The value of informative priors in Bayesian inference with sparse data

Journal of Marketing Research

Volumn 46, Issue 6, 2009, Pages 832-845

  Lenk, Peter ^a   Orme, Bryan ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b Sawtooth Software

Author keywords

Choice based conjoint; Effects coding; Hierarchical bayes; Priors; Variance estimation; Willingness to pay

Indexed keywords

EID: 73649144526     PISSN: 00222437     EISSN: None     Source Type: Journal    
DOI: 10.1509/jmkr.46.6.832     Document Type: Article

References (63)

1. Allenby, Greg M., Neeraj Arora, and Jim L. Ginter (1995), "Incorporating Prior Knowledge into the Analysis of Conjoint Studies, "Journal of Marketing Research, 32 (May), 152-62.
2. Allenby, Greg M., Neeraj Arora, and Jim L. Ginter (1998), "On the Heterogeneity of Demand, "Journal of Marketing Research, 35 (August), 384-89.
3. Allenby, Greg M. and Jim L. Ginter (1995), "Using Extremes to Design Products and Segment Markets, "Journal of Marketing Research, 32 (November), 392-403.
4. Allenby, Greg M. and Peter Lenk (1994), "Modeling Household Purchase Behavior with Logistic Normal Regression, "Journal of the American Statistical Association, 83 (428), 1218-31.
5. Antoniak, Charles E. (1974), "Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems, "Annals of Statistics, 2 (6), 1152-74.
6. Arora, Neeraj and Joel Huber (2001), "Improving Parameter Estimates and Model Prediction by Aggregate Customization in Choice Experiments, "Journal of Consumer Research, 28 (2), 273-83.
7. Bennet, Jeff and Russell Blarney (2001), The Choice Modelling Approach to Environmental Valuation. Cheltenham, UK: Edward Elgar.
8. Berger, James O, (1985), Statistical Decision Theory and Bayesian Analysis, 2d ed. New York: Springer-Verlag.
9. Berger, James O, and Jose M. Bernardo (1989), "Estimating a Product of Means: Bayesian Analysis with Reference Priors, "Journal of the American Statistical Association, 84 (405), 200-207.
10. Berger, James O, and Jose M. Bernardo (1992), "Ordered Group Reference Priors with Application to the Multinomial Problem, "Biometrika, 79 (1), 25-37.
11. Berger, James O, and Dongchu Sun (2008), "Objective Priors for the Bivariate Normal Model, "Annals of Statistics, 36 (2), 963-82.
12. Bernardo, Jose M. (1979), "Reference Posterior Distributions for Bayesian Inference, "Journal of the Royal Statistical Society: Series B, 41 (2), 113-47.
13. Bernardo, Jose M. (2007), "Objective Bayesian Point and Region Estimation in Location-Scale Models, "SORT-Statistics and Operations Research Transactions, 31 (1), 3-44.
14. Bernardo, Jose M. and Jose" M. Ram6n (1998), "An Introduction to Bayesian Reference Analysis: Inference on the Ratio of Multinomial Parameters, "Journal of the Royal Statistical Society: Series D-The Statistician, 47 (1), 101-135.
15. Bernardo, Jose M. and Adrian RM. Smith (1994), Bayesian Theory. West Sussex, UK: John Wiley and Sons.
16. Blackwell, David and James B. MacQueen (1973), "Ferguson Distributions via Polya Urn Schemes, "Annals of Statistics, 1 (2), 353-55.
17. Boatwright, Peter, Robert E. McCulloch, and Peter E. Rossi (1999), "Account-Level Modeling for Trade Promotion: An Application of a Constrained Parameter Hierarchical Model, "Journal of the American Statistical Association, 94 (448), 1063-1073.
18. Carlsson, Fredrik and Peter Martinsson (2001), "Do Hypothetical and Actual Marginal Willingness to Pay Differ in Choice Experiments?" Journal of Environmental Economics Management, 41 (2), 179-92.
19. Chung, Jaihak and Vithala R. Rao (2003), "A General Choice Model for Bundles with Multiple-Category Products: Applications to Market Segmentation and Optimal Pricing for Bundles, "Journal of Marketing Research, 40 (May), 115-30.
20. Craven, Peter and Grace Wahba (1979), "Smoothing Noisy Data with Spline Functions: Estimating the Correct Degree of Smoothing by the Method of Generalized Cross-Validation, "Numerische Mathematik, 31 (4), 377-403.
21. Datta, Gauri Sankar and Malay Ghosh (1995), "Some Remarks on Noninformative Priors, "Journal of the American Statistical Association, 90 (432), 1357-63.
22. De Finetti, Bruno (1937), "La Prévision: Ses Lois Logiques, Ses Sources Subjectives," Annales de i'lnstitut Henri Poincaré, 1 (1), 1-68 [translated as "Foresight: Its Logical Laws, Its Subjective Sources", in Studies in Subjective Probability, H. E. Kyburg Jr. and H. E. Smokier, eds. Huntington, NY: Robert E. Krieger Publishing Company, 1980].
23. DeGroot, Morris H. (1970), Optimal Statistical Decisions. New York: McGraw-Hill.
24. Diciccio, Thomas, Peter Hall, and Joseph P. Romano (1991), "Empirical Likelihood Is Bartlett-Correctable, "Annals of Statistics, 19 (2), 1053-1061.
25. Doob, Joseph L. (1953), Stochastic Processes. New York: John Wiley and Sons.
26. Efron, Bradley (1987), "Better Bootstrap Confidence Intervals, "Journal of the American Statistical Association, 82 (397), 171-95.
27. Evgeniou, Theodoras, Pontil Massimiliano, and Poggio Tomaso (2000), "Regularization Networks and Support Vector Machines, "Advances in Computational Mathematics, 13 (1), 1-50.
28. Fader, Peter S., James M. Lattin, and John D. Little (1992), "Estimating Nonlinear Parameters in the Multinomial Logit Model, "Marketing Science, 11 (4), 372-85.
29. Ferguson, Thomas S. (1967), Mathematical Statistics: A Decision Theoretic Approach. New York: Academic Press.
30. Ferguson, Thomas S. (1973), "A Bayesian Analysis of Some Nonparametric Problems, "Annals of Statistics, 1 (2), 209-230.
31. Geisser, Seymour (1975), "Predictive Sample Reuse Method with Applications, "Journal of the American Statistical Association, 70 (350), 320-28.
32. Gelfand, Allen E., Adrian F. M. Smith, and Tai-Ming Lee (1992), "Bayesian Analysis of Constrained Parameter and Truncated Data Problems Using Gibbs Sampling, "Journal of the American Statistical Association, 87 (418), 523-32.
33. Gilbride, Timothy J. and Greg M. Allenby (2004), "A Choice Model with Conjunctive, Disjunctive, and Compensatory Screening Rules, "Marketing Science, 23 (3), 391-406.
34. Good, I. J. and R. A. Gaskins (1980), "Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data, "Journal of the American Statistical Association, 75 (369), 42-56.
35. Helland, Inge S. (2004), "Statistical Inference Under Symmetry, "International Statistical Review, 72 (3), 409-422.
36. Huber, Joel, Dick R. Wittink, John A. Fielder, and Richard Miller (1993), "The Effectiveness of Alternative Preference Elicitation Procedures in Predicting Choice, "Journal of Marketing Research, 30 (February), 104-114.
37. Jeffreys, Harold (1946), "An Invariant Form for the Prior Probability in Estimation Problems, "Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, 186 (1007), 453-61.
38. Jen, Lichung, Chien-Heng Chou, and Greg M. Allenby (2009), "The Importance of Modeling Temporal Dependence of Timing and Quantity in Direct Marketing, "Journal of Marketing Research, 46 (August), 482-93.
39. Kass, Robert E. and Larry Wasserman (1996), "The Selection of Prior Distributions by Formal Rules, "Journal of the American Statistical Association, 91 (435), 1343-70.
40. Lenk, Peter (1992), "Hierarchical Bayes Forecasts of Multinomial Dirichlet Data Applied to Coupon Redemptions, "Journal of Forecasting, 11 (7), 603-619.
41. Lenk, Peter (1993), "A Bayesian Nonparametric Density Estimator, " Journal of Nonparametric Statistics, 3 (1), 53-69.
42. Lenk, Peter (1999), "Bayesian Inference of Semiparametric Regression, "Journal of the Royal Statistical Society: Series B, 61 (4), 863-79.
43. Lenk, Peter (2003), "Bayesian Semiparametric Density Estimation and Model Verification Using a Logistic-Gaussian Process, "Journal of Computational and Graphical Statistics, 12 (3), 548-65.
44. Lenk, Peter and Wayne DeSarbo (2000), "Bayesian Inference for Finite Mixtures of Generalized Linear Models with Random Effects, " Psychometrika, 65 (1), 93-119.
45. Lenk, Peter and Wayne DeSarbo, Paul Green, and Martin Young (1996), "Hierarchical Bayes Conjoint Analysis: Recovery of Partworth Heterogeneity from Reduced Experimental Designs, "Marketing Science, 15 (2), 173-91.
46. Lenk, Peter and Ambar Rao (1990), "New Models from Old: Forecasting Product Adoption by Hierarchical Bayes Procedures, "Marketing Science, 9 (1), 42-53.
47. Lloyd, Andrew J. (2003), "Threats to the Estimation of Benefit: Are Preference Elicitation Methods Accurate?" Health Economics, 12 (5), 393-402.
48. Louviere, Jordan, David Hensher, and Joffre Swait (2000), Stated Choice Methods: Applications in Marketing, Transportation and Environmental Evaluation. Cambridge, UK: Cambridge University Press.
49. Mackenzie, John (1993), "Comparison of Contingent Preference Models, "American Journal of Agricultural Economics, 75 (3), 593-603.
50. Marshall, Pablo and Eric T. Bradlow (2002), "A Unified Approach to Conjoint Analysis Models, "Journal of the American Statistical Association, 97 (459), 674-82.
51. Meijer, Eric and Jan Rouwendal (2006), "Measuring Welfare Effects in Models with Random Coefficients, "Journal of Applied Econometrics, 21 (2), 227-44.
52. Ripley, Brian D. (1987), Stochastic Simulation. New York: John Wiley and Sons.
53. Rossi, Peter E., Robert E. McCulloch, and Greg M. Allenby (1996), "The Value of Purchase History Data in Target Marketing, "Marketing Science, 15 (4), 321-40.
54. Ryan, Mandy and Jenny Hughes (1997), "Using Conjoint Analysis to Assess Women's Preferences for Miscarriage Management, "Health Economics, 6 (3), 261-73.
55. Seetharaman, P. B., Andrew Ainslie, and Pradeep Chintagunta (1999), "Investigating Household State Dependence Effects Across Categories, "Journal of Marketing Research, 36 (November), 488-500.
56. Singh, Vishal P., Karsten T. Hansen, and Sachin Gupta (2005), "Modeling Preferences for Common Attributes in Multicategory Brand Choice, "Journal of Marketing Research, 42 (May), 195-209.
57. Sonnier, Garrett, Andrew Ainslie, and Thomas Otter (2007), "Heterogeneity Distributions of Willingness-to-Pay in Choice Models, "Quantitative Marketing and Economics, 5 (3), 313-31.
58. Stone, M. (1974), "Cross-Validatory Choice and Assessment of Statistical Prediction, "Journal of the Royal Statistical Society: Series B, 36 (2), 111-47.
59. Stone, M. and Philip A. Dawid (1973), "Un-Bayesian Implications of Improper Bayes Inference in Routine Statistical Problems, " Biometrika, 59 (2), 369-75.
60. Train, Kenneth E. and Terry Atherton (1995), "Rebates, Loans, and Customers Choice of Appliance Efficiency Level: Combining Started and Revealed-Preference Data, "Energy Journal, 16 (1), 55-69.
61. Viscusi, W. Kipp, Wesley A. Magat, and Joel Huber (1991), "Pricing Environmental Health Risks: Survey Assessments of Risk-Risk and Risk-Dollar Tradeoffs for Chronic Bronchitis, "Journal of Environmental Economics and Management, 21 (1), 32-51.
62. Wahba, Grace (1983), "Bayesian 'Confidence Intervals' for the Cross-Validated Smoothing Spline, "Journal of the Royal Statistical Society: Series B, 45 (1), 133-50.
63. Zellner, Arnold (1971), An Introduction to Bayesian Inference in Econometrics. New York: John Wiley and Sons.