Parameter Estimation in Softmax Decision-Making Models With Linear Objective Functions

• Published in: IEEE transactions on automation science and engineering Vol. 13; no. 1; pp. 54 - 67
• Main Authors: Reverdy, Paul, Leonard, Naomi Ehrich
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic methods; Asymptotic properties; Automation; Biological system modeling; Convergence; Data models; Decision making; estimation; Estimators; Human; Human behavior; Linear programming; Mathematical models; Maximum likelihood method; Parameter estimation; Stochastic models; Stochastic processes
• ISSN: 1545-5955; 1558-3783
• DOI: 10.1109/TASE.2015.2499244

We contribute to the development of a systematic means to infer features of human decision-making from behavioral data. Motivated by the common use of softmax selection in models of human decision-making, we study the maximum-likelihood (ML) parameter estimation problem for softmax decision-making models with linear objective functions. We present conditions under which the likelihood function is convex. These allow us to provide sufficient conditions for convergence of the resulting ML estimator and to construct its asymptotic distribution. In the case of models with nonlinear objective functions, we show how the estimator can be applied by linearizing about a nominal parameter value. We apply the estimator to fit the stochastic Upper Credible Limit (UCL) model of human decision-making to human subject data. The fits show statistically significant differences in behavior across related, but distinct, tasks.