Simulation Estimation of Mixed Discrete Choice Models with the Use of Randomized Quasi-Monte Carlo Sequences: A Comparative Study
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This paper numerically compares the overall performance of the quasi-Monte Carlo (QMC) sequences proposed by Halton and Faure, and their scrambled versions, against each other and against the Latin Hypercube Sampling sequence in the context of the simulated likelihood estimation of a Mixed Multinomial Logit model of choice. In addition, the efficiency of the QMC sequences generated with and without scrambling across observations is compared, and the performance of the Box-Muller and Inverse Normal transform procedures is tested. The numerical experiments were performed in 5 dimensions with 25, 125 and 625 draws, and in 10 dimensions with 100 draws. The results of our analysis indicate that the Faure sequence consistently outperforms the Halton sequence, and the scrambled versions of the Faure sequence show the best performances overall.
At the time of publication A. Sivakumar and C.R. Bhat were at the University of Texas at Austin; and G. Okten was at Ball State University.