Designed Quadrature to Approximate Integrals in Maximum Simulated Likelihood Estimation

Maximum likelihood estimation of mixed multinomial logit (MMNL) or probit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as Halton sequences or modified latin hypercube sampling are generally used to approximate this integral. A few earlier studies explored the potential of sparse grid quadrature (SGQ), but this technique suffers due to negative weights. As an alternative to QMC and SGQ methods, the authors look into the recently developed designed quadrature (DQ) method, which requires fewer evaluations of the conditional likelihood (i.e., lower computation time), is as easy to implement, ensures positivity of weights, and can be created on any general polynomial spaces. To compare the performance of DQ with QMC methods, the authors estimated MMNL models with different random parameters (3, 5, and 10) and variance-covariance structures (zero, low, and high covariance). Whereas DQ significantly outperformed QMC in the diagonal variance-covariance scenario, DQ could achieve a better model fit and recover true parameters with fewer function evaluations across all considered scenarios. Finally, the authors evaluated the performance of DQ on a case study to understand preferences for mobility-on-demand services in New York City. In estimating MMNL with five random parameters, DQ achieved better fit and statistical significance of parameters with just 200 evaluations as compared to 500 modified latin hypercube sampling (MLHS) draws.

  • Supplemental Notes:
    • This paper was sponsored by TRB committee ABJ80 Standing Committee on Statistical Methods.
  • Corporate Authors:

    Transportation Research Board

  • Authors:
    • Bansal, Prateek
    • Keshavarzzadeh, Vahid
    • Guevara, Angelo
    • Daziano, Ricardo A
  • Conference:
  • Date: 2019


  • English

Media Info

  • Media Type: Digital/other
  • Features: References; Tables;
  • Pagination: 8p

Subject/Index Terms

Filing Info

  • Accession Number: 01697893
  • Record Type: Publication
  • Report/Paper Numbers: 19-04953
  • Files: TRIS, TRB, ATRI
  • Created Date: Dec 7 2018 9:41AM