve allows the computational model to account not only for the basic raw effects of all of the compatibility tasks in the dimensional overlap taxonomy, but also the time-courses of the effects that appear when the irrelevant stimulus is presented at different intervals before or after the relevant stimulus (see Kornblum et al. 1999).



Now that you have been introduced to the overall theory of the model, you may want to try it out for yourself! You can play with a fully functioning online implementation of the model, adjusting parameters and seeing the results for different types of consistency tasks.

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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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What is Consistency?

While dimensional overlap (DO) is a property of sets, consistency is a property of individual trials in a task.  The different ways that elements from overlapping dimensions can be combined to construct individual trials gives rise to a variety of types of consistency.

S-S consistency: Consider an ensemble with dimensional overlap between a relevant and an irrelevant stimulus set.  Trial draws on the same value from each dimension, then that trial has S-S consistency.   For example: in a task where the relevant stimulus is color and the irrelevant stimulus is a color word, the relevant and irrelevant stimulus sets overlap on the dimension of color.

On a trial where the color BLUE is presented with the word “BLUE” the stimulus is S-S consistent. On a trial where the color BLUE is presented with the word “GREEN”, on the other hand, the stimulus is S-S inconsistent.

Irrelevant S-R consistency: Consider an ensemble with a relevant and an irrelevant stimulus set, plus a response set,  with dimensional overlap between the irrelevant stimulus and the response. For example, suppose a blue or green light can appear on the left or right side, and the color of the light is assigned to a left or right key press. In this task, the irrelevant stimulus and the response overlap on the dimension of left-right position.

On a trial where the color assigned to a left key press also appears on the left side, the trial is S-R consistent. On a trial where the color assigned to a left key press also appears on the right side, the trial is S-R inconsistent.

Relevant S-R consistency (Congruent/Incongruent mapping): Consider an ensemble with a relevant stimulus and a response set (there may or may not also be an irrelevant stimulus set), and the relevant stimulus and response sets have dimensional overlap. A trial which on which one of the relevant stimuli and now mapped onto one of the responses is called Relevant Consistent.

In the case of relevant S-R consistency, if the instructions map the stimuli onto their corresponding response (e.g. “respond to the left light with the left key, and to the right light with the right key”) that mapping is said to be congruent. If the instructions map the stimuli onto non-corresponding responses keys (e.g. respond to the left light with the right key,and to the right light with the left key), that mapping is said to be incongruent.


The different types of consistencies reflects the functional role that Dimensional Overlap plays at the level of trials. The different patterns of DO found in ensembles, results in different types of tasks.  This is captured in the DO taxonomy.

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What is Dimensional Overlap?

Dimensional Overlap (DO) is a property of sets.

A set is a collection of items.  When these items have one or more attributes in common they form a category (cf. Kornblum, Hasbroucq & Osman; Kornblum & Lee).  This category is identified by the common attribute which is also the dimension of that category.  When two or more sets are included in a larger set this larger set is called an ensemble.

Dimensional Overlap is the degree to which a stimulus set, and a response set, or two or more stimulus sets are perceptually, structurally or conceptually similar.  Similarity is a continuous variable, going from “almost identical” to “they have nothing to do with each other”, and different levels of  similarity are carried over to differences in degrees of DO. These differences are dealt with in the computational model as different strengths of the “automatic association lines” between different mental representation units. (More info: The Computational Model)

The best way to understand the ideas of perceptual, conceptual, and structural similarity is to consider some examples of tasks with dimensional overlap  based on such similarities.

A.  An experimental subject is sitting in front of a screen.  On the screen is the outline drawing of two outstretched hands.  The subject has his own outstretched hands positioned on eight response keys, and he is instructed to press the key under the finger that corresponds to the finger outline on the screen, when an “X” appears in the tip of that finger.  The stimulus set (i.e. the outline drawing of the hands with an X in any fingertip), and the response set (i.e. the set of potential key presses with one of the fingers) are perceptually similar, giving that ensemble dimensional overlap.

B.  In this task, the subject must press the left key when he hears a sound in the left ear, and the right key when he hears a sound in the right ear.  Laterality is the attribute, or dimension, that the stimulus and the response sets have in common, and which makes them perceptually similar, thus giving the ensemble dimensional overlap.

C.  In this task, the subject says the name of a color that is presented (e.g. when you see Blue you say “Blue”, and when you see Green, you say “Green”). Here, the attribute that the stimulus set (Blue and Green) and the response set (“Blue” and “Green”) have in common is COLOR.  These two sets are conceptually similar, thus giving this SR ensemble Dimensional Overlap.

D.  Take the set of symbols 1, 2, 3, 4, 5. They form a category called “integers”; it could also be called “digits”, or any of several other names.  Next, take the set of words “one”, “two”, “three”, “four”, “five”…They form a category called “digit name”.  Both of these sets are tokens for numerals, and are conceptually similar.  The ensemble comprising these two sets, therefore, has dimensional overlap.

In this case, as well as in the case of colors (in C above),  the correspondence between the elements of the stimulus set and the response set are so exact as to give their similarity level (hence the level of DO) an especially high value.

E.  The set of symbols B, C, D, F, G…are members of a category called “consonants”.  Likewise, the set of symbols A, E, I, O, U are members of a category called “vowels”.  Both of these sets are sets of “letters”.  Letters may, therefore, be viewed as the attribute that they have in common, on which they overlap, and makes them conceptually similar.  An ensemble with both of these sets has dimensional overlap.

F.  Now let us consider the set of integers (1, 2, 3, 4, 5…), and the set of letters (A, B, C, D, E,).  Both of these sets share the property of being the first consecutive elements of two sequential series (the alphabet and the integers).  Thus making them structurally similar, and giving them dimensional overlap.

G.  Finally, consider a set of weather reports: “hot, mild, cold, and freezing”.  To the extent that this set may also be viewed as consecutive items on an abstract sequential series of items (this would be true whether high and low temperatures are indicated by a numeric scale, or in some other way), this set of weather reports is similar to the set of digits, and the set of letters, and to the extent that all three sets share the same dimension, they are all structurally  similar to one another, and together would form an ensemble with dimensional overlap.  This particular pattern of DO is at the basis of what we have called “cross modal” tasks.  (More info: Cross-Modal Tasks)


Relevant and Irrelevant Stimuli

In all the tasks that we have used to illustrate different sorts of similarities, the stimulus set that overlaps with the response set has always been a set of relevant stimuli. (cf, “Why Study Compatibility”)   Relevant stimuli are those that the subject is instructed to attend to, and respond to.  Of course, any “stimulus” has many features that could, in principle, be selected to play that role.  However, in the mapping instructions for all tasks, specific features are selected for that precise purpose, while other features are explicitly excluded and are to be ignored by the subject.  Those “to be ignored” features are the irrelevant stimuli.  The correlation between the relevant stimuli and the response, is 1.0,  the correlation between the irrelevant stimuli and the response is zero.

Even though they are irrelevant to the task, and the subject is told to ignore them, irrelevant stimuli are sometimes difficult to ignore.  For example, let’s go back to the experimental set up we used in case B above, and introduce a small change: Instead of presenting the same tone to the left and the right ear, let the tone now be either a high or low pitch tone.  Again, it will be randomly presented to the left or the right ear, just as in B above..  However, this time, instead of mapping the side of the ear to the key, the subject is instructed to make a left or right key-press according to the pitch of the tone, and to ignore in which ear the tone was presented: “press the right key to the high pitch tone, the left key to the low pitch tone, and ignore the ear to which the tone is presented”.  With these instructions, and the experimental set up, pitch is the relevant stimulus, and ear is the irrelevant stimulus. When these irrelevant (i.e. “to be ignored”) stimuli have dimensional overlap with the response, or with some other aspects of the tasks, it results in significant changes in performance.

The eight combinations of the presence/absence of relevant/irrelevant, stimulus-response ensembles, and stimulus-stimulus ensembles are presented in the Taxonomy of DO Ensembles.  (More info: Taxonomy of DO Ensembles)


Consistency and Inconsistency

When the relevant and the irrelevant stimuli denote the same attribute, this gives rise to S-S Consistency / Inconsistency.  For example: if the color BLUE is the relevant stimulus, and the name of the color “BLUE” is the irrelevant stimulus, the dimension on which they overlap is COLOR, and the fact that they both represent the same feature (i.e. BLUE) makes this an S-S CONSISTENT  pair of stimuli.

If this match between the color and the name does not hold, then this is an S-S INCONSISTENT pair.

When the irrelevant stimulus and the response denote the same attribute, this gives rise to S-R Consistency / Inconsistency. For example, if the color of a light is the relevant stimulus, and a left/right key-press is the response, and the light can be turned on either on the left or on the right, then the location of the lights (left or right) and the position of the response keys (left or right) make this ensemble S-R CONSISTENT.  The dimension on which they overlap is “lateral position in space”.

If the match between the location of the lights and the position of the response key does not hold, then this is an S-R INCONSISTENT pair. (More Info: What is consistency?)


Dimensional Overlap is a GENERAL mental phenomenon

Some sets sometimes seem so physically different from other sets – for instance when the sensory channel for the one is vision and for the other is audition – that the similarity (the DO) between them seems far fetched.  Yet, they give rise to compatibility effects in performance, which verifies that there is some set-level similarity between the mental representations (cf. Robert Melara and Lawrence Marks (1990; Marks, 1987; Melara, 1989).

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Why a computational model?

It is not always easy to figure out what a psychological model can or cannot explain, just based on a list of its assumptions.  For example, for a long time psychologists took for granted that any model assuming the dimensional overlap hypothesis could not explain the S-S consistency effects found in 2-to-1 mapping tasks.  However, it turns out that this was based on the implicit assumption of a static stimulus identification process.  If a dimensional overlap model instead assumes flexible stimulus identification, it can account for these data.  Because the response selection and dimensional overlap models were evaluated with the implicit assumption of static stimulus identification, it was difficult to evaluate and compare them clearly and accurately.

Moreover, when a model contains a large number of assumptions, trying to account for effects that interact with one another, reading through arguments about the model’s explanations and predictions can also be confusing.  A good example of this might be the argument that dimensional overlap models can account for the electrophysiological data in S-S consistency tasks.  This argument introduces a number of ideas about processing, such as the notion that stimulus identification can make a “mistake” that can later be corrected, that are not intrinsic to dimensional overlap models.  It would not be surprising or unexpected for the reader to want to take a step back, and wonder:  Does this model really fulfill the requirements of a dimensional overlap model?  Can it actually account for the data that it is purported to account for?  Or, is there a slip in the logic somewhere that is being glossed over through vague words and convoluted argumentation?

One way of addressing these problems in to develop psychological models that can be implemented as computational algorithms.  This approach is very natural, in fact, for anyone taking the information processing approach to understanding how the mind works.  If mental life is all about how information is represented by mental codes and transformed by mental processes, then it has a natural analog in a computer program, which represents information with variables and data structures and transforms that information with functions and procedures.  By taking assumptions about mental codes and mental processes, and implementing them as a program with variables and functions, we create a very concrete and unambiguous form of psychological model.

The first and most obvious advantage to doing this is that a computer program cannot be vague, and must be completely explicit about all of its assumptions.  This not only keeps things honest, but also allows for a more concrete direct comparison of different models: for example, if two computational models are completely identical except for one parameter, and there is a difference in the predictions of the two models, then it is clear that the difference in performance must be due to that one parameter.

Moreover, just in case slick words and convoluted logical arguments can leave you wondering, “Can this model really explain that result?”, a computational model can provide a compelling existence proof.  That is, a computer program is one of the most compelling demonstrations that a system with a certain set of assumptions about the representation and processing of information can explain a certain pattern of results.  Computer programs do not engage in fast-talking or hand-waving.

Finally, computer programs provide actual numerical predictions about people’s reaction times, rather than vague predictions like “people are faster when X than when Y.”  If the particular set of assumptions that are implemented in a computer program accurately reflects how our minds work, then the (simulated) time it takes the program to go from stimulus information to the formation of a motor code should be proportional to the time it takes people to do the same thing (i.e. their reaction time).

Unfortunately, there is also a cost to implementing models as computer programs.  In order to run, a computer program must be more specific than the psychological hypotheses that it is designed to implement.  For example, the generic dimensional overlap and generic response selection models are characterized by a list of critical defining assumptions (i.e. the assumptions in the coding model framework, plus either the dimensional overlap hypothesis or the response selection hypothesis).  A number of details about cognitive processing are left unspecified: for example, how mental codes actually form over time, how information is transferred from stimulus codes to response codes, and how the formation of one mental code influences the formation of other alternative codes of the same type (i.e. stimulus or response).  These details are deliberately left unspecified, in order to allow the models to focus on the critical assumptions about cognitive processing to be examined.

However, these other details have to be specified in order to get a computer program to run.  As a result, implementing computational versions of these models involves making arbitrary decisions – decisions about information processing not inherent in the models that they are based on.  In contrast with the critical assumptions of the models, these are auxiliary assumptions, or implementation details, associated with the computational models.  They have to be there for the computational implementation to run, but they do not represent crucial psychological hypotheses.

Because of this, the “existence proof” mentioned above does not work in reverse: if a particular computational model cannot explain a particular result, this does not mean that the psychological model it is based on cannot predict that result.  If a computational model were implemented with the same set of critical assumptions, but a different set of auxiliary assumptions, it could very well make different predictions.  This means that whenever a computational model can or cannot explain some finding, a great deal of care must be taken to ascertain why: what aspect of the model leads to its success or failure? A critical assumption, an auxiliary assumption, or an interaction between the two?

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Abstract code representation

Many models of reaction time assume that performance can be understood in terms of the formation of mental codes. That is, the process of identifying the stimulus in a task is understood as a process of forming a mental representation of the stimulus, or a stimulus code.  Similarly, the process of selecting a response in a task is understood as a process for forming a mental representation of the desired response, or a response code.

Stimulus and response codes represent abstract properties of stimuli and responses in a task. For example, spatial stimuli are coded in terms of their location relative to the other possible locations in the stimulus set, rather than their absolute location in the visual field; similarly, spatial responses are coded in terms of their desired outcomes, relative to other outcomes in the response set, instead of in terms of specific actions or muscular movements.

Simon and his colleagues (Craft & Simon, 1970; Simon, Craft & Small, 1971; Simon, Small, Ziglar & Craft, 1970) demonstrated that the spatial S-R consistency effect in a Simon task depends on where you perceive the stimulus to be, and not on what ear, eye or visual hemi-field is actually stimulated. Umilta and colleagues (Umilta & Nicoletti, 1985, exp. 2 and 4; Umilta & Liotti, 1987, exp. 3) later showed that a spatial S-R consistency effect can also be found for relative stimulus positions: that is, when both stimulus positions appear on the left side of a display, but one stimulus position is farther left than the other. These experiments indicate that stimulus codes are formed based on your perception of the current irrelevant stimulus relative to other elements in the set, rather than on physical sensory stimulation or absolute stimulus position.

Other experiments have shown that response codes are also represented in terms of abstract properties, such as the desired outcome of the response. For example, when the subjects’ goal is to “press a key” in the Simon task, performance is determined by the relationship between the stimulus position and the response key position, even when subjects crossed their hands (Simon, Hinrichs & Craft, 1970; Wallace, 1971), cross their fingers (Riggio, Gawryszewski, & Umilta, 1986), or press keys using only one finger from one hand (Bauer & Miller, 1982), or using two fingers from the same hand (Heister, Ehrenstein & Schroeder-Heister, 1987). However, when pressing a key also lights up a light on the opposite side (i.e. pressing a left key lights up a light on the right side, pressing a right key lights up a light on the left side), and subjects are told to respond by “lighting up a light” rather than “pressing a key,” performance is determined by the relationship between the stimulus position and the light position. That is, when the stimulus and the light position are on the same side (but the response key is on the opposite side), subjects respond faster, while when the stimulus and the response light are on the opposite side (but the response key is on the same side as the stimulus), subjects respond more slowly (Hommel, 1993a).

The assumption of abstract code representation allows coding models to explain the appearance of consistency effects under a diverse set of stimulus and response conditions using a single explanatory mechanism (see Nicoletti & Umilta, 1984; Riggio, Gawryszewski, & Umilta, 1986; Umilta & Nicoletti, 1990). The coding model framework leaves open for debate the question of how mental codes are formed (e.g. Heister, Schroeder-Heister & Ehrenstein, 1990; Proctor, Reeve, & van Zanddt, 1992; Rubichi et al., 1997; Stoffer, 1991; Stoffer & Umilta, 1997; Weeks, Chua, & Hamblin, 1996); however, once it is taken as given that appropriate abstract mental codes are formed, these models then only need to specify how the relationship between different mental codes influences performance in order to explain the effects in all of these diverse task conditions.

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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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