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

With an eye towards human-centered automation, this paper contributes to the development of a systematic means to infer features of human decision making from behavioral data. Because softmax selection figures centrally in human decision-making models, we study the maximum likelihood parameter estimation problem for softmax decision-making models with linear objective functions. We derive conditions under which the likelihood function is convex, which allows us to provide sufficient conditions for convergence of the resulting maximum likelihood estimator and construct its asymptotic distribution. To extend these results to 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 to human subject data and show statistically significant differences in behavior across related, but distinct, tasks.