Agnostic Utility Function Approximation via Cubic Bezier Splines
Lee, S., Glaze, C. M. Bradlow, E. T., & Kable, J. W.
In revision for Journal of Marketing Research
Utility functions are heavily used for modeling economic decision-making such as intertemporal and risky choice. Researchers have used both parametric and non-parametric approaches to model utility functions. Parametric models are simple and easy to fit, but they often require formal assumptions that can be hard to justify, especially given the myriad of different models that exist with no consensus. Non-parametric approaches require relatively large datasets and specially designed procedures to elicit the utility functions. Here we present a novel method – cubic Bezier splines (CBS) – as an ‘agnostic’ model that approximates utility functions without rigid formal assumptions. CBS is flexible like non-parametric approaches but does not require large or specially designed datasets. CBS provides smooth functions like parametric models but without many of their assumptions. We demonstrate via simulation and real data that CBS accurately recovers a diverse variety of utility models and shows higher predictive accuracy than alternatives. We also demonstrate that CBS can detect important heterogeneity and consistent granular patterns in choice data that cannot be detected with many parametric models.