Investigation of Underlying Distributional Assumption in Nested Logit Model Using Copula-Based Simulation and Numerical Approximation

This paper proposes a practical approach for drawing random samples that satisfy the underlying distributional assumptions in the nested logit model. This approach is a combined application of a series of statistical and numerical techniques including copula-based characterization of joint distributions, quasi-Monte Carlo integration, coordinate conversion, dichotomous approximation, and linear interpolation. With this approach, one may efficiently sample from and directly observe the distribution of common random components that result in correlation between random utilities in the nested logit model. Monte Carlo studies are conducted for two- and three-level nested logit models to evaluate the performance of random samples to recover model coefficients in nested logit models. Simulation experiments show that the relative differences are no more than 3% between mean values of estimators and their true values, indicating the proposed approach's high level of accuracy in reproducing random components in nested logit models.