Mina Kwon 2020. 04. 09. vs vs Preference Gaze influence - - PowerPoint PPT Presentation

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Mina Kwon 2020. 04. 09. vs vs Preference Gaze influence - - PowerPoint PPT Presentation

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Mina Kwon 2020. 04. 09. vs vs Preference Gaze influence Fixation Choice A HIGH B LOW Dataset Dataset Task description Dataset Task description Set size Binary choice Dataset Task description Set size Trinary choice Dataset

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Mina Kwon

  • 2020. 04. 09.
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vs

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Preference Gaze influence Fixation Choice A HIGH B LOW

vs

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Dataset

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Dataset

Task description

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Dataset

Task description

Set size Binary choice

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Dataset

Task description

Set size Trinary choice

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Dataset

Task description

Choice domain Value-based choice

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Dataset

Task description

Choice domain Perceptional choice

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Behavioral data

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Behavioral data

  • Mean RT (Mean response time)
  • P(choosing best) (Mean probability of choosing the best item)
  • Gaze influence

1) Probability of choosing the item : based on item value 2) Residual choice probability = observed data – probability of choosing the item 3) Gaze influence on choice = π‘žπ‘π‘‘π‘—π‘’π‘—π‘€π‘“ 𝑕𝑏𝑨𝑓 π‘π‘’π‘€π‘π‘œπ‘’π‘π‘•π‘“β€™s Residual choice probability – π‘œπ‘“π‘•π‘π‘’π‘—π‘€π‘“ 𝑕𝑏𝑨𝑓 π‘π‘’π‘€π‘π‘œπ‘’π‘π‘•π‘“β€™s Residual choice probability

Three behavioral metrics

* π‘žπ‘π‘‘π‘—π‘’π‘—π‘€π‘“ 𝑕𝑏𝑨𝑓 π‘”π‘—π‘œπ‘π‘š π‘π‘’π‘€π‘π‘œπ‘’π‘π‘•π‘“ : fraction of time fixated on the item > average fixated time for the others * π‘œπ‘“π‘•π‘π‘’π‘—π‘€π‘“ 𝑕𝑏𝑨𝑓 π‘”π‘—π‘œπ‘π‘š π‘π‘’π‘€π‘π‘œπ‘’π‘π‘•π‘“ : fraction of time fixated on the item < average fixated time for the others Value-based task (a, b, c) : item with higher likeness rating Perceptional task (d) : item with smaller angular distance Observed data (1: chosen, 0: otherwise)

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Behavioral Results

Behavioral data

Individual difference in the behavioral metrics

Positive Gaze influence score: 98% Gaze influence: -11% ~ 72%

Associations between the behavioral metrics ↑ Gaze influence, ↓ p(choosing best)

  • Fig. 2
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Computational model

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  • Linear stochastic horse race model

GLAM: Gaze-weighted Linear Accumulator Model

Computational model

b

For more information about previous DDM (Ian Krajbich et al., 2010; 2011; 2012; 2015)

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  • Linear stochastic horse race model

GLAM: Gaze-weighted Linear Accumulator Model

Computational model

b

For more information about previous DDM (Ian Krajbich et al., 2010; 2011; 2012; 2015)

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Accumulated relative evidence Drift term Relative evidence Stationary absolute evidence signal

𝑕! = relative gaze = 𝑠

! = item value

𝛿 = gaze bias parameter

π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ π‘π‘œ 𝑗𝑒𝑓𝑛 𝑗 π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ

𝛿 = 1 : No gaze bias 𝛿 < 1 : Gaze bias

πœ‰ = velocity parameter (speed of accumulation) 𝑒 = time point 𝜏 = standard deviation 𝑆 = Drift term

Logistic transformation

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Accumulated relative evidence Drift term Relative evidence Stationary absolute evidence signal

𝑕! = relative gaze = 𝑠

! = item value

𝛿 = gaze bias parameter

π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ π‘π‘œ 𝑗𝑒𝑓𝑛 𝑗 π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ

𝛿 = 1 : No gaze bias 𝛿 < 1 : Gaze bias

πœ‰ = velocity parameter (speed of accumulation) 𝑒 = time point 𝜏 = standard deviation 𝑆 = Drift term

Logistic transformation scaling parameter

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Accumulated relative evidence Drift term Relative evidence Stationary absolute evidence signal

𝑕! = relative gaze = 𝑠

! = item value

𝛿 = gaze bias parameter

π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ π‘π‘œ 𝑗𝑒𝑓𝑛 𝑗 π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ

𝛿 = 1 : No gaze bias 𝛿 < 1 : Gaze bias

πœ‰ = velocity parameter (speed of accumulation) 𝑒 = time point 𝜏 = standard deviation 𝑆 = Drift term

Logistic transformation

Distribution of Gaze

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Accumulated relative evidence Drift term Relative evidence Stationary absolute evidence signal

𝑕! = relative gaze = 𝑠

! = item value

𝛿 = gaze bias parameter

π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ π‘π‘œ 𝑗𝑒𝑓𝑛 𝑗 π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ

𝛿 = 1 : No gaze bias 𝛿 < 1 : Gaze bias

πœ‰ = velocity parameter (speed of accumulation) 𝑒 = time point 𝜏 = standard deviation 𝑆 = Drift term

Logistic transformation

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Accumulated relative evidence Drift term Relative evidence Stationary absolute evidence signal

𝑕! = relative gaze = 𝑠

! = item value

𝛿 = gaze bias parameter

π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ π‘π‘œ 𝑗𝑒𝑓𝑛 𝑗 π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ

𝛿 = 1 : No gaze bias 𝛿 < 1 : Gaze bias

πœ‰ = velocity parameter (speed of accumulation) 𝑒 = time point 𝜏 = standard deviation 𝑆 = Drift term

Logistic transformation Logistic transformation

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Accumulated relative evidence Drift term Relative evidence Stationary absolute evidence signal

𝑕! = relative gaze = 𝑠

! = item value

𝛿 = gaze bias parameter

π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ π‘π‘œ 𝑗𝑒𝑓𝑛 𝑗 π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ

𝛿 = 1 : No gaze bias 𝛿 < 1 : Gaze bias

πœ‰ = velocity parameter (speed of accumulation) 𝑒 = time point 𝜏 = standard deviation 𝑆 = Drift term

Logistic transformation

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

𝑄% 𝑒 : Probability of 𝐹% reaching 𝑐 at time 𝑒, before any other accumulator has reached.

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Resulting choice likelihood 𝑄% 𝑒 : Probability of 𝐹% reaching 𝑐 at time 𝑒, before any other accumulator has reached.

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Computational results

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Parameter recovery

Computational results

  • S. Fig. 7: Results of a parameter recovery study of the GLAM
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Presence of individual difference in gaze bias

Computational results

Model comparison using WAIC (Widely Applicable Information Criterion)

1) Full GLAM model 2) No-Gaze-bias GLAM variant (gaze bias parameter 𝛿 = 1) Γ¨ Full GLAM model fitted 109/118 participants (98%) better than No bias model

Individual parameter estimates of 𝜹

[-1.03 ~ 0.97] Γ¨ Non-trivial difference in Gaze bias!

  • Fig. 4
  • S. Fig. 1
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Model simulation

Computational results

  • Predicted choices (3 behavioral metrics) & RT
  • Train set: Even-numbered trials
  • Test set: Odd-numbered trials
  • S. Fig. 5 & 6
  • Fig. 5

Choice prediction RT prediction

Full GLAM No-Gaze-Bias Model

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Model simulation

Computational results

Out-of-sample predicted data Observed data

  • Behavioral metrics prediction
  • Fig. 2
  • S. Fig. 4
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Individual’s response behavior & parameter

Computational results

  • Associations between the model parameters & response behavior
  • a. ↑ velocity parameter, ↓ mean RT
  • b. ↑ Gaze influence (↓ 𝛿), ↑ Gaze influence score
  • c. ↑ Gaze influence (↓ 𝛿), ↓ p(choosing best)
  • Fig. 6
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Discussion

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Discussion

  • Test the model GLAM using 4 different datasets.

1) Compared model with & without gaze bias Γ¨ Individual variability in gaze bias exists, since model with bias better explained individual’s choice behavior. 2) Model simulation of GLAM Γ¨ GLAM accurately predicted observed behavioral data and their associations. 3) Associations between the model parameter & behavioral data Γ¨ Stronger gaze influence in the model was associated with stronger gaze influence score & inconsistent choice with item value in individuals’ response.

Summary

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Discussion

  • GLAM enables trial specific prediction and prediction in Multiple choice situation.
  • GLAM doesn’t require a simulation of eye movement.
  • Analyses span across two set sizes & two choice domains.
  • Found individual difference in influence of gaze on choice behavior.

Γ¨ Are these differences trait, state, or both?

Strength & Implication

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Reference

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Reference

Krajbich, I., Armel, C., & Rangel, A. (2010). Visual fixations and the computation and comparison of value in simple choice. Nature Neuroscience, 13(10), 1292–1298. https://doi.org/10.1038/nn.2635 Krajbich, I., Lu, D., Camerer, C., & Rangel, A. (2012). The attentional drift-diffusion model extends to simple purchasing decisions. Frontiers in Psychology, 3, 193. https://doi.org/10.3389/fpsyg.2012.00193 Krajbich, I., & Rangel, A. (2011). Multialternative drift-diffusion model predicts the relationship between visual fixations and choice in value- based decisions. Proceedings of the National Academy of Sciences of the United States of America, 108(33), 13852–13857. https://doi.org/10.1073/pnas.1101328108 Krajbich, I., & Smith, S. M. (2015). Modeling Eye Movements and Response Times in Consumer Choice. Journal of Agricultural & Food Industrial Organization, 13(1), 55–72. https://doi.org/10.1515/jafio-2015-0016

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Thank you

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Additional Slides

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Behavioral Results

Behavioral data

Individual difference in the behavioral metrics

Positive Gaze influence score: 98% Gaze influence: -11% ~ 72%

Difference across datasets

2 options: ↓ RT, ↑ p(choosing best), ↓ gaze influence Value-based task: ↓ RT, ↑ p(choosing best)

Associations between the behavioral metrics ↑ Gaze influence, ↓ p(choosing best)

  • Fig. 2
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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Accumulated relative evidence Drift term Relative evidence Stationary absolute evidence signal

𝑕! = relative gaze = 𝑠

! = item value

𝛿 = gaze bias parameter

π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ π‘π‘œ 𝑗𝑒𝑓𝑛 𝑗 π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ

𝛿 = 1 : No gaze bias 𝛿 < 1 : Gaze bias

πœ‰ = velocity parameter (speed of accumulation) 𝑒 = time point 𝜏 = standard deviation 𝑆 = Drift term

Logistic transformation

Example 𝑕% = 0.7; 𝑕& = 0.3

𝛿 = 𝟐 𝛿 = 𝟏 𝛿 = βˆ’πŸ Equation

𝑠! 𝑕! + 1 βˆ’ 𝑕! = 𝑠! 𝑠! 𝑕! + 1 βˆ’ 𝑕! 𝛿 = 𝑠! βˆ— 𝑕! 𝑠! 𝑕! + 1 βˆ’ 𝑕! 𝛿 = 𝑠! βˆ— (𝑕! βˆ’ 1 + 𝑕!)

𝑩𝒋 𝑠

"

𝑠

" βˆ— 0.7

𝑠

" βˆ— 0.4

π‘©π’Œ 𝑠

$

𝑠

$ βˆ— 0.3

𝑠

$ βˆ— βˆ’0.4

No gaze bias Gaze bias Gaze bias

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GLAM: Gaze-weighted Linear Accumulator Model

Computational model

Accumulated relative evidence Drift term Relative evidence Stationary absolute evidence signal

𝑕! = relative gaze = 𝑠

! = item value

𝛿 = gaze bias parameter

π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ π‘π‘œ 𝑗𝑒𝑓𝑛 𝑗 π‘ˆπ‘π‘’π‘π‘š π‘”π‘—π‘¦π‘π‘’π‘—π‘π‘œ

𝛿 = 1 : No gaze bias 𝛿 < 1 : Gaze bias

πœ‰ = velocity parameter (speed of accumulation) 𝑒 = time point 𝜏 = standard deviation 𝑆 = Drift term

Logistic transformation

i j k 10 3 5

= 10 – 5 = 5 Example