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 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.