Slides for my talk at the Experimental Psychology Society conference, London, UK. January 2016.

1. flankr: An R Package Implementing
Computational Models of Attentional
Selectivity
Jim Grange
j.a.grange@keele.ac.uk

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Eriksen & Eriksen (1974)
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3. Flanker Task
• Response times are slower to incongruent
trials compared to congruent
– The “congruency effect”
• Attentional selectivity improves with
processing time (Gratton et al., 1998)
– Evidence for this gathered using so-called
Conditional Accuracy Functions (CAFs)

5. Improvement of Attentional Selectivity
• Continuous Improvement of attentional
selectivity
– Shrinking attentional spotlight reduces the effect
of flankers on response selection as processing
time progresses (Heitz & Engle, 2007; White et al.,
2011)

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e.g., Heitz & Engle (2007)

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e.g., Heitz & Engle (2007)

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e.g., Heitz & Engle (2007)

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e.g., Heitz & Engle (2007)

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e.g., Heitz & Engle (2007)

14. Improvement of Attentional Selectivity
• Discrete Improvement of attentional
selectivity
– Attentional selectivity rather poor in a first stage
of processing, but switches to a focussed
processing mode at discrete time-point (Huebner
et al., 2010).

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e.g., Huebner et al. (2010)

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e.g., Huebner et al. (2010)

17. ProportionCorrect

18. Probability of entering
second stage increases
with processing time
ProportionCorrect

19. Improvement of Attentional Selectivity
• Two competing theories for improvement of
attentional selectivity:
– Continuous improvement
– Discrete improvement
• These accounts are hard to disambiguate at
the behavioural level
– Both predict the observed improvement of
attentional selectivity with time

20. Computational Implementations
• Computational models are advantageous for
model comparison
– Precise, quantitative (cf., verbal models), model
predictions can be directly compared to observed
data
– Statistical competitive model comparison
techniques can be used to select best-fitting
model

21. Behavior Research Methods, in press
Dual-Stage, Two-
Phase Model
(Huebner et al.,
2010)
Shrinking Spotlight
Model (White et
al., 2011)

22. The Models

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Correct Response Boundary

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Correct Response Boundary
Error Response Boundary

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Early Attentional Selection

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Late Attentional Selection

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40. Time

41. Time

42. Time

43. Time

45. Overview of flankr

46. flankr
• flankr is a package which extends R statistics,
written with C++ and R
– Hence the “r” on flankr…
– R is a free statistical programming language

47. flankr
• You do NOT need to know R to use flankr
– The paper is written with an R-novice in mind

48. flankr
• You do NOT need to know R to use flankr
– The paper is written with an R-novice in mind
www.r-project.org

49. flankr
• You do NOT need to know R to use flankr
– The paper is written with an R-novice in mind
www.rstudio.com

50. flankr
• You do NOT need to know R to use flankr
– The paper is written with an R-novice in mind
www.rstudio.com

51. www.github.com/JimGrange/flankr

52. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

53. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

54. Simulating Data

55. Simulating Data

56. Simulating Data

57. Simulating Data

58. Simulating Data

59. Simulating Data

61. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

62. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

63. Fitting Empirical Data

64. Warning Signal
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65. Fitting Empirical Data

66. Cumulative Distribution
Function
Conditional Accuracy
Function

67. Fitting Empirical Data

68. Fitting Empirical Data

69. Fitting Empirical Data

70. Fitting Empirical Data

72. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

73. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

76. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

77. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

78. Model Comparison
• Fit DSTP model to data
– Get bBIC_DSTP
• Fit SSP model to data
– Get bBIC_SSP
• Fit with the lowest bBIC is to be preferred
– Parameters are penalised via M, so simpler
models are preferred, all else equal…

80. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

81. Overview of flankr
• Simulate data from the DSTP and SSP models
– Useful for exploring model characteristics
• Fit DSTP and SSP model to user data
– Fit to congruent & incongruent trials
– Fit group data or individual subjects
– Multiple parameter optimisation methods
supported
• Plot model fits to user data
• Model comparison via statistical tests
• Bootstrapping & Jack-knifing of model fits

82. Bootstrapping
• Often, fits to individual subjects are too noisy
• Group fits are therefore preferred when trial
numbers are low
• How to examine differences of parameter
values between experimental conditions?
– We only have one set of parameter values for
each condition

83. Bootstrapping

84. Best Model
Parameters
(Condition
A)
Sim.
1
simDSTP Fit
1
fitDSTP

85. Best Model
Parameters
(Condition
A)
Sim.
1
simDSTP Fit
1
fitDSTP
Sim.
2
Sim.
3
Sim.
N
Fit
2
Fit
3
Fit
N

86. Best Model
Parameters
(Condition
A)
Sim.
1
simDSTP Fit
1
fitDSTP
Sim.
2
Sim.
3
Sim.
N
Fit
2
Fit
3
Fit
N

90. Current Work
• Due to ability to simulate data from each
model, flankr can be used for detailed model
comparison studies
• Current work examining model mimicry
– The extent to which each model makes unique
predictions of data

91. Model Mimicry
• If models make unique predictions, then data
simulated from one model should be better fit
by that generating model
DSTP
DSTP
Data
DSTP
bBIC
SSP
bBIC

92. DSTP Generated Data

93. DSTP Generated Data
DSTP Model
Preferred

94. DSTP Generated Data
SSP Model
Preferred

95. DSTP Generated Data
Model Mimicry
(Both models fit
equally well)

96. Model Mimicry
• 1,000 data sets simulated for each model
• Each data set then fit by each model & plotted
on landscape
DSTP
DSTP
Data
DSTP
bBIC
SSP
bBIC

97. DSTP Generating Model

98. 56%
44%

99. SSP Generating Model

100. 74%
26%

101. Model Mimicry
• The DSTP model generates data that is equally
well fit by the SSP model
– Some degree of model mimicry
• The SSP model generates relatively unique
data that the DSTP model cannot predict
– But SSP model not as well fit to human data,
generally

102. Model Mimicry
• More diagnostic data might be required to
establish the dynamics of attentional
selectivity

103. Incon.Con.
LEFT RIGHT
Congruent
Incongruent
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104. Thank You!
A copy of these slides will be available
on my website:
www.jimgrange.wordpress.com