Bootstrap standard error estimations of nonlinear transport models based on linearly projected data

Abstract

Linear data projection is a commonly leveraged data scaling method for unbiased traffic data estimation. However, recent studies have shown that model estimations based on linearly projected data would certainly result in biased standard errors. Although methods have been developed to remove such biases for linear regression models, many transport models are nonlinear regression models. This study outlines the practical difficulties of the traditional approach to standard error estimation for generic nonlinear transport models, and proposes a bootstrapping mean value restoration method to accurately estimate the parameter standard errors of all nonlinear transport models based on linearly projected data. Comprehensive simulations with different settings using the most commonly adopted nonlinear functions in modeling traffic flow demonstrate that the proposed method outperforms the conventional method and accurately recovers the true standard errors. A case study of estimating a macroscopic fundamental diagram that illustrates situations necessitating the proposed method is presented.