A Study for Recent Development of Generalized Linear Mixed Model

일반화된 선형 혼합 모형(GENERALIZED LINEAR MIXED MODEL: GLMM)에 관한 최근의 연구 동향

  • 이준영 (고려대학교 의과대학 예방의학교실 및 환경의학연구소, 연구강사)
  • Published : 2000.09.01

Abstract

The generalized linear mixed model framework is for handling count-type categorical data as well as for clustered or overdispersed non-Gaussian data, or for non-linear model data. In this study, we review its general formulation and estimation methods, based on quasi-likelihood and Monte-Carlo techniques. The current research areas and topics for further development are also mentioned.

일반화된 선형 혼합 모형(GLMM)은 자료가 계수의 형태로 나타나는 범주형 자료의 경우, 혹은 집락의 형태나 과산포된 비정규 자료, 또는 비선형 모형에 따르는 자료를 다루기 위한 모형 설정에 사용된다. 본 연구에서는 이에 대한 개요와 더불어, 이 모형의 적합을 위해 제시된 통계적 기법들중 의사가능도(quasi-likelihood: QL)를 이용한 추정 방법 및 Monte-Carlo 기법을 이용한 추정 방법들에 대해 조사하였다. 또한 GLMM에 대한 현재의 연구 방향 및 앞으로의 연구 가능 주제들에 대해서도 언급하였다.

Keywords

References

  1. 응용 통계 v.14 일반화된 선형 혼합 모형; 선형 혼합 모형과 일반화된 선형 모형의 연결 이준영
  2. Statistics in Medicine v.12 Distribution-free fitting of logistic models with random effects of repeated categorical responses Agresti, A.
  3. GLIM Newsletter v.25 Fitting overdispersed generalized linear models by nonparametric maximum likelihood Aitkin, M.;Francis, B. J.
  4. Journal of the Royal Statistical Society, Series B. v.47 Variance component models with binary responses: Interviewer variability Anderson, D. A.;Aitkin, M.
  5. Psychometrika v.46 Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm Bock, R. D.;Aitkin, M.
  6. Proceedings of the 10th International Workshop on Statistical Modelling v.104 Bootstrap methods for generalized linear mixed models with applications to small area estimation Booth, J. G.
  7. Journal of the American Statistical Association v.93 Standard errors of prediction in generalized linear mixed models Booth, J. G.;Hobert, J. P.
  8. Journal of the Royal Statistical Society, Series B. v.61 Maximizing generalized linear mixed model likelihoos with an automated Monte-Carlo EM algorithm Booth, J. G.;Hobert, J. P.
  9. Journal of the American Statistical Association v.88 Approximate inference in generalized linear mixed models Brelow, N. E.;Clayton, D. G.
  10. Biometrika v.82 Bias correction in generalized linear mixed models with a single component of dispersion Brelow, N. E.;Lin, X.
  11. Statistics in Medicine v.16 Using a generalized linear mixed model to analyse unbalanced repeated measures and longitudinal data Cnaan, A.;Laird, N. M.;Slasor, P.
  12. Biometrics v.53 Maximum likelihood estimation for probit-linear mixed models with correlated random effects Chan, J. S. K.;Kuk, A. Y. C.
  13. Technometrics v.34 Case-deletion diagnostics for mixed models Christensen, R.;Pearson, L. M.;Johnson, W.
  14. Journal of the American Statistical Association v.94 Hierarchical generalized linear models in the analysis of variations in health care utilization Daniels, M. J.;Gatsonis, C.
  15. Biometrics v.51 A caveat concerning independence estimating equations with multivariate binary data Fitzmaurice, G. M.
  16. Statistical Science v.9 Small area estimation: An appraisal Ghosh, M.;Rao, J. N. K.
  17. Journal of the American Statistical Association v.93 Generalized linear models for small area estimation Ghosh, M.;Natarajan, K.;Stroud, T.;Carlin, B.
  18. Journal of the American Statistical Association v.89 A random-effects probit model for predicting medical malpractice claims Gibbons, R. D.;Hedeker, D.;Charle, S. C.;Frisch, P.
  19. Biometrics v.49 Random-effects models for longitudinal data using Gibbs sampling Gilks, W. R.;Wang, C. C.;Yvonnet, B.;Coursaget, P.
  20. Biometrika v.72 The analysis of binomial data by a generalized linear mixed model Gilmour, A. R.;Anderson, R. D.;Rae, A. L.
  21. Biometrika v.78 Nonlinear multilevel models, with an application to discrete response data Goldstein, H.
  22. Journal of the American Statistical Association v.72 Maximum likelihood approaches to variance component estimation and to related problems Harville, D. A.
  23. Biometrics v.40 A mixed-model procedure for analyzing ordered categorical data Harville, D. A.;Mee, R. W.
  24. Biometrics v.50 A random-effects ordinal regression model for multilevel analysis Hedeker, D.;Gibbons, R. D.
  25. Journal of the American Statistical Association v.91 The effect of improper priors on Gibbs sampling in hierachical linear mixed models Hobert, J. P.;Casella, G.
  26. Journal of the Royal Statistical Society, Series, B. v.60 Some algebra and geometry for hierachical models, applied to diagnostics Hodges, J. S.
  27. Journal of the American Statistical Association v.93 Consistent estimators in generalized linear mixed models Jiang, J.
  28. Proceedings of the Kansas State University of Applied Statistics in Agriculture Generalized linear mixed models: an application Kachman, S. D.;Stroup, W. W.
  29. Biometrika v.65 Empirical Bayes methods for two-way contingency tables Laird, N. M.
  30. Land Economics v.70 Using a generalized linear mixed models to analyze dichotomous choice contingent variation data Langford, I. H.
  31. Annals of Statistics v.17 Assessing normality in random effects modesl Lange, N.;Ryan, L.
  32. Journal of the Royal Statistical Society, Series, B. v.58 Hierachical generalized linear models Lee, Y.;Nelder, J. A.
  33. Annals of Statistics v.17 Regression analysis under link violation Li, K. -C.;Duan, N.
  34. Biometrika v.84 Variance component testing in generalized linear mixed models with random effects Lin, X.
  35. Biometrics v.55 SIMEX variance component tests in generalized linear mixed measurement error models Lin, X.;Carroll, R. J.
  36. Biometrics v.50 Performance of generalized estimating equations in practical situations Lipsitz, S. R.;Fitzmaurice, G. M.;Orav, E. J.;Laird, N. M.
  37. SAS System for Mixed Models Littell, R. C.;Milliken, G. A.;Stroup, W. W.;Wolfinger, R. D.
  38. Biometrika v.81 A note on Gauss-Hermite quadrature Liu, Q.;Pierce, D. A.
  39. Biometrika v.81 Generalized linear models with unknown link functions Mallick, B. K.;Gelfand, A. E.
  40. Generlized linear models McCullagh, P.;Nelder, J.
  41. Journal of the American Statistical Association v.89 Maximum likelihood variance components estimation for binary data McCulloch, C. E.
  42. Journal of the American Statistical Association v.2 Maximum likelihood algorithms for generalized linear mixed models McCulloch, C. E.
  43. Department of Statistics v.8 no.12 NSF/CBMS Rgional conference on generalized linear mixed models and related topics McCulloch, C. E.
  44. Journal of the American Statistical Association v.81 Child health, breast-feeding, and survival in Malaysia: A random-effects logit approach Montgomery, M. R.;Richards, T.;Braun, H. I.
  45. Demography v.35 Family and sociodemographic influences of patterns of leaving home in postwar Britain Murphy, D. M.;Wang, D.
  46. Biometrika v.82 A note on existence of the posterior distribution for a class of mixed models for binomial responses Natarajan, R.;McCulloch, C. E.
  47. Biometrics v.55 Modeling heterogeneity in nested survival data Natarajan, R.;McCulloch, C. E.
  48. American Journal of Sociology v.101 The emergence of a market society: Changing mechanisms of stratification in China Nee, V.
  49. Biometrika v.79 The effects of mixture distribution misspecification when fitting mixed-effects logistic models Neuhaus, J. M.;Hauck, W. W.;Kalbfleisch, J. D.
  50. The Canadian Journal of Statistics v.22 Conditions for consistent estimation in mixed-effects models for binary matched-pairs data Neuhaus, J. M.;Kalbfleisch, J. D.;Hauck, W. W.
  51. Biometrika v.58 Recovery of inter-block information when block sizes are unequal Patterson, H. D.;Thompson, R.
  52. Journal of the American Statistical Association v.81 Comparisons of alternative predictors under the balanced con-way random model Peixoto, J.;Harville, D. A.
  53. Journal of Computational and Graphical Statistics v.4 Approximations to the log-likelihood function in the non-linear mixed-effects model Pinheiro, J. C.;Bates, D. M.
  54. Institute of Education MLn software for multilevel analysis Prosser, R.;Rasbash, J.;Goldstein, H.
  55. Applied Statistics v.29 Goodness of link tests for generalized linear models Pregibon, D.
  56. Proceedings of the 4th Berkley Symposium on Mathematical Statistics and Probability v.4 On general laws and the meaning of measurement in psychology Rasch, G.
  57. Statistical Sciences v.6 That BLUP in a good thing: The estimation of random effects Robinson, G. K.
  58. Science v.227 Neighborhoods and violent crime: A multilevel study of collective efficacy Sampson, R. J.;Raudenbush, S. W.;Earls, R.
  59. The NLMIXED procedure SAS Institute Inc.
  60. Variance Components Searle, S. R.;Casella, G.;McCulloch, C. E.
  61. Biometrics v.40 Random-effects models for serial observations with binary responses Stiratelli, R.;Laird, N.;Ware, J. H.
  62. Proceedings of the Kansas State University Conference of Applied Statistics in Agriculture Generalized linear mixed models - an overview Stroup, W. W.;Kachman, S. D.
  63. Journal of the American Statistical Association v.93 Bias analysis and SIMEX approach in generalized linear mixed measurement error models Wang, N.;Lin, X.;Gutierrez, R. G.;Carroll, R. J.
  64. Journal of the American Statistical Association v.85 A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms Wei, G. C. G.;Tanner, M. A.
  65. Annals of statistics v.22 Adapting for the missing link Weisberg, S.;Welsh, A. H.
  66. Journal of Statistical Computation and Simulation v.48 Generalized linear mixed models: A pseudo-likelihood approach Wolfinger, R. D.;O'Connell, M.
  67. Journal of the American Statistical Association v.91 A linear mixed-effects model with heterogeneity in the random-effects population Verbeke, G.;Lesaffire, E.
  68. In: Modelling longitudinal and spatially correlated data: Methods, applications and future directions Scaled link functions for heterogeneous ordinal response data Xie, M.;Simpson, D. G.;Carroll, R. J.;T. G. Gregoire(ed.)
  69. Journal of the American Statistical Association v.86 Generalized linear models with random effects: a Gibbs sampling approach Zeger, S. L.;Karim, M. R.
  70. Biometrics v.44;45 Models for longitudinal data: A generalized estimating equation approach Zeger, S. L.;Liang, K. -Y.;Albert, P. S.
  71. The American Statistician v.53 Comparisons of software packages for generalized linear multilevel models Zou, X. -H.;Perkins, A. J.;Hui, S. L.