Bayesian analysis of nested logit model by Markov chain Monte Carlo

Journal of Econometrics

Volumn 111, Issue 1, 2002, Pages 103-133

  Lahiri, Kajal ^a   Gao, Jian ^a  

^a STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

Discrete choice; MCMC; Mixing speed; Random utility maximization

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; COMPUTER SIMULATION; MONTE CARLO METHODS;

DISCRETE CHOICE MODELS; NESTED MULTINOMIAL LOGIC (NMNL);

MARKOV PROCESSES;

EID: 0042202792     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(02)00125-2     Document Type: Article

References (72)

1. Amemiya T. Advanced Econometrics. 1985;Harvard University Press, Cambridge, MA.
2. Amemiya, T., Kim, D., 1992. A generalization of the nested logit model. Working paper, Department of Economics, Stanford University.
3. Amemiya T., Shimono K. An application of nested logit models to the labor supply of elderly. The Economic Studies Quarterly. 40:1989;14-22.
4. Berkovec J., Rust J. A nested logit model of automobile holdings for one-vehicle households. Transportation Research. 19B:1985;275-285.
5. Besage J., Green P.J. Spatial statistics and Bayesian computation. Journal of the Royal Statistical Society B. 55:1993;25-37.
6. Börsch-Supan A. On the compatibility of nested logit models with utility maximization. Journal of Econometrics. 43:1990;373-388.
7. Brooks S.P., Roberts G.O. Assessing convergence of Markov chain Monte Carlo algorithm. Statistics and Computing. 8:1998;319-335.
8. Brownstone D., Small K.A. Efficient estimation of nested logit models. Journal of Business and Economic Statistics. 7:1989;67-74.
9. Cameron T.A. A nested logit model of energy conservation activity by owners of existing single family dwellings. Review of Economics and Statistics. 67:1985;205-211.
10. Casella G., George E.I. Explaining the Gibbs sampler. The American Statistician. 46:1992;167-174.
11. Chib S., Greenberg E. Understanding the Metropolis-Hastings algorithm. The American Statistician. 49:1995;327-335.
12. Chib S., Greenberg E. Markov chain Monte Carlo simulation methods in econometrics. Econometric Theory. 12:1996;409-431.
13. Chib, S., Greenberg, E., Chen, Y., 1998. MCMC methods for fitting and comparing multinomial response models. Working Paper John M. Olin school of Business, Washington University.
14. Cowles M.K., Carlin B.P. Markov chain Monte Carlo convergence diagnostics: a comparative reviews. Journal of the American Statistical Association. 91:1996;883-904.
15. Daly A., Zachary S. Improved multiple choice models. Hensher D., Dalvi Q. Identifying and Measuring the Determinants of Model Choice. 1979;335-357 Teakfield, London.
16. Dubin J.A. Studies in Consumer Demand - Econometric Methods Applied to Market Data. 1998;Kluwer Academic Publishers, Dordrecht.
17. Falaris E.M. A model of occupational choice. Research in Population Economics. 5:1984;289-307.
18. Falaris E.M. A nested logit migration model with selectivity. International Economic Review. 28:1987;429-443.
19. Gelfand A.E., Dey D.K. Bayesian model choice: asymptotics and exact calculation. Journal of the Royal Statistical Association B. 56:1994;501-514.
20. Gelfand, A.E., Dey, D.K., Chang, H., 1992. Model determination using predictive distributions with implementation via sampling-based methods. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics, Vol. 4. Oxford University Press, Oxford, pp. 147-167.
21. Gelfand E.A., Sahu S.K., Carlin B.P. Efficient parameterization for normal linear mixed models. Biometrika. 82:1995;479-488.
22. Gelman A., Rubin D.B. Inference from iterative simulation using multiple sequences. with discussions Statistical Science. 7:1992;457-511.
23. Gelman, A., Rubin, D.B., 1992b. A single sequence from the Gibbs sampler gives a false sense of security. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Simith, A.F.M. (Eds.), Bayesian Statistics, Vol. 4. Oxford University Press, Oxford, pp. 625-631.
24. Gelman A., Rubin D.B. Rejoinder: replication without contrition. Statistical Science. 7:1992;503-511.
25. Gelman, A., Roberts, G.O., Gilks, W.R., 1995. Efficient metropolis jumping rules. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics, Vol. 5. Oxford University Press, Oxford, pp. 599-607.
26. Geweke J. Bayesian inference in econometric models using Monte Carlo integration. Econometrica. 57:1989;1317-1339.
27. Geweke, J., 1992. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Simith, A.F.M. (Eds.), Bayesian Statistics, Vol. 4. Oxford University Press, Oxford, pp. 169-193.
28. Geweke J. Priors for macroeconomic time series and their application. Econometric Theory. 10:1994;609-632.
29. Geweke J. Using simulation methods for Bayesian econometric models: inference, development and communication. Econometric Reviews. 18:1999;1-126.
30. Geyer C.J. Practical Markov chain Monte Carlo. Statistical Science. 7:1992;473-511.
31. Geyer C.J., Thompson E.A. Annealing Markov chain Monte Carlo with applications to ancestral inference. Journal of the American Statistical Association. 90(431):1995;909-920.
32. Greene, W., 1995. LIMDEP, Version 7.0: User's Manual. Econometric Software, Bellport, NY.
33. Guimaraes P., Robert R.J., Douglas W.P. Regional incentives and industrial location in Puerto Rico. International Regional Science Review. 21:1998;119-138.
34. Hastings W.K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika. 57:1970;97-109.
35. Hausman J.A., Leonard G.K., McFadden D. A utility-consistent discrete choice and count data model: assessing recreational use losses due to national resource damage. Journal of Public Economics. 56:1995;1-30.
36. Hensher, D.A., 1986. Sequential and full information maximum likelihood estimation of a nested logit model. The Review of Economics and Statistics 68, 657-667.
37. Herriges J.A., Kling C.L. Testing the consistency of nested logit models with utility maximization. Economics Letters. 50:1996;33-39.
38. Hills S.E., Smith A.F.M. Parameterization issues in Bayesian inference. Bayesian Statistics. 4:1992;227-246.
39. Hoffman S.D., Duncan G.J. A comparison of choice-based multinomial and nested logit models. The Journal of Human Resources. 23:1988;550-602.
40. Hu J., Lahiri K., Vaughan D., Wixon B. A structural model of social security's disability determination process. Review of Economics and Statistics. 83:2001;348-361.
41. Jennison C. Discussion on the meeting on the Gibbs sampler and other Markov chain Monte Carlo methods. Journal of the Royal statistical Society B. 55:1993;54-56.
42. Kling C.L., Herriges J.A. An empirical investigation of the consistency of nested logit models with utility maximization. American Journal of Agricultural Economics. 77:1995;875-884.
43. Kling C.L., Thomson C.J. The implications of model specification for welfare estimation in nested logit models. American Journal of Agricultural Economics. 78:1996;103-114.
44. Koning R.H., Ridder G. On the compatibility of nested logit models with utility maximization - a comment. Journal of Econometrics. 63:1994;389-396.
45. Koop G., Poirier D.J. Bayesian analysis of logit models using natural conjugate priors. Journal of Econometrics. 56:1993;323-340.
46. Lahiri K., Vaughan D.R., Vixon B. Modeling SSA's sequential disability determination process using matched SIPP data. Social Security Bulletin. 58:1995;3-42.
47. Maddala G.S. Limited Dependent and Qualitative Variables in Econometrics. 1983;Cambridge University Press, Cambridge.
48. Matthews P. A slowly mixing Markov chain with implications for Gibbs sampling. Statistics and Probability Letters. 17:1993;231-236.
49. McFadden D. The revealed preference of a government bureaucracy: theory. The Bell Journal of Economics. 6:1975;401-416.
50. McFadden D. The revealed preference of a bureaucracy: empirical evidence. The Bell Journal of Economics. 7:1976;55-72.
51. McFadden, D., 1977. Quantitative methods for analyzing travel behavior of individuals: some recent developments. Cowles Foundation Discussion Paper, No. 474.
52. McFadden D. Modelling the choice of residential location. Karlgvist A., et al. Spatial Interaction Theory and Residential Location. 1978;75-96 North-Holland, Amsterdam.
53. McFadden D. Econometric models for probabilistic choice among products. Journal of Business. 53:1980;S13-S29.
54. McFadden D. Econometric models of probabilistic choice. Manski C.F., McFadden D. Structural Analysis of Discrete Data with Econometric Applications. 1981;198-272 MIT Press, Cambridge, MA.
55. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equations of state calculations by fast computing machines. Journal of Chemical Physics. 21:1953;1087-1092.
56. Meyn S.P., Tweedie R.L. Markov Chains and Stochastic Stability. 1993;Springer, London.
57. Naylor J.C., Smith A.F.M. Applications of a method for the efficient computation of posterior distributions. Annals of Statistics. 31:1982;214-225.
58. Newbold K.B. Primary, return and onward migration in the U.S. and Canada: is there a difference? Papers in Regional Science. 76:1997;175-198.
59. Nummelin E. General Irreducible Markov Chains and Nonnegative Operators. 1984;Cambridge University Press, Cambridge.
60. Poirier D.J. A Bayesian analysis of nested logit models. Journal of Econometrics. 75:1996;163-181.
61. Raftery, A.E., Lewis, S.M., 1992. How many iterations in the Gibbs sampler? In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Simith, A.F.M. (Eds.), Bayesian Statistics, Vol. 4. Oxford University Press, Oxford, pp. 763-773.
62. Ripley B.D. Stochastic Simulation. 1987;Wiley, New York.
63. Roberts G.O., Smith A.F.M. Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms. Stochastic Processes and their Applications. 49:1994;207-216.
64. Sims C.A. Comment on "To criticize the Critics" by Peter C.B. Phillips. Journal of Applied Econometrics. 6:1991;423-434.
65. Smith A.F.M., Roberts G.O. Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society B. 55:1993;3-23.
66. Tierney L. Markov chain for exploring posterior distributions. The Annals of Statistics. 4:1994;1701-1762.
67. Tierney L., Kadane J.B. Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association. 81:1986;82-86.
68. Train K.E. A structured logit model of auto ownership and choice. Review of Economic Studies. 47:1980;357-369.
69. Train K.E., Ben-Akiva M., Atherton T. Consumption patterns and self-selecting tariffs. Review of Economics and Statistics. 71:1989;62-73.
70. Weiler W.C. A flexible approach to modeling enrollment choice behavior. Economics of Education Review. 8:1989;277-283.
71. Zellner A. An Introduction to Bayesian Inference in Econometrics. 1971;Wiley, New York, NY. (reprinted in 1987, Krieger Publishing Co., Malabar, FL).
72. Zellner A., Min C. Gibbs sampler convergence criteria. Journal of The American Statistical Association. 90:1995;921-927.