A practical method to draw from multivariate extreme value distributions

Abstract

Generating random draws from multivariate extreme value (MEV) distributions plays an important role in the microsimulation of travel behaviors, which can effectively avoid heavy computational burdens from simulation based on calculated probability values, particularly in simulations for a large population or choice behaviors from a large choice set. However, there are few practical and effective methods for drawing from MEV distributions. This paper proposes a simple and computationally efficient approach for drawing from MEV distributions in the nested logit (NL), cross-nested logit (CNL), and paired combinatorial logit (PCL) models. The proposed approach to draw from the MEV distribution for a CNL model provides a new perspective to understand the underlying choice mechanism of the CNL model. To our knowledge, this is the first study to draw from an MEV distribution in the PCL model. Random draws from the proposed approach approximately follow the standard Gumbel distribution, which is the marginal distribution of NL/CNL/PCL models, and approximate correlations among alternatives well. Simulation results of NL/CNL/PCL models show that the proposed approach provides high-level accuracy in recovering model parameters with the overall mean absolute percentage bias being less than 3%. The proposed approach is computationally more efficient than similar ones because it only needs to draw from Gumbel distributions. The proposed approach can be used to simulate NL/CNL/PCL models with a large choice set or a multiple discrete-continuous generalized extreme value model in various application settings such as joint destination-mode choices, time use allocations, etc.