Journal of the Korean Statistical Society

  • 제32권2호
  • /
  • Pages.121-150
  • /
  • 2003
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

BAYES EMPIRICAL BAYES ESTIMATION OF A PROPORT10N UNDER NONIGNORABLE NONRESPONSE

  • Choi, Jai-Won (Office of Research and Methodology, National Center for Health Statistics) ;
  • Nandram, Balgobin (Department of Mathematical Sciences, Worcester Polytechnic Institute)
  • 발행 : 2003.06.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The National Health Interview Survey (NHIS) is one of the surveys used to assess the health status of the US population. One indicator of the nation's health is the total number of doctor visits made by the household members in the past year, There is a substantial nonresponse among the sampled households, and the main issue we address here is that the nonrespones mechanism should not be ignored because respondents and nonrespondents differ. It is standard practice to summarize the number of doctor visits by the binary variable of no doctor visit versus at least one doctor visit by a household for each of the fifty states and the District of Columbia. We consider a nonignorable nonresponse model that expresses uncertainty about ignorability through the ratio of odds of a household doctor visit among respondents to the odds of doctor visit among all households. This is a hierarchical model in which a nonignorable nonresponse model is centered on an ignorable nonresponse model. Another feature of this model is that it permits us to "borrow strength" across states as in small area estimation; this helps because some of the parameters are weakly identified. However, for simplicity we assume that the hyperparameters are fixed but unknown, and these hyperparameters are estimated by the EM algorithm; thereby making our method Bayes empirical Bayes. Our main result is that for some of the states the nonresponse mechanism can be considered non-ignorable, and that 95% credible intervals of the probability of a household doctor visit and the probability that a household responds shed important light on the NHIS.

키워드

참고문헌

  1. Bayesian Statistics(3rd) Bayesian estimation of Poisson means using hierarchical log-linear model ,;M.H.DeGroat;D.V.Lindley;A.F.M.Smith(eds.)
  2. DEELY, J. J. AND LlNDLEY, D. V. (1981). 'Bayes empirical Bayes', Journal of the American StatisticaI Association, 76, 833-841 https://doi.org/10.2307/2287578
  3. DE HEER, W. (1999). 'International response trends : Results of an international survey', Journal of Official Statistics, 15, 129-142
  4. DEMPSTER, A. P., LAIRD, N. M. AND RuBiN, D. B. (1977). 'Maximum likelihood from incomplete data via the EM algorithm', Journal of the Royal Statistical Society, B39, 1-22
  5. DRAPER, D. (1995). 'Assessment and propagation of model uncertainty (with discussion)' JournaI of the Royal Statisttcal Society, B57, 45-97
  6. FORSTER, J. J. AND SMITH, P. W. F. (1998). 'Model-based inference for categorical survey data subject to non-ignorable non-response', Journal of the Royal Statistical Society, B60, 57-70
  7. GROVES, R. M. AND COUPER, M. P. (1998). Nonresponse in Househotd Interview Surveys, Wiley, New York
  8. HECKMAN, J. (1976). ' The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models', AnnaIs of Economic and Social Measurement, 5, 475-492
  9. KADANE, J. B. (1993). 'Subjective Bayesian analysis for surveys with missing data', Statis-tician, 42, 415-426 https://doi.org/10.2307/2348475
  10. LlTTLE, R. J. A. (1982). 'Models for nonresponse in sample surveys', Journal of the American Statistical Association, 77, 237-250 https://doi.org/10.2307/2287227
  11. LlTTLE, R. J. A. (1993). 'Pattern-mixture models for multivariate incomplete data', Journalof the American Statistical Association, 88, 125-134 https://doi.org/10.2307/2290705
  12. LlTTLE, R. J. A. AND RuBlN, D. B. (1987). Statistical Analysis with Missing Data, Wiley, New York
  13. NANDRAM, B. (1998). 'A Bayesian analysis ofthe three-stage hierarchical multinomial model', Journal of Statistical Computation and SimuIation, 61, 97-126 https://doi.org/10.1080/00949659808811904
  14. NORDHEIM, E. V. (1984). 'Inference from nonrandomly missing categorical data : An ex-ample from a genetic study on Turner's syndrome', JournaI of the American StatisticaI Association, 79, 772-780 https://doi.org/10.2307/2288707
  15. OLSON, R. L. (1980). 'A least square correction for selectivity bias', Econometrica, 48, 1815-1820 https://doi.org/10.2307/1911938
  16. PHILLIPS, M. J. (1993). 'Contingency tables with missing data', Statistician, 42, 415-426 https://doi.org/10.2307/2348475
  17. PREGIBON, D. (1977). 'Typical survey data : Estimation and imputation', Survey Methodol-ogy, 2, 70-102
  18. RUBIN, D. B. (1976). 'Inference and missing data', Biometrika, 63, 581-590 https://doi.org/10.1093/biomet/63.3.581
  19. RUBIN, D. B. (1977). 'Formalizing subjective notions about the effect of nonrespondents in sample surveys', Journal of the American Statistical Association, 72, 538-543 https://doi.org/10.2307/2286214
  20. RUBIN, D. B. (1987). Multiple Imputation for Nonresponse in Surveys, Wiley, New York
  21. STASNY, E. A. (1991). 'Hierarchical models for the probabilities of a survey classification and nonresponse : An example from the national crime survey', Journal of the American Statistical Association. 86. 296-303 https://doi.org/10.2307/2290561