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Comparing different sampling schemes for approximating the integrals involved in the efficient design of stated choice experiments

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  • Yu, Jie
  • Goos, Peter
  • Vandebroek, Martina

Abstract

The semi-Bayesian approach for constructing efficient stated choice designs requires the evaluation of the design selection criterion value over numerous draws taken from the prior parameter distribution assumed when generating the design. The semi-Bayesian D-criterion value of a design is then calculated as the average value of the D-errors over all the draws taken. The traditional way to take draws from a distribution is to use the Pseudo-Monte Carlo approach. However, other sampling approaches are available as well. Examples are Quasi-Monte Carlo approaches using Halton sequences, Faure sequences, modified Latin hypercube sampling and extensible shifted lattice points, a Gauss-Hermite quadrature approach and a method using spherical-radial transformations. Not much is known in general about which sampling scheme is most efficient for calculating semi-Bayesian D-errors when constructing efficient stated choice designs. In this study, we compare the performance of these approaches under various scenarios and identify the most efficient sampling scheme for each situation. The method based on a spherical-radial transformation is shown to outperform the other methods when small numbers of draws are used.

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  • Yu, Jie & Goos, Peter & Vandebroek, Martina, 2010. "Comparing different sampling schemes for approximating the integrals involved in the efficient design of stated choice experiments," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1268-1289, December.
  • Handle: RePEc:eee:transb:v:44:y:2010:i:10:p:1268-1289
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    as
    1. Bhat, Chandra R., 2000. "A multi-level cross-classified model for discrete response variables," Transportation Research Part B: Methodological, Elsevier, vol. 34(7), pages 567-582, September.
    2. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    3. Sándor, Zsolt & Train, Kenneth, 2004. "Quasi-random simulation of discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 313-327, May.
    4. Tuffin Bruno, 1996. "On the use of low discrepancy sequences in Monte Carlo methods," Monte Carlo Methods and Applications, De Gruyter, vol. 2(4), pages 295-320, December.
    5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    6. Vermeulen, Bart & Goos, Peter & Vandebroek, Martina, 2008. "Models and optimal designs for conjoint choice experiments including a no-choice option," International Journal of Research in Marketing, Elsevier, vol. 25(2), pages 94-103.
    7. Rose, John M. & Bliemer, Michiel C.J. & Hensher, David A. & Collins, Andrew T., 2008. "Designing efficient stated choice experiments in the presence of reference alternatives," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 395-406, May.
    8. Bliemer, Michiel C.J. & Rose, John M. & Hensher, David A., 2009. "Efficient stated choice experiments for estimating nested logit models," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 19-35, January.
    9. Pierre L'Ecuyer & Christiane Lemieux, 2000. "Variance Reduction via Lattice Rules," Management Science, INFORMS, vol. 46(9), pages 1214-1235, September.
    10. Tan, Ken Seng & Boyle, Phelim P., 2000. "Applications of randomized low discrepancy sequences to the valuation of complex securities," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1747-1782, October.
    11. Louviere,Jordan J. & Hensher,David A. & Swait,Joffre D. With contributions by-Name:Adamowicz,Wiktor, 2000. "Stated Choice Methods," Cambridge Books, Cambridge University Press, number 9780521788304, October.
    12. Ortúzar, Juan de Dios & Iacobelli, Andrés & Valeze, Claudio, 2000. "Estimating demand for a cycle-way network," Transportation Research Part A: Policy and Practice, Elsevier, vol. 34(5), pages 353-373, June.
    13. Jie Yu & Peter Goos & Martina Vandebroek, 2009. "Efficient Conjoint Choice Designs in the Presence of Respondent Heterogeneity," Marketing Science, INFORMS, vol. 28(1), pages 122-135, 01-02.
    14. Zsolt Sándor & Michel Wedel, 2002. "Profile Construction in Experimental Choice Designs for Mixed Logit Models," Marketing Science, INFORMS, vol. 21(4), pages 455-475, February.
    15. Kessels, Roselinde & Jones, Bradley & Goos, Peter & Vandebroek, Martina, 2009. "An Efficient Algorithm for Constructing Bayesian Optimal Choice Designs," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 279-291.
    16. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800, Elsevier.
    17. Kenneth Train ., 2000. "Halton Sequences for Mixed Logit," Economics Working Papers E00-278, University of California at Berkeley.
    18. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, October.
    19. David A. Hensher, 2001. "Measurement of the Valuation of Travel Time Savings," Journal of Transport Economics and Policy, University of Bath, vol. 35(1), pages 71-98, January.
    20. Bhat, Chandra R., 2001. "Quasi-random maximum simulated likelihood estimation of the mixed multinomial logit model," Transportation Research Part B: Methodological, Elsevier, vol. 35(7), pages 677-693, August.
    21. David Hensher, 2001. "The valuation of commuter travel time savings for car drivers: evaluating alternative model specifications," Transportation, Springer, vol. 28(2), pages 101-118, May.
    22. Hess, Stephane & Train, Kenneth E. & Polak, John W., 2006. "On the use of a Modified Latin Hypercube Sampling (MLHS) method in the estimation of a Mixed Logit Model for vehicle choice," Transportation Research Part B: Methodological, Elsevier, vol. 40(2), pages 147-163, February.
    23. Bhat, Chandra R., 2003. "Simulation estimation of mixed discrete choice models using randomized and scrambled Halton sequences," Transportation Research Part B: Methodological, Elsevier, vol. 37(9), pages 837-855, November.
    24. Kessels, Roselinde & Goos, Peter & Vandebroek, Martina, 2008. "Optimal designs for conjoint experiments," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2369-2387, January.
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    2. Nicolas Depraetere & Martina Vandebroek, 2017. "A comparison of variational approximations for fast inference in mixed logit models," Computational Statistics, Springer, vol. 32(1), pages 93-125, March.
    3. Palhazi Cuervo, Daniel & Kessels, Roselinde & Goos, Peter & Sörensen, Kenneth, 2016. "An integrated algorithm for the optimal design of stated choice experiments with partial profiles," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 648-669.
    4. Prateek Bansal & Vahid Keshavarzzadeh & Angelo Guevara & Shanjun Li & Ricardo A Daziano, 2022. "Designed quadrature to approximate integrals in maximum simulated likelihood estimation [Evaluating simulation-based approaches and multivariate quadrature on sparse grids in estimating multivariat," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 301-321.
    5. Akinc, Deniz & Vandebroek, Martina, 2018. "Bayesian estimation of mixed logit models: Selecting an appropriate prior for the covariance matrix," Journal of choice modelling, Elsevier, vol. 29(C), pages 133-151.
    6. Crabbe, Marjolein & Akinc, Deniz & Vandebroek, Martina, 2014. "Fast algorithms to generate individualized designs for the mixed logit choice model," Transportation Research Part B: Methodological, Elsevier, vol. 60(C), pages 1-15.
    7. Yu, Jie & Goos, Peter & Vandebroek, Martina, 2011. "Individually adapted sequential Bayesian conjoint-choice designs in the presence of consumer heterogeneity," International Journal of Research in Marketing, Elsevier, vol. 28(4), pages 378-388.
    8. Crabbe, M. & Vandebroek, M., 2012. "Improving the efficiency of individualized designs for the mixed logit choice model by including covariates," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2059-2072.
    9. John M. Rose & Michiel C.J. Bliemer, 2014. "Stated choice experimental design theory: the who, the what and the why," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 7, pages 152-177, Edward Elgar Publishing.
    10. KESSELS, Roselinde & BRADLEY, Jones & GOOS, Peter, 2012. "A comparison of partial profile designs for discrete choice experiments with an application in software development," Working Papers 2012004, University of Antwerp, Faculty of Business and Economics.

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