Tom Stafford Department of Psychology University of Sheffield tstaffordshefacuk Galway 15 th of January 2010 Conclusions It is not possible to infer discrete processing stages from the appearance of additive factors ID: 201697
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Slide1
Using the psychophysics of choice behaviours to infer mental structure from reaction times
Tom
Stafford, Department
of Psychology, University of
Sheffield, t.stafford@shef.ac.uk
Galway, 15
th
of January, 2010Slide2
ConclusionsIt is not possible to infer discrete processing stages from the appearance of additive factorsExperimental and modelling work involving Pieron’s Law gives a worked exampleBUT It is also unlikely that simple perceptual decision making is simple, even in paradigmatic cases30/07/09
© The University of SheffieldSlide3
Image thanks to Roger CarpenterSlide4
30/07/09© The University of SheffieldSlide5
The additive factors method30/07/09© The University of Sheffield
Sternberg, S. (1969) The discovery of processing stages: Extensions of
Donders
' method.
In W. G.
Koster
(Ed.), Attention and performance II.
Acta
Psychologica
, 30
, 276-315.
Input
Stage 1
Stage 2
Output
Factor A
Factor B
Effect A
Effect B
Factors A + B
Effect A + B?Slide6
Additive Factors Method (AFM)
The application of this method has produced consistent support for the existence of separate stages in decision making,
particularly the independence of stimulus processing and response selection (e.g.
Stoffels
, 1996;
Wildenberg
&
Molen
, 2004)
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© The University of Sheffield
6
Stoffels
, E. J. (1996). On stage robustness and response selection routes: Further
evidence.
Acta
Psychologica
, 91
(1), 67-88.
Wildenberg
, W. P. van den, &
Molen
, M. W. van der. (2004). Additive factors
analysis of inhibitory processing in the stop-signal paradigm.
Brain & Cognition,
56
(2), 253-66.Slide7
Stages to decision making? (1)
‘‘Most research on AFM shows consistent and robust evidence in
favor
of seven successive processing stages in traditional choice reactions” (Sanders, 1990)
“information is transmitted discretely between perceptual and response stages of processing” (Woodman et al, 2008)
30/07/09
© The University of Sheffield
7
Sanders, A. F. (1990). Issues and trends in the debate on discrete
vs
continuous
processing of information.
Acta
Psychologica
, 74
(2-3), 123-167.
Woodman, G. F., Kang, M. S., Thompson, K., &
Schall
, J. D. (2008). The effect of visual search efficiency on response preparation:
neurophysiological
evidence for discrete flow.
Psychological Science, 19
(2), 128-136.Slide8
Stages to decision making? (2)
PDP framework (Rumelhart et al, 1986) explicitly rejects stage models, in favour of continuous processing (McClelland, 1979)
Most successful model of RTs is single stage, Ratcliff's diffusion model
30/07/09
© The University of Sheffield
8
Rumelhart, D., McClelland, J. & the PDP Research Group (Eds.),
Parallel distributed processing: Explorations in the microstructure of cognition
. Cambridge, MA: MIT Press.
McClelland, J. (1979). On the time-relations of mental processes: An examination of systems of processes in cascade.
Psychological Review, 86
, 287-330.Slide9
30/07/09
© The University of Sheffield
9
The diffusion model of decision making
Ratcliff, R. (1978). A theory of memory retrieval.
Psychological Review
,
85
(2), 59-108.
Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks.
Neural computation
,
20
(4), 873-922. Slide10
30/07/09© The University of Sheffield
Gold, J. I., &
Shadlen
, M. N. (2002).
Banburismus
and the brain decoding the relationship between sensory stimuli, decisions, and reward.
Neuron, 36
(2), 299-308.
Neural instantiation of ‘accumulated evidence’ found in area LIP?
Figure 4, Gold &
Shadlen
(2002)Slide11
30/07/09
© The University of Sheffield
11
Modelling
decision
making
‘decision making’ research has focused on perceptual decisions (e.g. Gold &
Shadlen
, 2007)
Diffusion model has been shown to be optimal (
Bogacz
et al, 2006)
Optimal processing seems to require integration of factors influencing a decision into a single variable (e.g. Ratcliff, 2001?)
Bogacz
, R., Brown, E.,
Moehlis
, J., Holmes, P., & Cohen, J. D. (2006). The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks.
Psychological Review, 113
(4), 700-65.
Gold, J. I., &
Shadlen
, M. N. (2007). The neural basis of decision making.
Annual Review of Neuroscience, 30
, 535-574
Ratcliff, R. (2001). Putting noise into
neurophysiological
models of simple decision making.
Nature Neuroscience, 4
(4), 336-336.Slide12
Task: to inspect RTs in a more complex choice task, something that is not just a perceptual decision
...a decision which involves two factors, which provide evidence that (we might assume) is represented at different stages
Are reaction times affected additively by these two factors?
Can existing single stage models account for the pattern of results?Slide13
The Stroop
Task
30/07/09
© The University of Sheffield
13
Stroop
, J. (1935). Studies of interference in serial verbal reactions.
Journal of Experimental Psychology, 18
, 643-662.
Stafford, T., & Gurney, K. (2007). Biologically constrained action selection improves cognitive control in a model of the
Stroop
task.
Philosophical Transactions of the Royal Society London, Series B, 362
, 1671-1684.
Stroop
(1935)Slide14
The Stroop Task
Name the colour
Control
SHOE
30/07/09
© The University of Sheffield
14Slide15
The Stroop Task
Name the colour
Control
SHOE
Congruent
GREEN
30/07/09
© The University of Sheffield
15Slide16
The Stroop Task
Name the colour
Control
SHOE
Congruent
GREEN
Conflict
BLUE
30/07/09
© The University of Sheffield
16Slide17
30/07/09
© The University of Sheffield
17
The stimulus intensity – reaction time function
aka ‘Piéron’s Law’
RT = R
0
+
k
I
-
β
Pieron, H. (1952).
The sensations; their functions, processes and mechanisms: Their Functions, Processes, and Mechanisms
. Yale University Press.Slide18
Pieron's
Law found for white light, pure tones, taste...(Luce, 1986)
...and in simple choice decisions (Pins & Bonnet, 1996)
“luminance processing and any further processing due to the specific requirements of the psychophysical task combine additively”
Rumelhart
, D., McClelland, J. & the PDP Research Group (Eds.),
Parallel distributed processing: Explorations in the microstructure of cognition
. Cambridge, MA: MIT Press.
Luce, R. D. (1986).
Response times: Their role in inferring elementary mental organization.
Oxford University
Press.
Pins, D., & Bonnet, C. (1996). On the relation between stimulus intensity and processing time:
Piéron's
law and choice reaction time.
Perception and Psychophysics, 58
(3), 390-400Slide19
30/07/09
© The University of Sheffield
19
Piéron’s Law inherent in any rise-to-threshold decision process
Stafford, T., & Gurney, K. N. (2004). The role of response mechanisms in determining reaction time performance:
Pieron’s
law revisited.
Psychonomic
Bulletin & Review
,
11
(6), 975-987
.
Palmer, J.,
Huk
, A. C., &
Shadlen
, M. N. (2005). The effect of stimulus strength on the speed and accuracy of a perceptual decision.
Journal of Vision, 5
(5), 376-404.Slide20
30/07/09
© The University of Sheffield
20
Expt 1:
A Stroop task with varying levels of colour saturationSlide21
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© The University of Sheffield
21
If saturation and response conflict information are integrated then the different Stroop conditions should differ by different amounts at each level of saturationSlide22
InteractiveSlide23
Additive
InteractiveSlide24
Expt 1 Results, i
30/07/09
© The University of Sheffield
24
Colour saturation (%)
Reaction Time (ms)Slide25
Expt 1 Results, ii
30/07/09
© The University of Sheffield
25Slide26
30/07/09
© The University of Sheffield
26
Expt 2:
A Stroop task with varying levels of colour saturation,
with word and colour elements of the stimulus separated in spaceSlide27
Expt 2 Results, i
30/07/09
© The University of Sheffield
27
Colour saturation (%)
Reaction Time (ms)Slide28
Expt 2 Results, ii
30/07/09
© The University of Sheffield
28Slide29
30/07/09
© The University of Sheffield
29
Cohen et al’s (1990) model of Stroop processing
Cohen, J. D., Dunbar, K., & McClelland, J. L. (1990). On the control of automatic processes - a parallel distributed-processing account of the stroop effect.
Psychological Review, 97
(3), 332-361.Slide30
30/07/09
© The University of Sheffield
30
S
S
Stimulus
Stimulus-Response
Translation
RTSlide31
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© The University of Sheffield
31
Stimulus
Stimulus-Response
Translation
RT
S
SSlide32
30/07/09
© The University of Sheffield
32
S
Stimulus
Stimulus-Response
Translation
RT
SSlide33
30/07/09
© The University of Sheffield
33
Simulation Results, iSlide34
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© The University of Sheffield
34
Simulation Results, iiSlide35
Interim conclusions (1/2)
Empirical findings
Pi
é
ron’s
Law holds for colour saturation…
….in a complex choice task
30/07/09
© The University of Sheffield
35Slide36
Interim conclusions (2/2)
Stimulus intensity and response conflict appear additive in a colour-saturation variant of the
Stroop
task
...but existing continuous-processing single-stage models of the
Stroop
task are adequate to account for this result
We must be careful before inferring discrete stages from additive RT data
30/07/09
© The University of Sheffield
36
Stafford, T., Gurney, K.N. & Ingram, L. (2009).
Piéron’s
Law holds in conditions of response conflict. In N.A.
Taatgen
& H. van Rijn (Eds.),
Proceedings of the 31th Annual Conference of the Cognitive Science Society
. Cognitive Science Society.Slide37
Modelling explorationsAppearance of additive and interactive factors can be generated by both single stage and multiple stage modelsFor the current task, another factor determines additivity --- whether stimulus inputs are bound together or not
30/07/09
© The University of SheffieldSlide38
Currently…
‘locked inputs’
S
S
(‘single stage’/continuous processing)Slide39
Now…
Independent inputs
S
1
(Still ‘single stage’)Slide40
Simulation independent inputs, single stage,
Result: interactive factorsSlide41
Locked inputs, ‘two stage’
1
S
1
SSlide42
Result: additive factors
Simulation: locked inputs, two stageSlide43
Independent inputs, two stage
1
S
1
1Slide44
Results: interactive factors
Simulation: independent inputs, two stagesSlide45
30/07/09© The University of SheffieldInputs: ‘Locked’ Independent
Decision making:
Single stage
/continuous
Multiple stage
/discrete
Additive
Additive
Interactive
InteractiveSlide46
Modelling conclusionAn illustration of the phenomenon of model-mimickry (Townsend & Wenger, 2004) and more generally of the dangers of judging models solely by the goodness of fit to data (Roberts & Pashler, 2000).
30/07/09
© The University of Sheffield
Townsend, J. T., & Wenger, M. J. (2004). The serial-parallel dilemma: A case study in a linkage of theory and method.
Psychonomic
Bulletin & Review, 11
(3), 391-418. (1069-9384)… See also Thomas, R. D. (2006). Processing time predictions of current models of perception in the classic additive factors paradigm.
Journal Of Mathematical Psychology, 50
(5), 441-455.
Roberts, S., &
Pashler
, H. (2000). How persuasive is a good fit? a comment on theory testing.
Psychological Review, 107
(2), 358-367.Slide47
Conclusions, speculations & suggestions (1/4)It is definitely not possible to infer back from additive factors to underlying architectures (or, more precisely, you need many additional – and possibly unexpected – assumptions to make this inference)30/07/09
© The University of SheffieldSlide48
Conclusions, speculations & suggestions (2/4)In the Stroop task, despite physical separation of the stimulus elements they are still bound by attention
i.e. locked inputs
30/07/09
© The University of SheffieldSlide49
Conclusions, speculations & suggestions (3/4)Despite optimality requirement that decision making be single stage, evidence for ‘additive factors’ in decision making is undeniable and is not negated by plausibility of continuous processing, PDP-style, conceptions of neural processes.
30/07/09
© The University of SheffieldSlide50
Conclusions, speculations & suggestions (4/4)Unlikely that ‘simple perceptual decision making’ is simple, even in paradigmatic cases such as the RDK30/07/09
© The University of SheffieldSlide51
30/07/09© The University of SheffieldSlide52
what next?Show that presence/absence of attentional binding can make processing additive or interactive.Demonstrate
additivity
(i.e. non-optimality) in random dot
kinegrams
(properly)
30/07/09
© The University of SheffieldSlide53
Stafford, T., Gurney, K.N. & Ingram, L. (2009). Piéron’s
Law holds in conditions of response conflict. In N.A.
Taatgen
& H. van Rijn (Eds.),
Proceedings of the 31th Annual Conference of the Cognitive Science Society
. Cognitive Science Society.
CogSci
2009, Amsterdam, 2
nd
of
August
We thank Sarah Fox for help running the experiments, David Lawrence & David Yates for reading drafts and Marius Usher and Eddy
D
ave
laar
for useful discussion of the material.