Random Coefficient Mixed Logit Models Based on Generalized Antithetic Halton Draws and Double Base Shuffling

Abstract

Mixed logit models based on quasi-random draws are increasingly being used in discrete choice analysis because of their flexibility. Currently used mixed logit models are too expensive, and their performance degrades with increasing dimensionality. To overcome those shortcomings, two new simple and practical techniques are proposed, namely, quasi Monte Carlo (QMC) with generalized antithetic draws and the double base shuffling method (QMC with generalized antithetic draws and double base shuffling). In a comparison of the performance on probability evaluation, the proposed methods are found to be statistically superior (more accurate and precise) to conventional Halton draws for various dimensions. Results show that proposed methods, unlike conventional Halton draws, are less susceptible to dimensional deterioration even at higher dimensions. Computational experiments with real and synthetic data sets also reveal that the proposed methods are significantly faster for simulated estimation of mixed logit models (at higher dimensions) than other benchmark models [standard Halton, modified Latin hypercube sampling (MLHS), and shuffled Halton draws] to achieve similar accuracy levels. For the real data, the proposed method is 2.1 times faster than conventional QMC for 15 dimensions. The speedup of the proposed methods with synthetic data sets of 15 and 30 dimensions is even greater. The speedup ratio of the proposed methods is 3.3 to 3.4 with respect to conventional Halton draws, and the factor ranges from 2 to 3.2 with respect to MLHS and shuffled Halton draws. Thus, the proposed QMC methods offer promise for the development of richer and more flexible discrete choice models in large dimensional choice contexts.