Approximate Bayes factors and accounting for model uncertainty in generalised linear models

Biometrika

Volumn 83, Issue 2, 1996, Pages 251-266

  Raftery, Adrian E ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Bayesian model averaging; Laplace method; Log linear model; Logistic regression; Odds ratio; Overdispersion; Reference prior; Relative risk

Indexed keywords

EID: 0000297493     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/83.2.251     Document Type: Article

References (29)

1. AKAIKE, H. (1983). Information measures and model selection. Bull Int. Statist. Inst. 50, 277-90.
2. BARTLETT, M. S. (1957). A comment on D. V. Lindley's statistical paradox. Biometrika 44, 533-4.
3. BERGER, J. O. (1985). Statistical Decision Theory and Bayesian Inference. New York: Springer-Verlag.
4. BERGER, J. O. & SELLKE, T. (1987). Testing a point null hypothesis: the irreconcilability of P values and evidence. J. Am. Statist. Assoc. 82, 112-22.
5. BISHOP, Y. M. M., FIENBERG, S. E. & HOLLAND, P. W. (1975). Discrete Multivariate Analysis. Cambridge, MA: MIT Press.
6. CHOW, G. C. (1981). A comparison of the information and posterior probability criteria for model selection. J. Econometrics 16, 21-33.
7. EFRON, B. & HINKLEY, D. V. (1978). Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information (with Discussion). Biometrika 65, 457-87.
8. GELFAND, A. E., DEY, D. K. & CHANG, H. (1992). Model determination using predictive distributions with implementations via sampling-based methods (with Discussion). In Bayesian Statistics 4, Ed. J. M. Bernardo, J. Berger, A. P. Dawid and A. F. M. Smith, pp. 147-68. Oxford: Oxford University Press.
9. JEFFREYS, H. (1961). Theory of Probability, 3rd ed. Oxford: Oxford University Press.
10. KASS, R. E. & RAFTERY, A. E. (1995). Bayes factors. J. Am. Statist. Assoc. 90, 773-95.
11. KASS, R. E. & VAIDYANATHAN, S. (1992). Approximate Bayes factors and orthogonal parameters, with application to testing equality of two binomial proportions. J. R. Statist. Soc. B 54, 129-44.
12. KASS, R. E. & WASSERMAN, L. (1995). A reference Bayesian test for nested hypotheses with large samples. J. Am. Statist. Assoc. 90, 928-34.
13. LEAMER, E. E. (1978). Specification Searches: Ad Hoc Inference with Nonexperimental Data. New York: Wiley.
14. LINHART, H. & ZUCCHINI, W. (1986). Model Selection. New York: Wiley.
15. MADIGAN, D. & RAFTERY, A. E. (1994). Model selection and accounting for model uncertainty in graphical models using Occam's window. J. Am. Statist. Assoc. 89, 1335-46.
16. MADIGAN, D., RAFTERY, A. E., YORK, J. C., BRADSHAW, J. M. & ALMOND, R. G. (1994). Strategies for graphical model selection. In Selecting Models from Data: AI and Statistics IV, Ed. P. Cheeseman and R. W. Oldford, pp. 91-100. New York: Springer-Verlag.
17. MADIGAN, D. & YORK, J. (1995). Bayesian graphical models for discrete data. Int. Statist. Rev. 63, 215-32.
18. MCCULLAGH, P. (1983). Quasi-likelihood functions. Ann. Statist. 11, 59-67.
19. MCCULLAGH, P. & NELDER, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman and Hall.
20. PAYNE, C. D. (1986). The GLIM Manual, Release 3.77. Oxford: Numerical Algorithms Group.
21. PREGIBON, D. (1980). Goodness of link tests for generalized linear models. Appl. Statist. 29, 15-24.
22. SCHALL, R. & ZUCCHINI, W. (1990). Model selection and the estimation of odds ratios in the presence of extraneous factors. Statist. Med. 9, 1131-41.
23. SCHLESSELMAN, J. J. (1982). Case-Control Studies: Design, Conduct and Analysis. Oxford: Oxford University Press.
24. SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6, 461-4.
25. SHAPIRO, S., SLONE, D., ROSENBERG, D. W., STOLLEY, P. D. & MIETINNEN, O. S. (1979). Oral-contraceptive use in relation to myorcardial infarction. Lancet i, 743-7.
26. SWEETING, T. J. (1981). Scale parameters: A Bayesian treatment. J. R. Statist. Soc. B 43, 333-8.
27. TIERNEY, L. & KADANE, J. B. (1986). Accurate approximations for posterior moments and marginal densities. J. Am. Statist. Assoc. 81, 82-6.
28. WEST, M. (1985). Generalized linear models: Scale parameters, outlier accomodation, and prior distributions. In Bayesian Statistics 2, Ed. J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, pp. 531-58. Amsterdam: North-Holland.
29. WHITTAKER, J. (1990). Graphical Models in Applied Multivariate Statistics. New York: Wiley.