DOI QR코드

DOI QR Code

Bayesian information criterion accounting for the number of covariance parameters in mixed effects models

  • Heo, Junoh (Department of Statistics, Chung-Ang University) ;
  • Lee, Jung Yeon (Department of Psychiatry, New York University School of Medicine) ;
  • Kim, Wonkuk (Department of Applied Statistics, Chung-Ang University)
  • 투고 : 2019.12.03
  • 심사 : 2019.12.18
  • 발행 : 2020.05.31

초록

Schwarz's Bayesian information criterion (BIC) is one of the most popular criteria for model selection, that was derived under the assumption of independent and identical distribution. For correlated data in longitudinal studies, Jones (Statistics in Medicine, 30, 3050-3056, 2011) modified the BIC to select the best linear mixed effects model based on the effective sample size where the number of parameters in covariance structure was not considered. In this paper, we propose an extended Jones' modified BIC by considering covariance parameters. We conducted simulation studies under a variety of parameter configurations for linear mixed effects models. Our simulation study indicates that our proposed BIC performs better in model selection than Schwarz's BIC and Jones' modified BIC do in most scenarios. We also illustrate an example of smoking data using a longitudinal cohort of cancer patients.

키워드

과제정보

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07050012) and supported by the Chung-Ang University Graduate Research Scholarship in 2018.

참고문헌

  1. Ahn JH and Yoo JK (2011). A short note on empirical penalty term study of BIC in K-means clustering inverse regression, Communications for Statistical Applications and Methods, 18, 267-275. https://doi.org/10.5351/CKSS.2011.18.3.267
  2. Akaike H (1973). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory (Petrov BN and Csaki F eds, pp. 267-281), Akademia Kiado, Budapest.
  3. Akaike H (1974). A new look at the statistical model identification, IEEE Transactions on Automatic Control, 19, 716-723. https://doi.org/10.1109/TAC.1974.1100705
  4. Bozdogan H (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions, Psychometrika, 52, 345-370. https://doi.org/10.1007/BF02294361
  5. Burnham KP and Anderson DR (1998). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer-Verlag, New York.
  6. Carroll AJ, Kim K, Miele A, Olonoff M, Leone FT, Schnoll RA, and Hitsman B (2019). Longitudinal associations between smoking and affect among cancer patients using varenicline to quit smoking, Addictive Behaviors, 95, 206-210. https://doi.org/10.1016/j.addbeh.2019.04.003
  7. Diggle PJ (1988). An approach to the analysis of repeated measurements, Biometrics, 44, 959-971. https://doi.org/10.2307/2531727
  8. Gassiat G (2002). Likelihood ratio inequalities with applications to various mixtures, Annales De L Institut Henri Poincare-Probabilites Et Statistiques, 38, 897-906. https://doi.org/10.1016/S0246-0203(02)01125-1
  9. Hannan EJ and Quinn BG (1979). The determination of the order of an autoregression, Journal of the Royal Statistical Society. Series B, 41, 190-195.
  10. Hodges JS and Sargent DJ (2001). Counting degrees of freedom in hierarchical and other richly parameterized models, Biometrika, 88, 367-379. https://doi.org/10.1093/biomet/88.2.367
  11. Hurvich CM and Tsai CL (1989). Regression and time series model selection in small samples, Biometrika, 76, 297-307. https://doi.org/10.1093/biomet/76.2.297
  12. Jennrich RI and Schluchter MD (1986). Unbalanced repeated-measures models with structured co-variance matrices, Biometrics, 42, 805-820. https://doi.org/10.2307/2530695
  13. Jones RH (2011). Bayesian information criterion for longitudinal and clustered data, Statistics in Medicine, 30, 3050-3056. https://doi.org/10.1002/sim.4323
  14. Kim J and Cheon S (2013). Bayesian multiple change-point estimation and segmentation, Communications for Statistical Applications and Methods, 20, 439-454. https://doi.org/10.5351/CSAM.2013.20.6.439
  15. Kim W (2014). Time-varying comovement of KOSPI 200 sector indices returns, Communications for Statistical Applications and Methods, 21, 335-347. https://doi.org/10.5351/CSAM.2014.21.4.335
  16. Laird NM and Ware JH (1982). Random-effects models for longitudinal data, Biometrics, 38, 963-974. https://doi.org/10.2307/2529876
  17. Lee JY, KimW, and Brook JS (2019). Triple comorbid trajectories of alcohol, cigarette, and marijuana use from adolescence to adulthood predict insomnia in adulthood, Addictive Behaviors, 90, 437-443. https://doi.org/10.1016/j.addbeh.2018.11.026
  18. McCullagh P and Nelder JA (1989). Generalized Linear Models (2nd ed), London and Boca Raton, Florida.
  19. Nishii R (1984). Asymptotic properties of criteria for selection of variables in multiple regression, The Annals of Statistics, 12, 758-765. https://doi.org/10.1214/aos/1176346522
  20. Schnoll R (2018). Bidirectional Longitudinal Associations between Smoking and Affect among Cancer Patients Using Varenicline to Quit Smoking, Inter-University Consortium for Political and Social Research.
  21. Schwarz G (1978). Estimating the dimension of a model, The Annals of Statistics, 6, 461-464. https://doi.org/10.1214/aos/1176344136
  22. Vaida F and Blanchard S (2005). Conditional Akaike information for mixed-effects models, Biometrika, 92, 351-370. https://doi.org/10.1093/biomet/92.2.351