Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model

Ben-Akiva, M., Bolduc, D., 1996. Multinomial probit with a logit kernel and a general parametric specification of the covariance structure, working paper, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA and Département d'économique, Université Laval, Sainte-Foy, Qc, Canada Bhat, 1998, Accommodating flexible substitution patterns in multi-dimensional choice modeling: formulation and application to travel mode and departure time choice, Transportation Research, 32B, 425 Bhat, 1998, Accommodating variations in responsiveness to level-of-service measures in travel mode choice modeling, Transportation Research, 32A, 495 Bhat, C.R., 1999a. A multi-level cross-classified model for discrete response variables. Transportation Research, accepted Bhat, C.R., 1999b. Incorporating observed and unobserved heterogeneity in urban work travel mode choice modeling.Transportation Science (forthcoming) Bratley, 1988, Implementing Sobol's quasi-random sequence generator, ACM Transactions on Mathematical Software, 14, 88, 10.1145/42288.214372 Bratley, 1992, Implementation and tests of low-discrepancy sequences, ACM Transactions on Modeling and Computer Simulation, 2, 195, 10.1145/146382.146385 Brownstone, 1999, Forecasting new product penetration with flexible substitution patterns, Journal of Econometrics, 89, 109, 10.1016/S0304-4076(98)00057-8 Cools, R., 1992. A survey of methods for constructing cubature formulae. In: Espelid, T.O., Genz, A.C. (Eds.), Numerical Integration: Recent Development, Software and Application. Kluwer Academic Publishers, Dordrecht, pp. 1–24 Cools, 1993, Monomial cubature rules since Stroud: a compilation, Journal of Computational and Applied Mathematics, 43, 309, 10.1016/0377-0427(93)90027-9 Fang, 1994 Halton, 1970, A retrospective and prospective survey of the Monte Carlo method, SIAM Review, 12, 1, 10.1137/1012001 Hajivassiliou, 1996, Simulation of multivariate normal rectangle probabilities and their derivatives: theoretical and computational results, Journal of Econometrics, 72, 85, 10.1016/0304-4076(94)01716-6 Hajivassiliou, V.A., Ruud, P.A., 1994. Classical estimation methods for LDV models using simulation. In: Engle, R.F., McFadden, D.L. (Eds.), Handbook of Econometrics 4, 2383–2441 Kocis, 1997, Computational investigation of low-discrepancy sequences, ACM Transactions on Mathematical Software, 23, 266, 10.1145/264029.264064 Krommer, 1994 Lee, 1992, On the efficiency of methods of simulated moments and maximum simulated likelihood estimation of discrete response models, Econometric Theory, 8, 518, 10.1017/S0266466600013207 Metropolis, 1949, The Monte Carlo method, Journal of the American Statistical Association, 44, 335, 10.2307/2280232 Morokoff, 1995, Quasi-Monte Carlo integration, Journal of Computational Physics, 122, 218, 10.1006/jcph.1995.1209 Mullen, G.L., Mahalanabis, A., Niederreiter, H., 1995. Tables of (T,M,S)-net and (T,S)-sequence parameters. In: Niederreiter, H., Shiue, J.-S. (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Springer, New York, pp. 58–86 Niederreiter, H., 1995. New developments in uniform psuedo-random number and vector generation. In: Niederreiter, H., Shiue, J.-S. (Eds.), Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Springer, New York, pp. 94–112 Owen, 1997, Scrambled net variance for integrals of smooth functions, The Annals of Statistics, 25, 1541, 10.1214/aos/1031594731 Owen, 1998, Latin supercube sampling for very high dimensional simulations, ACM Transactions on Modeling and Computer Simulation, 8, 71, 10.1145/272991.273010 Papageorgiou, 1997, Faster evaluation of multidimensional integrals, Risk, 9, 63 Paskov, S.H., 1997. New methodology for valuing derivatives. In: Pliska, S., Dempster, M. (Eds.), Mathematics of Derivative Securities. Isaac Newton Institute, Cambridge University Press, Cambridge Press, 1992 Revelt, D., Train, K., 1998. Mixed logit with repeated choices: households' choices of appliance efficiency level. Review of Economics and Statistics (forthcoming) Sloan, I.H., Joe, S., 1994. Lattice Methods for Multiple Integration. Clarendon Press, Oxford Sloan, 1998, When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?, Journal of Complexity, 14, 1, 10.1006/jcom.1997.0463 Spanier, 1994, Quasi-random methods for estimating integrals using relatively small samples, SIAM Review, 36, 18, 10.1137/1036002 Stroud, 1971 Train, 1998, Recreation demand models with taste differences over people, Land Economics, 74, 230, 10.2307/3147053 Wozniakowski, 1991, Average case complexity of multivariate integration, Bulletin of the American Mathematical Society, 24, 185, 10.1090/S0273-0979-1991-15985-9