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 Task description Choice domain Value-based choice
Dataset Task description Choice domain Perceptional choice
Behavioral data
Behavioral data Three behavioral metrics ● Mean RT (Mean response time) Value-based task (a, b, c) : item with higher likeness rating ● P(choosing best) (Mean probability of choosing the best item) Perceptional task (d) : item with smaller angular distance ● Gaze influence 1) Probability of choosing the item : based on item value Observed data 2) Residual choice probability = observed data – probability of choosing the item (1: chosen, 0: otherwise) 3) Gaze influence on choice = 𝑞𝑝𝑡𝑗𝑢𝑗𝑤𝑓 𝑏𝑨𝑓 𝑏𝑒𝑤𝑏𝑜𝑢𝑏𝑓 ’s Residual choice probability – 𝑜𝑓𝑏𝑢𝑗𝑤𝑓 𝑏𝑨𝑓 𝑏𝑒𝑤𝑏𝑜𝑢𝑏𝑓 ’s Residual choice probability * 𝑞𝑝𝑡𝑗𝑢𝑗𝑤𝑓 𝑏𝑨𝑓 𝑔𝑗𝑜𝑏𝑚 𝑏𝑒𝑤𝑏𝑜𝑢𝑏𝑓 : fraction of time fixated on the item > average fixated time for the others * 𝑜𝑓𝑏𝑢𝑗𝑤𝑓 𝑏𝑨𝑓 𝑔𝑗𝑜𝑏𝑚 𝑏𝑒𝑤𝑏𝑜𝑢𝑏𝑓 : fraction of time fixated on the item < average fixated time for the others
Behavioral data Behavioral Results 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
Computational model
Computational model GLAM: Gaze-weighted Linear Accumulator Model ● Linear stochastic horse race model b For more information about previous DDM (Ian Krajbich et al., 2010; 2011; 2012; 2015)
Computational model GLAM: Gaze-weighted Linear Accumulator Model ● Linear stochastic horse race model b For more information about previous DDM (Ian Krajbich et al., 2010; 2011; 2012; 2015)
Computational model GLAM: Gaze-weighted Linear Accumulator Model Accumulated relative evidence 𝜉 = velocity parameter (speed of accumulation) 𝑢 = time point 𝜏 = standard deviation 𝑆 = Drift term Logistic transformation Drift term Relative evidence Stationary absolute evidence signal 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑝𝑜 𝑗𝑢𝑓𝑛 𝑗 ! = relative gaze = 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑠 ! = item value 𝛿 = 1 : No gaze bias 𝛿 = gaze bias parameter 𝛿 < 1 : Gaze bias
Computational model GLAM: Gaze-weighted Linear Accumulator Model Accumulated relative evidence 𝜉 = velocity parameter (speed of accumulation) 𝑢 = time point 𝜏 = standard deviation 𝑆 = Drift term Logistic transformation Drift term scaling parameter Relative evidence Stationary absolute evidence signal 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑝𝑜 𝑗𝑢𝑓𝑛 𝑗 ! = relative gaze = 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑠 ! = item value 𝛿 = 1 : No gaze bias 𝛿 = gaze bias parameter 𝛿 < 1 : Gaze bias
Computational model GLAM: Gaze-weighted Linear Accumulator Model Accumulated relative evidence Distribution of Gaze 𝜉 = velocity parameter (speed of accumulation) 𝑢 = time point 𝜏 = standard deviation 𝑆 = Drift term Logistic transformation Drift term Relative evidence Stationary absolute evidence signal 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑝𝑜 𝑗𝑢𝑓𝑛 𝑗 ! = relative gaze = 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑠 ! = item value 𝛿 = 1 : No gaze bias 𝛿 = gaze bias parameter 𝛿 < 1 : Gaze bias
Computational model GLAM: Gaze-weighted Linear Accumulator Model Accumulated relative evidence 𝜉 = velocity parameter (speed of accumulation) 𝑢 = time point 𝜏 = standard deviation 𝑆 = Drift term Logistic transformation Drift term Relative evidence Stationary absolute evidence signal 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑝𝑜 𝑗𝑢𝑓𝑛 𝑗 ! = relative gaze = 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑠 ! = item value 𝛿 = 1 : No gaze bias 𝛿 = gaze bias parameter 𝛿 < 1 : Gaze bias
Computational model GLAM: Gaze-weighted Linear Accumulator Model Accumulated relative evidence 𝜉 = velocity parameter (speed of accumulation) 𝑢 = time point 𝜏 = standard deviation 𝑆 = Drift term Logistic transformation Drift term Logistic transformation Relative evidence Stationary absolute evidence signal 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑝𝑜 𝑗𝑢𝑓𝑛 𝑗 ! = relative gaze = 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑠 ! = item value 𝛿 = 1 : No gaze bias 𝛿 = gaze bias parameter 𝛿 < 1 : Gaze bias
Computational model GLAM: Gaze-weighted Linear Accumulator Model Accumulated relative evidence 𝜉 = velocity parameter (speed of accumulation) 𝑢 = time point 𝜏 = standard deviation 𝑆 = Drift term Logistic transformation Drift term Relative evidence Stationary absolute evidence signal 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑝𝑜 𝑗𝑢𝑓𝑛 𝑗 ! = relative gaze = 𝑈𝑝𝑢𝑏𝑚 𝑔𝑗𝑦𝑏𝑢𝑗𝑝𝑜 𝑠 ! = item value 𝛿 = 1 : No gaze bias 𝛿 = gaze bias parameter 𝛿 < 1 : Gaze bias
Computational model GLAM: Gaze-weighted Linear Accumulator Model 𝑄 % 𝑢 : Probability of 𝐹 % reaching 𝑐 at time 𝑢 , before any other accumulator has reached.
Computational model GLAM: Gaze-weighted Linear Accumulator Model 𝑄 % 𝑢 : Probability of 𝐹 % reaching 𝑐 at time 𝑢 , before any other accumulator has reached. Resulting choice likelihood
Computational results
Computational results Parameter recovery S. Fig. 7: Results of a parameter recovery study of the GLAM
Computational results Presence of individual difference in gaze bias Fig. 4 S. Fig. 1 Individual parameter estimates of 𝜹 Model comparison using WAIC (Widely Applicable Information Criterion) [-1.03 ~ 0.97] 1) Full GLAM model 2) No-Gaze-bias GLAM variant (gaze bias parameter 𝛿 = 1) è Non-trivial difference in Gaze bias! è Full GLAM model fitted 109/118 participants (98%) better than No bias model
Computational results Model simulation ● Predicted choices (3 behavioral metrics) & RT - Train set: Even-numbered trials - Test set: Odd-numbered trials Full GLAM No-Gaze-Bias Model Fig. 5 S. Fig. 5 & 6 Choice prediction RT prediction
Computational results Model simulation ● Behavioral metrics prediction Fig. 2 S. Fig. 4 Out-of-sample predicted data Observed data
Computational results Individual’s response behavior & parameter ● 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
Discussion
Discussion Summary ● Test the model GLAM using 4 different datasets. 1) Compared model with & without gaze bias è Individual variability in gaze bias exists, since model with bias better explained individual’s choice behavior. 2) Model simulation of GLAM è GLAM accurately predicted observed behavioral data and their associations. 3) Associations between the model parameter & behavioral data è Stronger gaze influence in the model was associated with stronger gaze influence score & inconsistent choice with item value in individuals’ response.
Discussion Strength & Implication ● 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. è Are these differences trait, state, or both?
Reference
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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