统计Bayesian Model Selection in Social Research

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Bayesian Model Selection in Social Research

文献名称	Bayesian Model Selection in Social Research
文献作者	Adrian E. Raftery
作者所在单位	University of Washington
文献分类	已发表文献
学科一级分类	统计
学科二级分类	统计学
文献摘要	It is argued that P-values and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a single model, they ignore model uncertainty and so underestimate the uncertainty about quantities of interest. The Bayesian approach to hypothesis testing, model selection, and accounting for model uncertainty is presented. Implementing this is straightforward through the use of the simple and accurate BIC approximation, and it can be done using the output from standard software. Specific results are presented for most of the types of model commonly used in sociology. It is shown that this approach overcomes the difficulties with P-values and standard model selection procedures based on them. It also allows easy comparison of nonnested models, and permits the quantification of the evidence for a null hypothesis of interest, such as a convergence theory or a hypothesis about societal norms.
参考文献	Becker, Gary S. 1968. "Crime and Punishment: An Economic Approach." Journal of Political Economy 76:526-36. Berger, James 0., and Mohan Delampady. 1987. "Testing Precise Hypotheses (with Discussion)." Statistical Science 3:317-52. Berger, James 0., and Thomas Sellke. 1987. "Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence (with Discussion)." Journal of the American Statistical Association 82:112-22. Bernardo, Jose M., and Adrian F. M. Smith. 1994. Bayesian Theory. New York: Wiley. Bishop, Yvonne M. M., Steven E. Fienberg and Paul W. Holland. 1975. Discrete Multivariate Analysis. Cambridge: MIT Press. Bollen, Kenneth A. 1989. Structural Equations with Latent Variables. New York: Wiley. Brier, S. S., and Steven E. Fienberg. 1980. "Recent Econometric Modeling of Crime and Punishment: Support for the Deterrence Hypothesis?" Evaluation Review 4:147-91. Cox, David R. 1961. "Tests of Separate Families of Hypotheses." Proceedings of the Fourth Berkeley Symposium 1:105-23. 159 ADRIAN E. RAFTERY . 1962. "Further Results on Tests of Separate Families of Hypotheses." Journal of the Royal Statistical Society (Series B) 24:406-24. Draper, David. 1995. "Assessment and Propagation of Model Uncertainty (with Discussion)." Journal of the Royal Statistical Society (Series B), 57:45-98. Edwards, Ward, Harold Lindman, and Leonard J. Savage. 1963. "Bayesian Statistical Inference for Psychological Research." Psychological Review 70:193-242. Ehrlich, Isaac. 1973. "Participation in Illegitimate Activities: A Theoretical and Empirical Investigation." Journal of Political Economy 81:521-65. Featherman, David L., Frank L. Jones, and Robert M. Hauser. 1975. "Assumptions of Mobility Research in the United States: The Case of Occupational Status." Social Science Research 4:329-60. Fenech, A., and Peter Westfall. 1988. "The Power Function of Conditional Log- Linear Model Tests." Journal of the American Statistical Association 83: 198-203. Fienberg, Steven E., and William M. Mason. 1979. "Identification and Estimation of Age-Period-Cohort Effects in the Analysis of Discrete Archival Data." In Sociological Methodology 1979, edited by Karl F. Schuessler, 1-67. Washington: American Sociological Association. Freedman, David A. 1983. "A Note on Screening Regression Equations." The American Statistician 37 (2):152-55. Freedman, David A., W. C. Navidi, and Steven C. Peters. 1988. "On the Impact of Variable Selection in Fitting Regression Equations." In On Model Uncertainty and its Statistical Implications, edited by T. K. Dijkstra, pp. 1-16. Berlin: Springer-Verlag. Furnival, G. M., and R. W. Wilson Jr. 1974. "Regression by Leaps and Bounds." Technometrics 16:499-511. Grusky, David B., and Robert M. Hauser. 1983. "Comparative Social Mobility Revisited: Models of Convergence and Divergence in Sixteen Countries." Working paper, Center for Demography and Ecology, University of Wisconsin. ----. 1984. "Comparative Social Mobility Revisited: Models of Convergence and Divergence in Sixteen Countries." American Sociological Review 49: 19-38. Halaby, Charles L., and David L. Weakliem. 1993. "Ownership and Authority in the Earnings Function: Nonnested Tests of Alternative Specifications." American Sociological Review 58:16-30. Hazelrigg, Lawrence E., and Maurice A. Garnier. 1976. "Occupational Mobility in Industrial Societies: A Comparative Analysis of Differential Access to Occupational Ranks in Seventeen Countries." American Sociological Review 41:498-511. Hoeting, Jennifer A. 1994. "Accounting for Model Uncertainty in Linear Regression." Ph.D. diss., University of Washington. Hout, Michael. 1983. Mobility Tables. Beverly Hills: Sage. ----1984. "Status, Autonomy, and Training in Occupational Mobility." American Journal of Sociology 89:1379-409. 160 BAYESIAN MODEL SELECTION IN SOCIAL RESEARCH . 1988. "More Universalism, Less Structural Mobility: The American Occupational Structure in the 1980s." American Journal of Sociology 93:1358-400. Jeffreys, Harold. 1935. "Some Tests of Significance, Treated by the Theory of Probability." Proceedings of the Cambridge Philosophical Society 31:203-22. . 961. Theory of Probability, 3rd ed. Oxford: Oxford University Press. . 1980. "Some General Points in Probability Theory." In Bayesian Analysis in Econometrics and Statistics, edited by A. Zellner, 451-54, Amsterdam: North-Holland. Johnstone, David. 1990a. "Interpreting Statistical Insignificance: A Bayesian Perspective." Psychological Reports 66:115-21. . 1990b. "Sample Size and the Strength of Evidence." Abacus 26:17-35. Kass, Robert E. 1991. "About Theory of Probability." Chance 4:13. Kass, Robert E., and Adrian E. Raftery. 1995. "Bayes Factors. Journal of the American Statistical Association, 90:377-95. Kass, Robert E., and Larry Wasserman. 1992. "A Reference Bayesian Test for Nested Hypotheses with Large Samples." Technical Report No. 567, Department of Statistics, Carnegie Mellon University. Kotz, Samuel, and Norman L. Johnson, eds. 1985. Encyclopaedia of Statistical Sciences, vol. 5. New York: Wiley. Leamer, Edward E. 1978. Specification Searches: Ad Hoc Inference with Nonexperimental Data. New York: Wiley. Lee, Peter M. 1989. Bayesian Statistics: An Introduction. Oxford: Oxford University Press. Lipset, Seymour M., and H. L. Zetterberg. 1959. "Social Mobility in Industrial Societies." In Social Mobility in Industrial Society edited by S. M. Lipset and R. Bendix, 11-75. Berkeley: University of California Press. Lye, Diane, and April Greek. 1994. "The Emerging Two-Child Norm in America." Working paper no. 95-1, Center for Studies in Demography and Ecology, University of Washington. Madigan, David, and Adrian E. Raftery. 1994. "Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window." Journal of the American Statistical Association, 89:1535-46. McCullagh, Peter, and John A. Nelder. 1989. Generalized Linear Models. London: Chapman and Hall. Miller, Alan J. 1984. "Selection of Subsets of Regression Variables (with Discussion)." Journal of the Royal Statistical Society (Series A) 147:389-425. . 1990. Subset Selection in Regression. London: Chapman and Hall. Morrison, Denton E., and Ramon E. Henkel, eds. 1970. The Significance Test Controversy. Chicago: Aldine. Neyman, Jerzy, and Egon S. Pearson. 1933. "On the Problem of the Most Efficient Tests of Statistical Hypotheses." Philosophical Transactions of the Royal Society A 231:289-337. Press, S. James 1989. Bayesian Statistics: Principles, Models and Applications. New York: Wiley. Raftery, Adrian E. 1986a. "A Note on Bayes Factors for Log-Linear Contin- 161 ADRIAN E. RAFTERY gency Table Models with Vague Prior Information." Journal of the Royal Statistical Society (Series B) 48:249-50. . 1986b. "Choosing Models for Cross-Classifications." American Sociological Review 51:145-46. . 1988. "Approximate Bayes Factors for Generalized Linear Models." Technical Report No. 121, Department of Statistics, University of Washington. . 1993a. "Bayesian Model Selection in Structural Equation Models." In Testing Structural Equation Models, edited by K. A. Bollen and J. S. Long, 163-80. Beverly Hills: Sage. --- 1993b. "Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models." Technical Report 255, Department of Statistics, University of Washington. Raftery, Adrian E., Steven M. Lewis, and Akbar Aghajanian. 1995. "Demand or Ideation? Evidence from the Iranian Marital Fertility Decline." Demography 32:159-82. Raftery, Adrian E., Steven M. Lewis, Akbar Aghajanian, and Michael J. Kahn. 1995. "Event-History Modeling of World Fertility Survey Data." Mathematical Population Studies, forthcoming. Raftery, Adrian E., David Madigan, and Jennifer A. Hoeting. 1993. "Model Selection and Accounting for Model Uncertainty in Linear Regression Models." Technical Report no. 262, Department of Statistics, University of Washington. Raftery, Adrian E., David Madigan, and Chris T. Volinsky. 1995. "Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance (with Discussion)." In Bayesian Statistics 5, edited by J. M. Bernardo et al. Oxford: Oxford University Press, forthcoming. Raftery, Adrian E., and Sylvia Richardson. 1995. "Model Selection for Generalized Linear Models via GLIB, with Application to Epidemiology." In Bayesian Biostatistics edited by D. A. Berry and D. K. Stangl. New York: Dekker, forthcoming. Ragin, Charles C. 1987. The Comparative Method. Berkeley: University of California Press. Schwarz, Gideon. 1978. "Estimating the Dimension of a Model." Annals of Statistics 6:461-64. Stigler, George J. 1970. "The Optimum Enforcement of Laws." Journal of Political Economy 78:526-36. Tierney, Luke, and Kadane, Joseph B. 1986. "Accurate Approximations for Posterior Moments and Marginal Densities." Journal of the American Statistical Association 81:82-86. Vandaele, Walter. 1978. "Participation in Illegitimate Activities: Ehrlich Revisited." In Deterrence and Incapacitation, edited by A. Blumstein, J. Cohen, and D. Nagin. 270-335. Washington: National Academy of Sciences. Weakliem, David L. 1992. "Comparing Nonnested Models for Contingency Tables." In Sociological Methodology 1992, edited by Peter V. Marsden, 147- 78. Oxford: Blackwell Publishers. 162 BAYESIAN MODEL SELECTION IN SOCIAL RESEARCH 163 Weisberg, Sanford. 1985. Applied Linear Regression. New York: Wiley. Xie, Yu. 1992. "The Log-Multiplicative Layer Effect for Comparing Mobility Tables." American Sociological Review 57:380-95. . 1994. "The Log-Multiplicative Models for Discrete-Time, Discrete- Covariate Event-History Data." In Sociological Methodology 1994, edited by Peter V. Marsden, 301-40. Oxford: Blackwell Publishers.
关键字	Bayesian Model Selection ; Social Research
发表所在刊物（或来源）	Sociological Methodology, Vol. 25 (1995), pp. 111-163
发表时间	1995
适用研究领域	统计学
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