Combining Choice and Response Time Data: A Drift-Diffusion Model of Mobile Advertisements

References

• Alili L, Patie P, Pedersen JL (2005) Representations of the first hitting time density of an Ornstein-Uhlenbeck process. Stochastic Models 21(4):967–980.Crossref, Google Scholar
• Alós-Ferrer C (2018) A dual-process diffusion model. J. Behav. Decision Making 31(2):203–218.Crossref, Google Scholar
• Alós-Ferrer C, Fehr E, Netzer N (2021) Time will tell: Recovering preferences when choices are noisy. J. Political Econom. 129(6):1828–1877.Crossref, Google Scholar
• Baldassi C, Cerreia-Vioglio S, Maccheroni F, Marinacci M, Pirazzini M (2020) A behavioral characterization of the drift diffusion model and its multialternative extension to choice under time pressure. Management Sci. 66(11):5075–5093.Google Scholar
• Block H, Marschak J (1959) Random orderings and stochastic theories of responses. Cowles Foundation Discussion Papers, 289. https://elischolar.library.yale.edu/cowles-discussion-paper-series/289.Google Scholar
• Bogacz R, Brown E, Moehlis J, Holmes P, Cohen JD (2006) The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced-choice tasks. Psych. Rev. 113(4):700–765.Crossref, Google Scholar
• Busemeyer JR, Townsend JT (1992) Fundamental derivations from decision field theory. Math. Social Sci. 23(3):255–282.Crossref, Google Scholar
• Callaway F, Rangel A, Griffiths T (2020) Fixation patterns in simple choice reflect optimal information sampling. PLoS Comput. Biology 17(3):e1008863.Crossref, Google Scholar
• Chiong K, Chen R (2017) An empirical model of mobile advertising platforms. Working paper, University of Texas at Dallas, Dallas.Google Scholar
• Clithero JA (2018a) Improving out-of-sample predictions using response times and a model of the decision process. J. Econom. Behav. Organ. 148:344–375.Crossref, Google Scholar
• Clithero JA (2018b) Response times in economics: Looking through the lens of sequential sampling models. J. Econom. Psych. 69:61–86.Crossref, Google Scholar
• Crawford GS, Shum M (2005) Uncertainty and learning in pharmaceutical demand. Econometrica 73(4):1137–1173.Crossref, Google Scholar
• Drugowitsch J (2016) Fast and accurate Monte Carlo sampling of first-passage times from wiener diffusion models. Sci. Rep. 6:20490.Crossref, Google Scholar
• Dukes AJ, Liu Q, Shuai J (2022) Skippable Ads: Interactive advertising on digital media platforms. Marketing Sci. 41(3):528–547.Google Scholar
• Echenique F, Saito K (2017) Response time and utility. J. Econom. Behav. Organ. 139:49–59.Crossref, Google Scholar
• Erdem T, Keane MP (1996) Decision-making under uncertainty: Capturing dynamic brand choice processes in turbulent consumer goods markets. Marketing Sci. 15(1):1–20.Link, Google Scholar
• Fehr E, Rangel A (2011) Neuroeconomic foundations of economic choice—recent advances. J. Econom. Perspect. 25(4):3–30.Crossref, Google Scholar
• Fisher G (2021) Intertemporal choices are causally influenced by fluctuations in visual attention. Management Sci. 67(8):4961–4981.Link, Google Scholar
• Frydman C, Krajbich I (2022) Using response times to infer others’ private information: An application to information cascades. Management Sci. 68(4):2970–2986.Google Scholar
• Frydman C, Nave G (2016) Extrapolative beliefs in perceptual and economic decisions: Evidence of a common mechanism. Management Sci. 63(7):2340–2352.Link, Google Scholar
• Fudenberg D, Newey W, Strack P, Strzalecki T (2020) Testing the drift-diffusion model. Proc. Natl. Acad. Sci. USA 67(1):33141–33148.Crossref, Google Scholar
• Fudenberg D, Strack P, Strzalecki T (2018) Speed, accuracy, and the optimal timing of choices. Amer. Econom. Rev. 108:3651–3684.Crossref, Google Scholar
• Gold JI, Shadlen MN (2002) Banburismus and the brain: Decoding the relationship between sensory stimuli, decisions, and reward. Neuron 36(2):299–308.Crossref, Google Scholar
• Gold JI, Shadlen MN (2007) The neural basis of decision making. Annual Rev. Neuroscience 30:535–574.Crossref, Google Scholar
• Gossner O, Steiner J, Stewart C (2021) Attention please! Econometrica 89(4):1717–1751.Crossref, Google Scholar
• Gwinn R, Leber AB, Krajbich I (2019) The spillover effects of attentional learning on value-based choice. Cognition 182:6–11.Crossref, Google Scholar
• Haaijer R, Kamakura W, Wedel M (2000) Response latencies in the analysis of conjoint choice experiments. J. Marketing Res. 37(3):376–382.Crossref, Google Scholar
• Hare TA, Schultz W, Camerer CF, O’Doherty JP, Rangel A (2011) Transformation of stimulus value signals into motor commands during simple choice. Proc. Natl. Acad. Sci. USA 108(44):18120–18125.Crossref, Google Scholar
• Hasson U, Landesman O, Knappmeyer B, Vallines I, Rubin N, Heeger DJ (2008) Neurocinematics: The neuroscience of film. Projections 2(1):1–26.Crossref, Google Scholar
• Hébert B, Woodford M (2023) Rational inattention when decisions take time. J. Econom. Theory 208:105612. https://doi.org/10.1016/j.jet.2023.105612.Google Scholar
• Hong H, Shum M (2006) Using price distributions to estimate search costs. RAND J. Econom. 37(2):257–275.Crossref, Google Scholar
• Honka E (2014) Quantifying search and switching costs in the us auto insurance industry. RAND J. Econom. 45(4):847–884.Crossref, Google Scholar
• Jeon YA, Son H, Chung AD, Drumwright ME (2019) Temporal certainty and skippable in-stream commercials: Effects of ad length, timer, and skip-ad button on irritation and skipping behavior. J. Interactive Marketing 47(1):144–158.Crossref, Google Scholar
• Kaufman L (2014) Chasing Their Star, on YouTube. New York Times (February 1), https://www.nytimes.com/2014/02/02/business/chasing-their-star-on-youtube.html.Google Scholar
• Ke T, Villas-Boas M (2019) Optimal learning before choice. J. Econom. Theory 180:383–437.Crossref, Google Scholar
• Konovalov A, Krajbich I (2019) Revealed strength of preference: Inference from response times, judgement and decision making. Working paper, University of Birmingham, Birmingham, UK.Google Scholar
• Krajbich I (2019) Accounting for attention in sequential sampling models of decision making. Current Opin. Psych. 29:6–11.Google Scholar
• Krajbich I, Armel C, Rangel A (2010) Visual fixations and the computation and comparison of value in simple choice. Nature Neuroscience 13(10):1292.Crossref, Google Scholar
• Krajbich I, Bartling B, Hare T, Fehr E (2015) Rethinking fast and slow based on a critique of reaction-time reverse inference. Nature Comm. 6:7455.Crossref, Google Scholar
• Latimer KW, Yates JL, Meister MLR, Huk AC, Pillow JW (2015) Single-trial spike trains in parietal cortex reveal discrete steps during decision-making. Science 349(6244):184–187.Google Scholar
• Lehmann E (1959) Testing Statistical Hypotheses, 1st ed. (Wiley, New York).Google Scholar
• Lewis RA, Rao JM (2015) The unfavorable economics of measuring the returns to advertising. Quart. J. Econom. 130(4):1941–1973.Crossref, Google Scholar
• Link SW (1992) The Wave Theory of Difference and Similarity (Lawrence Erlbaum Associates, Inc., Mahwah, NJ).Google Scholar
• Lu J, Hutchinson JW (2017) Split-second decisions during online information search: Static vs. dynamic decision thresholds for making the first click. Technical report, Wharton School of Business, Philadelphia.Google Scholar
• Luce RD (1991) Response Times: Their Role in Inferring Elementary Mental Organization (Oxford University Press, Oxford, UK).Crossref, Google Scholar
• Marley AAJ, Colonius H (1992) The “horse race” random utility model for choice probabilities and reaction times, and its compering risks interpretation. J. Math. Psych. 36(1):1–20.Crossref, Google Scholar
• Mazurek ME, Roitman JD, Ditterich J, Shadlen MN (2003) A role for neural integrators in perceptual decision making. Cerebral Cortex 13(11):1257–1269.Crossref, Google Scholar
• Mormann M, Navalpakkam V, Koch C, Rangel A (2012) Relative visual saliency differences induce sizable bias in consumer choice. J. Consumer Psych. 22:67–74.Crossref, Google Scholar
• Morris S, Strack P (2019) The Wald problem and the relation of sequential sampling and ex-ante information costs. Preprint, submitted February 21, http://dx.doi.org/10.2139/ssrn.2991567.Google Scholar
• Norets A (2012) Estimation of dynamic discrete choice models using artificial neural network approximations. Econometric Rev. 31(1):84–106.Crossref, Google Scholar
• Otter T, Allenby GM, Van Zandt T (2008) An integrated model of discrete choice and response time. J. Marketing Res. 45(5):593–607.Crossref, Google Scholar
• Rao RC (1986) Estimating continuous time advertising-sales models. Marketing Sci. 5(2):125–142.Link, Google Scholar
• Ratcliff R, McKoon G (2008) The diffusion decision model: Theory and data for two-choice decision tasks. Neural Comput. 20(4):873–922.Crossref, Google Scholar
• Roitman J, Shadlen M (2002) Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. J. Neuroscience 22(21):9475–9489.Crossref, Google Scholar
• Rustichini A (2021) Neural and normative theories of stochastic choice. Working paper, University of Minnesota, Minneapolis.Google Scholar
• Rustichini A, Domenech P, Civai C, Deyoung C (2023) Working memory and attention in choice. PLOS One. Forthcoming.Google Scholar
• Seiler S, Pinna F (2017) Estimating search benefits from path-tracking data: Measurement and determinants. Marketing Sci. 36(4):565–589.Link, Google Scholar
• Shadlen M, Shohamy D (2016) Decision making and sequential sampling from memory. Neuron 90:927–939.Crossref, Google Scholar
• Shadlen MN, Hanks TD, Churchland AK, Kiani R, Yang T (2006) The speed and accuracy of a simple perceptual decision: A mathematical primer. Doya K, Ishii S, Pouget A, Rao R, eds. Bayesian Brain Probabilistic Approaches to Neural Coding (MIT Press, Cambridge, MA), 201–236.Crossref, Google Scholar
• Shapiro BT, Hitsch GJ, Tuchman AE (2021) TV advertising effectiveness and profitability: Generalizable results from 288 brands. Economterica 89(4):1855–1879.Google Scholar
• Smith PL (2000) Stochastic dynamic models of response time and accuracy: A foundational primer. J. Math. Psych. 44(3):408–463.Crossref, Google Scholar
• Smith S, Webb R, Krajbich I (2019) Estimating the dynamic role of attention via random utility. J. Econom. Sci. Assoc. 5(1):97–111.Crossref, Google Scholar
• Tajima S, Drugowitsch J, Patel N, Pouget A (2019) Optimal policy for multi-alternative decisions. Nature Neuroscience 22(9):1503–1511.Google Scholar
• Teoh YY, Yao Z, Cunningham WA, Hutcherson CA (2020) Attentional priorities drive effects of time pressure on altruistic choice. Nature Comm. 11(1):3534.Google Scholar
• Tusche A, Hutcherson CA (2018) Cognitive regulation alters social and dietary choice by changing attribute representations in domain-general and domain-specific brain circuits. eLife 7(1):e31185.Crossref, Google Scholar
• Ursu R, Wang Q, Chintagunta P (2018) Search duration. Marketing Sci. 39(5):849–871.Google Scholar
• Usher M, McClelland JL (2001) The time course of perceptual choice: The leaky, competing accumulator model. Psych. Rev. 108(3):550–592.Crossref, Google Scholar
• van Smeden M, de Groot JA, Moons KG, Collins GS, Altman DG, Eijkemans MJ, Reitsma JB (2016) No rationale for 1 variable per 10 events criterion for binary logistic regression analysis. BMC Medical Res. Methodology 16(1):163.Crossref, Google Scholar
• Vittinghoff E, McCulloch CE (2007) Relaxing the rule of ten events per variable in logistic and cox regression. Amer. J. Epidemiology 165(6):710–718.Crossref, Google Scholar
• Wald A (1973) Sequential Analysis (Wiley, New York).Google Scholar
• Wang XJ (2002) Probabilistic decision making by slow reverberation in cortical circuits. Neuron 36(5):955–968.Crossref, Google Scholar
• Webb R (2019) The (neural) dynamics of stochastic choice. Management Sci. 65:230–255.Link, Google Scholar
• Webb R, Glimcher PW, Louie K (2021) The normalization of consumer valuations: Context-dependent preferences from neurobiological constraints. Management Sci. 67(1):93–125.Link, Google Scholar
• Wiecki TV, Sofer I, Frank MJ (2013) HDDM: Hierarchical Bayesian estimation of the drift-diffusion model in python. Frontiers Neuroinformatics 7:14.Crossref, Google Scholar
• Woodford M (2014) Stochastic choice: An optimizing neuroeconomic model. Amer. Econom. Rev. 104(5):495–500.Crossref, Google Scholar
• Woodford M (2016) Optimal evidence accumulation and stochastic choice. Working paper, Columbia University, New York.Google Scholar