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

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 m...

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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1545-5955
1558-3783
DOI:10.1109/TASE.2015.2499244