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Simulation Estimation of Mixed Discrete Choice Models with the Use of Randomized Quasi–Monte Carlo Sequences

The overall performance of the quasi–Monte Carlo (QMC) sequences proposed by Halton and Faure, as well as their scrambled versions, are numerically compared 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 is compared across observations, and the performance of the Box–Muller and inverse normal transform procedures is tested. Numerical experiments were performed in five dimensions with 25, 125, and 625 draws and in 10 dimensions with 100 draws. Results indicate that the Faure sequence consistently outperforms the Halton sequence and that the scrambled versions of the Faure sequence perform best overall.