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Transportation Letters
The International Journal of Transportation Research
Volume 14, 2022 - Issue 10
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Research Article

Bayesian estimation of discrete choice models: a comparative analysis using effective sample size

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References

  • Albert, J. H., and S. Chib. 1993. “Bayesian Analysis of Binary and Polychotomous Response Data.” Source: Journal of the American Statistical Association 88.
  • Allenby, G. M., and P. J. Lenk. 1994. “Modeling Household Purchase Behavior with Logistic Normal Regression.” Journal of the American Statistical Association 89 (428): 1218–1231. doi:10.1080/01621459.1994.10476863.
  • Bansal, P., R. Krueger, M. Bierlaire, R. A. Daziano, and T. H. Rashidi. 2020. “Bayesian Estimation of Mixed Multinomial Logit Models: Advances and Simulation-Based Evaluations.” Transportation Research Part B 131: 124–142. doi:10.1016/j.trb.2019.12.001.
  • Ben-Akiva, M., D. McFadden, and K. Train. 2019. “Foundations of Stated Preference Elicitation: Consumer Behavior and Choice-Based Conjoint Analysis.” Foundations and Trends in Econometrics 10 (1–2): 1–144. doi:10.1561/0800000036. Now Publishers Inc.
  • Blei, D. M., A. Kucukelbir, and J. D. McAuliffe. 2016. “Variational Inference: A Review for Statisticians,” January. doi: 10.1080/01621459.2017.1285773.
  • Carpenter, B., M. D. Andrew Gelman, D. L. Hoffman, B. Goodrich, M. A. Michael Betancourt, J. G. Brubaker, L. Peter, and A. Riddell. 2017. “Stan: A Probabilistic Programming Language.” Journal of Statistical Software 76 (1). doi:10.18637/jss.v076.i01.
  • Dillon, J. V., I. Langmore, D. Tran, E. Brevdo, S. Vasudevan, D. Moore, B. Patton, A. Alemi, M. Hoffman, and R. A. Saurous. 2017. “TensorFlow Distributions.” http://arxiv.org/abs/1711.10604
  • Ding, C., Y. Wang, T. Tang, S. Mishra, and C. Liu. 2016. “Joint Analysis of the Spatial Impacts of Built Environment on Car Ownership and Travel Mode Choice.” Transportation Research Part D: Transport and Environment, August. doi:10.1016/j.trd.2016.08.004.
  • Duane, S. A., D. Kennedy, B. J. Pendleton, and D. Roweth. 1987. “Hybrid Monte Carlo.” Physics Letters B 195 (2): 216–222. doi:10.1016/0370-2693(87)91197-X.
  • Dumont, J., J. Keller, and C. Carpenter. 2019. “RSGHB.”
  • Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2020. Bayesian Data Analysis.3rd ed. Boca Raton, FL, FL: CRC Press. doi:10.1109/5992.931908.
  • Google Cloud. 2020a. “CPU Platforms.” https://cloud.google.com/compute/docs/cpu-platforms
  • Google Cloud. 2020b. “Machine Types.” https://cloud.google.com/compute/docs/machine-types
  • Griewank, A., and A. Walther. 2008. Evaluating Derivatives : Principles and Techniques of Algorithmic Differentiation. Frontiers in Applied Mathematics. 2nd ed. Society for Industrial and Applied Mathematic. doi:10.1137/1.9780898717761.
  • Guhl, D., and S. Gabel. 2016. “Discrete Choice Models in R.”
  • Guo, J., J. Gabry, B. Goodrich, and S. Weber. 2021. “Compute Summaries of MCMC Draws and Monitor Convergence.” https://mc-stan.org/rstan/reference/monitor.html
  • Hess, S., and D. Palma. 2019. “Apollo: A Flexible, Powerful and Customisable Freeware Package for Choice Model Estimation and Application.” Journal of Choice Modelling 32: 100170. doi:10.1016/j.jocm.2019.100170.
  • Hoffman, M. D., and A. Gelman. 2014. “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” Journal of Machine Learning Research 15: 1593–1623. http://mcmc-jags.sourceforge.net
  • Krueger, R., P. Bansal, and P. Buddhavarapu. 2020. “A New Spatial Count Data Model with Bayesian Additive Regression Trees for Accident Hot Spot Identification.” Accident Analysis and Prevention 144 (September): 105623. doi:10.1016/j.aap.2020.105623.
  • Kucukelbir, A., D. Tran, R. Ranganath, A. Gelman, and D. M. Blei. 2016. “Automatic Differentiation Variational Inference.” March. http://arxiv.org/abs/1603.00788
  • Lunn, D., C. Jackson, N. Best, A. Thomas, and D. Spiegelhalter. 2012. The Bugs Book: A Practical Introduction to Bayesian Analysis. The Bugs Book: A Practical Introduction to Bayesian Analysis. doi:10.1080/02664763.2013.816061.
  • Mcculloch, R. E., N. G. Polson, and P. E. Rossi. 1997. A Bayesian Analysis of the Multinomial Probit Model with Fully Identi—ed Parameters.
  • Molloy, J., F. Becker, B. Schmid, and K. W. Axhausen. 2021. “Mixl: An Open-Source R Package for Estimating Complex Choice Models on Large Datasets.” Journal of Choice Modelling 39 (June): 100284. doi:10.1016/J.JOCM.2021.100284.
  • Ranganath, R., J. Altosaar, D. Tran, and D. M. Blei. 2016. “Operator Variational Inference.” October. http://arxiv.org/abs/1610.09033
  • Rossi, P. 2019. “Bayesm: Bayesian Inference for Marketing/Micro-Econometrics.” October 15. https://cran.r-project.org/web/packages/bayesm/index.html
  • Salvatier, J., T. V. Wiecki, and C. Fonnesbeck. 2016. “Probabilistic Programming in Python Using PyMC3.” PeerJ Computer Science 2 (4): e55. doi:10.7717/peerj-cs.55.
  • Savage, J. 2018. “Hierarchical_bayes_full_covmat.” https://gist.github.com/khakieconomics/0333a54dff4fabf6204080ca5bf92cb6
  • Stan Development Team. 2020a. “Brief Guide to Stan’s Warnings.” https://mc-stan.org/misc/warnings.html#bulk-ess
  • Stan Development Team. 2020b. “Efficiency Tuning.” Stan User’s Guide. https://mc-stan.org/docs/2_23/stan-users-guide/optimization-chapter.html
  • Stan Development Team. 2020c. “RStan : The R Interface to Stan.” http://mc-stan.org/rstan/
  • TensorFlow developers. 2020. “XLA Architecture. https://www.tensorflow.org/xla/architecture
  • Tokuda, T., B. Goodrich, I. Mechelen, A. Gelman, and F. Tuerlinckx. 2019. “Visualizing Distributions of Covariance Matrices.” http://www.stat.columbia.edu/~gelman/research/unpublished/Visualization.pdf
  • Train, K. 2006. “Kenneth Train’s Software.” https://eml.berkeley.edu/~train/software.html
  • Train, K. E. 2009. “Bayesian Procedures.” In Discrete Choice Methods with Simulation. 2nd ed.
  • Vehtari, A., A. Gelman, D. Simpson, B. Carpenter, and P. C. Bürkner. 2019. “Rank-Normalization, Folding, and Localization: An Improved Rb for Assessing Convergence of MCMC.” ArXiv. doi:10.1214/20-ba1221.
  • Vehtari, A., A. Gelman, T. Sivula, P. Jylänki, D. Tran, S. Sahai, J. P. Paul Blomstedt, D. S. Cunningham, and C. P. Robert. 2020. “Expectation Propagation as A Way of Life: A Framework for Bayesian Inference on Partitioned Data.” Journal of Machine Learning Research 21 (December). http://arxiv.org/abs/1412.4869
  • Wang, K. 2020. Investigating Willingness to Pay for Autonomous Vehicles in Greater Toronto Area. University of Toronto.
  • Wang, Z., W. Yunan, and H. Chu. 2018. On Equivalence of the LKJ Distribution and the Restricted Wishart Distribution.
  • Yao, Y., A. Vehtari, D. Simpson, and A. Gelman. 2018. “Yes, but Did It Work?: Evaluating Variational Inference.” 35th International Conference on Machine Learning, ICML 2018 12: 8887–8895.

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