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준모수적 방법을 이용한 랜덤 절편 로지스틱 모형 분석

Semiparametric Approach to Logistic Model with Random Intercept

  • Kim, Mijeong (Department of Statistics, Ewha Womans University)
  • 투고 : 2015.11.24
  • 심사 : 2015.12.08
  • 발행 : 2015.12.31

초록

의학이나 사회과학에서 이진 데이터 분석 시 랜덤 절편(random intercept)을 갖는 로지스틱 모형이 유용하게 쓰이고 있다. 지금까지는 이러한 로지스틱 모형에서 랜덤 절편이 정규분포와 같은 모수 모형(parametric model)을 따른다는 가정과 설명변수와 랜덤 절편이 독립이라는 가정 하에 실행된 데이터 분석이 전반적이었다. 그러나 이러한 두 가지 가정은 다소 무리가 있다. 이 연구에서는 설명 변수와 랜덤 절편의 독립성을 가정하지 않고, 비모수 랜덤 절편을 따르는 로지스틱 모형의 방법론을 기존에 널리 쓰인 방법과 비교하여 설명하도록 한다. 케냐의 초등학생들의 영양 섭취 및 질병의 발병을 조사한 데이터에 이 방법을 적용하였다.

Logistic models with a random intercept are useful to analyze longitudinal binary data. Traditionally, the random intercept of the logistic model is assumed to be parametric (such as normal distribution) and is also assumed to be independent to variables. Such assumptions are very strong and restricted for application to real data. Recently, Garcia and Ma (2015) derived semiparametric efficient estimators for logistic model with a random intercept without these assumptions. Their estimator shows the consistency where we do not assume any parametric form for the random intercept. In addition, the method is computationally simple. In this paper, we apply this method to analyze toenail infection data. We compare the semiparametric estimator with maximum likelihood estimator, penalized quasi-likelihood estimator and hierarchical generalized linear estimator.

키워드

참고문헌

  1. Bickel, P. J., Klaassen, C. A. J., Ritov, Y. and Wellner, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models, The Johns Hopkins University Press, Baltimore.
  2. Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9-25.
  3. Garcia, T. P. and Ma, Y. (2015). Optimal estimator for logistic model with distribution-free random intercept, Scandinavian Journal of Statistics, in press.
  4. Hausman, J. A. (1978). Specification tests in econometrics, Econometrica, 46, 1251-1271. https://doi.org/10.2307/1913827
  5. Jang, W. and Lim, J. (2006). PQL estimation biases in generalized linear mixed models, Institute of Statistics and Decision Sciences, Duke University Springer-Verlag, Durham, NC, USA, 5-21.
  6. Newey, W. and Powell, J. L. (1990). Efficient estimation of linear and type I censored regression models under conditional quantile restrictions, Econometric Theory, 6, 295-317. https://doi.org/10.1017/S0266466600005284
  7. Neumann, C. G., Bwibo, N. O., Murphy, S. P., Sigman, M., Guthrie, D., Weiss, R. E., Allen, L. H. and Demment, M. W. (2003). Animal source foods improve dietary quality, micronutrient status, growth and cognitive function in Kenyan school children: background, study design and baseline findings, The Journal of Nutrition, 133, 3941S-3949S. https://doi.org/10.1093/jn/133.11.3941S
  8. Neumann, C. G., Bwibo, N. O., Jiang, L. and Weiss, R. E. (2013). School snacks decrease morbidity in Kenyan schoolchildren: A cluster randomized, controlled feeding intervention trial, Public Health Nutrition, 16, 1593-1604. https://doi.org/10.1017/S1368980013000876
  9. Raudenbush, S. W. and Bryk, A. S. (2002). Hierarchical Linear Models, 2nd Ed., Sage Publications, California.
  10. Schall, R. (1991). Estimation in generalized linear models with random effects, Biometrika, 78, 719-727. https://doi.org/10.1093/biomet/78.4.719
  11. Skrondal, A. and Rabe-Hesketh, S. (2009). Prediction in multilevel generalized linear models, Journal of the Royal Statistical Society: Series A (Statistics in Society), 172, 659-687. https://doi.org/10.1111/j.1467-985X.2009.00587.x
  12. Tsiatis, A. A. (2006). Semiparametric Theory and Missing Data, Springer, New York.
  13. Weiss, R. E. (2005). Modeling Longitudinal Data, Springer-Verlag, New York.