E VIDENCE FOR A SPEED - ACCURACY TRADE - OFF IN BILINGUALS : A DIFFUSION MODEL APPROACH TO THE ATTENTION N ETWORK TASK Joseph M. Burling

Crystal D. Tran

Hanako Yoshida

[email protected]

[email protected]

[email protected]

Observed Response Time Data

◦ There is a lot of ambiguity in the literature on bilingual advantage in cognitive domains such as attention. ◦ Measurements of attention are typically conducted by looking at response times, which are often analyzed by discarding parts of the data and/or interpreting accuracy and time separately. ◦ How do RT and response accuracy interact on the ANT given an individual’s previous language experience, and what is the role of this experience on influencing attention?

Adult, Correct

Model Predicted RT & Accuracy

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0.020 100

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Monolingual

0.015 2000

0.010 50

Our Main Contributions

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◦ The ANT measures certain aspects of attention such as alerting, orienting, and executive control. ◦ This is tested using specific combinations of cues and congruent/incongruent target orientations. ◦ After viewing a cue, adults used the keyboard to respond to the direction of the target (middle item), while children used a left/right mouse click to respond.

Monolingual & bilingual participants Adult ◦ Bilinguals: ◦ sample size = 31 ◦ age = 24.0 yrs ◦ range = (17, 44) ◦ Monolinguals: ◦ sample size = 32 ◦ age = 25.8 yrs ◦ range = (19, 56)

Child ◦ Bilinguals: ◦ sample size = 57 ◦ age = 79.5 mos ◦ range = (49, 108) ◦ Monolinguals: ◦ sample size = 68 ◦ age = 79.1 mos ◦ range = (45, 117)

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Posterior Distributions of Estimated Diffusion Parameters: Cautiousness, time required to respond

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Parameter τ

Parameter α

Initial bias toward correct

Information processing speed

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References

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Response time  |

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Motor response & encoding time

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Posterior density

◦ Parameters were estimated using an extension of the Hamiltonian Monte Carlo algorithm referred to as the No-UTurn Sampler ◦ Five MCMC chains were run in parallel for a total of 10,000 samples, with just as many allowed for initial tuning ◦ Vertical lines display the median of each posterior distribution ◦ In general, bilinguals have estimates which increase RT, except for processing speed δ

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Theoretical RT density using estimated model parameters. Inaccurate responses are indicated by a negative RT, while accurate are positive values.

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Response time * Accuracy {−1, 1}

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π α, τ, δ ∼ µ + tan(unif orm(0, )) 2 β ∼ beta(1.25, 1.25) µ=0

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Discussion of Results

Half-cauchy & Beta priors

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Parameter β

yˆij = wiener(αj , τj , βj , δj ) αj = α0 + α1 ∗ bilingual τj = τ 0 + τ 1 ∗ bilingual βj = β 0 + β 1 ∗ bilingual δj = δ 0 + δ 1 ∗ bilingual

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Wiener process likelihood

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The ANT time and accuracy data were modeled as a Wiener/Brownian process in which binary responses (correct/incorrect) and the time in takes to make them are decomposed into cognitive processes such as the speed/accuracy trade-off (α), processing speed of the individual (δ), initial bias toward a particular response (β), and motor response latency (τ ). These parameters determine the shape of the response time distributions for both accurate and inaccurate cases.

Task information & procedure

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Bayesian Diffusion Model

Stimuli (adult & child versions)

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Posterior density

Attention Network Task

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◦ Diffusion models allow for simultaneous evaluation of accuracy and response time data, which provides richer information about the underlying processes involved in binary, timed response tasks. ◦ We observed measurable differences in how bilinguals differ from monolinguals when responding to stimuli that measures general attentiveness. ◦ Process models such as these provide additional information about how language influences attention, which can’t be obtained with classical statistical analyses. ◦ Results suggest a higher probability of an incorrect response for biliguals given a speeded response, but delayed RT are overcome by faster processing speed over the monolingual group. ◦ Similar response time statistics between the two groups may be the result of different underlying processes driven by language history.

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Normalized Density

Introduction to the Problem

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1. Vandekerckhove, J., Tuerlinckx, F., & Lee, M. D. (2011). Hierarchical diffusion models for two-choice response times. Psychological Methods, 16, 44–62. 2. Stan Development Team (2014). Stan: A C++ Library for Probability Sampling, Version 2.2. http://mc-stan.org/

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The above figure illustrates how accurate response times between two groups may look similar (total RT), yet involve different processes in terms of the parameters estimated by the diffusion model. Bilinguals may exhibit slightly slower response times, due to a higher accuracy cost for speeded responses (speed/accuracy trade-off) and lower initial bias; however, RTs may be shortened by faster processing of the information. A history of language switching may generate tendencies for quickly processing information within the context of ANT, yet more evidence about the environment may be required before a bilingual individual can initiate this process.

3. Tran, D. N. & Yoshida, H. (2011). The developmental role of attentional control in language learning. In L. Carlson, C. Holscher, & T. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (p. 1747). Austin, TX: Cognitive Science Society.

Acknowledgments This research was supported in part by University of Houston, a National Institutes of Health grant (R01 HD058620), the Foundation for Child Development (Young Scholars Program), and University of Houston’s Grants to Enhance and Advance Research (GEAR) program. We would also like to thank the children and parents who participated in this study.

Poster Presented at the Boston University Conference on Language Development (BUCLD39)