The Importance of Response Time in Preference Elicitation: Asymptotic Results

Abstract

Response Time (RT) is readily available in computer-based discrete choice experiments. The sequential sampling model (SSM) is a predominant approach to model choice and RT data in cognitive psychology. However, their applications in economics are limited due to concerns regarding parameter identifiability and lack of theoretical underpinning of the benefits of integrating RT data. This study addresses these issues and highlights the importance of leveraging RT data in preference elicitation. Firstly, contextualizing the asymptotic theory for an SSM, we theoretically show that joint choice-RT (CRT) distribution leads to lower standard errors than the choice-only counterpart. Thus, integrating RT into preference elicitation reduces sample-size requirements. Secondly, a novel estimation procedure is proposed to utilize RT information, where the conditional distribution of choice outcome given RT (RTG) is used. Thirdly, we demonstrate that RT introduces additional variation in the loglikelihood relative to parameters, thereby ensuring the identifiability of SSM parameters. We validate theoretical properties in a simulation and an empirical study from frequentist and Bayesian perspectives. A comparison of CRT, RTG, and choice-only estimators reveals that RTG exhibits superior choice prediction accuracy, but CRT remains the most efficient estimator. This study thus makes a strong case to leverage RT in choice models.

Keywords: Discrete Choice Model, Sequential Sampling Models, Parameter Identification, Asymptotic Theory, Efficient Estimator, Information Matrix