Beyond Box-Cox: A diffusion-inspired functional framework for nonlinear demand and discrete choice modeling
提出一种受扩散过程启发的函数框架，用于非线性需求和离散选择建模，通过可验证的子函数性质保证单调性和曲率，易于用标准软件估计，在交通模式选择和车辆拥有案例中优于传统函数。
• Proposes a diffusion-inspired framework for nonlinear demand and choice modeling • Ensures monotonicity and curvature via verifiable sub-function properties • Enables socio-economic heterogeneity in a modular, bounded, low-parametric form • Easy to estimate using standard software; no special optimization required • Outperforms standard functions on real and simulated transport data This paper presents a new diffusion-inspired functional framework for modeling nonlinear demand and discrete choice, with applications in transportation and related fields. The framework goes beyond traditional transformations by combining a diffusion-like core function with upper and lower bound functions, linked through a transfer function. Key properties such as monotonicity and concavity or convexity are guaranteed by simple, verifiable conditions on the component functions. A key advantage of this approach is that it breaks the nonlinear structure into separate parts, making it easier to integrate socio-economic variables. This enables the model to capture non-linear shifts, damping, and scaling effects across different socio-economic groups. The framework is low-parametric, bounded, continuous, and modular, which makes it easy to estimate using standard software. Its flexibility and strengths are illustrated in two case studies: (i) a discrete choice model of transport mode selection, and (ii) a nonlinear logistic regression model of vehicle ownership. In both cases, the framework enhances model fit, facilitates better control over tail behavior, demonstrates how heterogeneity can be effectively integrated, and yields more precise and behaviorally plausible elasticity estimates. Controlled simulations further demonstrate the framework’s robustness across a broad range of nonlinear processes. Adjusting the individual sub-components leads to distinct functional behaviors, preventing convergence toward a single common shape. This diversity indicates that the framework avoids ”copy-cat” behavior or functional collapse. As a result, its flexible, bounded structure can be tailored or relaxed depending on the application, offering virtually limitless possibilities for adapting functions to address different problems.