A method for simultaneous variable selection and outlier identification in linear regression

Computational Statistics and Data Analysis

Volumn 22, Issue 3, 1996, Pages 251-270

  Hoeting, Jennifer ^a   Raftery, Adrian E ^b   Madigan, David ^b  

^a Department of Environmental and Radiological Health Sciences   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Bayesian model averaging; Markov chain Monte Carlo model composition; Masking; Model uncertainty; Posterior model probability

Indexed keywords

APPROXIMATION THEORY; COMPUTER SOFTWARE; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; PERFORMANCE; PROBABILITY; REGRESSION ANALYSIS;

BAYESIAN MODEL; LINEAR REGRESSION; MASKING; MODEL UNCERTAINTY; OUTLIER IDENTIFICATION; POSTERIOR MODEL PROBABILITIES; SIMULTANEOUS VARIABLE SELECTION;

COMPUTATIONAL METHODS;

EID: 0030194062     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-9473(95)00053-4     Document Type: Article

References (50)

1. Adams, J.L., A computer experiment to evaluate regression strategies, Proc. American Statistical Association Section on Statistical Computing (1991) 55-62.
2. Atkinson, A.C., Plots, transformations, and regression (Clarendon Press, Oxford, 1985).
3. Atkinson, A.C., Masking unmasked, Biometrika, 73 (1986a) 533-541.
4. Atkinson, A.C., Comments on "Influential Observations, High Leverage Points, and Outliers in Linear Regression," Statist. Sci., 1 (1986b) 397-402.
5. Atkinson, A.C., Transformations unmasked, Technometrics, 30 (1988) 311-318.
6. Barnett V. and T. Lewis, Outliers in statistical data, 3rd ed. (Wiley, New York, 1994).
7. Besag, J.E. and D.M. Higdon, Bayesian inference for agricultural field experiments, Bull. Int. Statist. Inst., 55 (1993) 121-136.
8. Blettner, M. and W. Sauerbrei, Influence of model-building strategies on the results of a case-control study, Statist. Med., 12 (1993) 1325-1388.
9. Bloomfield, P. and W.L. Steiger, Least absolute deviations: theory, applications, and algorithms, (Birkhäuser, Boston, 1983).
10. Box, G.E.P. and G.C. Tiao, A Bayesian approach to some outlier problems, Biometrika, 55 (1968) 119-129.
11. Brownlee, K.A., Statistical theory and methodology in science and engineering, 2nd edn. (Wiley, New York, 1965).
12. Chambers, R.L. and C.R. Heathcote, On the estimation of slope and identification of outliers in linear regression, Biometrika, 68 (1981) 21-33.
13. Chatterjee, S. and A.S. Hadi, Influential observations, high leverage points, and outliers in linear regression, Statist. Sci., 1 (1986) 379-416.
14. Clyde, M., H. DeSimone and G. Parmigiani, Prediction via orthogonalized model mixing (Institute of Statistics and Decision Sciences, Duke University, 1994)
15. Daniel, C. and F.S. Wood, Fitting equations to data (Wiley, New York, 1980).
16. Draper, D., Assessment and propagation of model uncertainty (with discussion), J. Roy. Statist. Soc. B, 57 (3995) 45-97.
17. Garthwaite, P.H. and J.M. Dickey, Elicitation of prior distributions for variable-selection problems in regression, Ann. Statist., 20 (1992) 1697-1719.
18. Geisser, S., Discussion on Sampling and Bayes' inference in scientific modeling and robustness (by G.E.P. Box), J. Roy. Statist. Soc. A, 143 (1980) 416-417.
19. George, E.I. and R.E. McCulloch, Variable selection via Gibbs sampling, J. Amer. Statist. Assoc., 88 (1993) 881-890.
20. George, E.I. and R.E. McCulloch, Fast Bayes variable selection, CSS Technical Report 94-01 (University of Texas at Austin, 1994).
21. Good, I.J., Rational decisions, J. Roy. Statist. Soc. B, 14 (1952) 107-114.
22. Guttman, I., R. Dutter, and P.R. Freeman, Care and handling of univariate outliers in the general linear model to detect spuriousity, Technometrics, 20 (1978) 187-193.
23. Hadi, A.S., A stepwise procedure for identifying multiple outliers in linear regression, Proc. American Statistical Association Section on Statistical Computing (1990) 137-142.
24. Hadi, A.S., A new measure of overall potential influence in linear regression, Comput. Statist. Data Anal., 14 (1992) 1-27.
25. Hawkins, D.M., Identification of outliers (Chapman and Hall, London, 1980).
26. Heiberger, R. and R.A. Becker, Design of an S function for robust regression using iteratively reweighted least squares, AT&T Statistics Research Report (1991).
27. Hettmansperger, T.P. and S.J. Sheather, A cautionary note on the method of least median squares, Amer. Statist., 46 (1992) 79-83.
28. Hoaglin, D.C., F. Mosteller and J.W. Tukey (Eds.) Understanding robust and exploratory data analysis (Wiley, New York, 1983).
29. Hoeting, J.A., Accounting for model uncertainty in linear regression, Ph.D. dissertation (University of Washington, 1994) (see http://www.stat.colostate.edu).
30. Hoeting, J., A.E. Raftery, D. Madigan, Simultaneous Variable and Transformation Selection in Linear Regression, Technical Report 9506 (Department of Statistics, Colorado State University, 1995).
31. Kadane, J.B., J.M. Dickey, R.L. Winkler, W.S. Smith and S.C. Peters, Interactive elicitation of opinion for a normal linear model, J. Amer. Statist. Assoc., 75 (1980) 845-854.
32. Kass, R.E. and A.E. Raftery, Bayes factors, J. Amer. Statist. Assoc., 90 (1995) 773-195.
33. Kianifard, F. and W.H. Swallow, Using recursive residuals, calculated on adaptively-ordered observations, to identify outliers in linear regression, Biometrics, 45 (1989) 571-585.
34. Lange, K.L., R.J.A. Little and J.M.G. Taylor, Robust statistical modeling using the t-distribution, J. Amer. Statist. Assoc., 84 (1989) 881-896.
35. Learner, E., Specification searches: ad hoc inference with nonexperimental data (Wiley, New York, 1978).
36. Madigan, D. and A.E. Raftery, Model selection and accounting for model uncertainty in graphical models using Occam's Window, J. Amer. Statist. Assoc., 89 (1994) 1535-1546.
37. Madigan, D. and J. York, Bayesian graphical models for discrete data, Internat. Statist. Rev., 63 (1995) 215-232.
38. Marasinghe, M.G., A multistage procedure for detecting several outliers in linear regression, Technometrics, 27 (1985) 395-399.
39. Neter, J., W. Wasserman and M. Kutner, Applied linear statistical models, (Irwin, Homewood, IL, 1990).
40. Pettit, L.I., Bayes factors for outlier models using the device of imaginary observations, J. Amer. Statist. Assoc., 87 (1992) 541-545.
41. Raftery, A.E., Approximate Bayes factors and accounting for model uncertainty in generalized linear models, Technical Report 255 (Department of Statistics, University of Washington, 1993). (See http://www.stat.washington.edu/tech.reports)
42. Raftery, A.E., D. Madigan and J. Hoeting, Bayesian model averaging for linear regression models, Technical Report 9412, (Department of Statistics, Colorado State University, 1994) (See http://www.stat.colostate.edu).
43. Regal, R. and E.B. Hook, The effects of model selection on confidence intervals for the size of a closed population, Statist. Med., 10 (1991) 717-721.
44. Rousseeuw, P.J., Least median of squares regression, J. Amer. Statist. Assoc., 79 (1984) 871-888.
45. Rousseeuw, P.J. and A.M. Leroy, Robust regression and outlier detection (Wiley, New York, 1987).
46. Smith, A.F.M. and G.O. Roberts, Bayesian computation via Gibbs sampler and related Markov chain Monte Carlo methods, J. Roy. Statist. Soc. B, 55 (1993) 3-24.
47. Taplin, R. and A.E. Raftery, Analysis of agricultural field trials in the presence of outliers and fertility jumps, Biometrics, 50 (1994) 764-781.
48. Verdinelli, I. and L. Wasserman, Bayesian analysis of outlier problems using the Gibbs sampler, Statist. Comput., 1 (1991) 105-117.
49. Weisberg, S., Applied linear regression (Wiley, New York, 1985).
50. West, M., Outlier models and prior distributions in Bayesian linear regression, J. Roy. Statist. Soc. B, 46 (1984) 431-439.