The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Sparse Matrix Computation in Mixed Effects Model

희소행렬 계산과 혼합모형의 추론

  • Son, Won (Department of Statistics, Seoul National University) ;
  • Park, Yong-Tae (Department of Industrial Engineering, Seoul National University) ;
  • Kim, Yu Kyeong (Department of Diagnostic Radiology, Seoul National University Hospital) ;
  • Lim, Johan (Department of Statistics, Seoul National University)
  • 손원 (서울대학교 통계학과) ;
  • 박용태 (서울대학교 산업공학과) ;
  • 김유경 (서울대학교 의과대학 핵의학교실) ;
  • 임요한 (서울대학교 통계학과)
  • Received : 2015.03.18
  • Accepted : 2015.04.01
  • Published : 2015.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study an approximate procedure to evaluate a penalized maximum likelihood estimator (MLE) for a mixed effects model. The procedure approximates the Hessian matrix of the penalized MLE with a structured sparse matrix or an arrowhead type matrix to speed its computation. In this paper, we numerically investigate the gain in computation time as well as approximation error from the considered approximation procedure.

본 연구에서는 혼합모형의 추론을 위한 벌점-최대우도추정량의 빠른 계산절차를 제안하다. 제안된 절차는 벌점-최대우도추정량을 위한 추정방정식에서 헷시안 행렬을 화살촉형태를 지닌 희소행렬을 통하여 근사 시킴으로써 계산속도의 향상을 가져왔다. 두 가지 가상실험을 통하여 제안된 근사식을 사용함으로써 얻게되는 계산시간의 감소와 동시에 이를 위하여 지불하여야 하는 근사오차에 대하여 살펴보았다.

Keywords

References

  1. Beckmann, C. F., Jenkinson, M. and Smith, S. M. (2003). General multilevel linear modeling for group analysis in FMRI, NeuroImage, 20, 1052-1063. https://doi.org/10.1016/S1053-8119(03)00435-X
  2. Demmel, J. W. (1997). Applied Numerical Linear Algebra, SIAM, Philadelphia, PA.
  3. Fleming, T. R. and Harrington, D. P. (2005). Counting Processes and Survival Analysis, John Wiley & Sons, Inc., Hoboken, NJ.
  4. Ha, I. D., Lee, Y. J. and Song, J.-K. (2001). Hierarchical likelihood approach for frailty models, Biometrika, 88, 233-243. https://doi.org/10.1093/biomet/88.1.233
  5. Hager, W. W. (1989). Updating the inverse of a matrix, SIAM Review, 31, 221-239. https://doi.org/10.1137/1031049
  6. Lee, Y. and Oh, H.-S. (2014). A new sparse variable selection via random-effect model, Journal of Multivariate Analysis, 125, 89-99. https://doi.org/10.1016/j.jmva.2013.11.016
  7. Park, S. (2007). Regression Analysis, 3/e, Minyoungsa, Seoul.
  8. Pinheiro, J. C. and Bates, D. M. (2000). Mixed Effects Model in S and S-PLUS, Springer, New York.
  9. Sohn, S., Chang, I. and Moon, H. (2007). Random effects Weibull regression model for occupational lifetime, European Journal of Operational Research, 179, 124-131. https://doi.org/10.1016/j.ejor.2006.03.008
  10. Therneau, T. M. and Grambsch, P. M. (2000). Modeling Survival Data: Extending the Cox Model, Springer, New York.
  11. Yoon, K. and Sohn, S. Y. (2007). Finding the optimal CSP inventory level for multi-echelon system in Air Force using random effects regression model, European Journal of Operational Research, 180, 1076-1085. https://doi.org/10.1016/j.ejor.2006.05.006
  12. Zhu, J. and Hastie, T. (2004). Classification of gene microarrays by penalized logistic regression, Biostatistics, 5, 427-443. https://doi.org/10.1093/biostatistics/kxg046