Parameter estimation in softmax decision-making models with linear objective functions

TL;DR

This paper develops a systematic approach for estimating parameters in softmax decision-making models with linear objectives, enabling better understanding of human decision behaviors from behavioral data.

Contribution

It introduces conditions for convexity of the likelihood function, ensuring convergence of maximum likelihood estimators, and extends the method to nonlinear models via linearization.

Findings

Successfully fit the UCL model to human data

Detected significant behavioral differences across tasks

Provided a framework for parameter estimation in decision models

Abstract

With an eye towards human-centered automation, 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 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 maximum likelihood 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 UCL (Upper Credible Limit) model of human decision-making to human subject data. We show statistically significant differences in behavior across related, but distinct, tasks.