IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i3p629-644.html
   My bibliography  Save this article

Conditional Akaike information criterion for generalized linear mixed models

Author

Listed:
  • Yu, Dalei
  • Yau, Kelvin K.W.

Abstract

In this study, a model identification instrument to determine the variance component structure for generalized linear mixed models (glmms) is developed based on the conditional Akaike information (cai). In particular, an asymptotically unbiased estimator of the cai (denoted as caicc) is derived as the model selection criterion which takes the estimation uncertainty in the variance component parameters into consideration. The relationship between bias correction and generalized degree of freedom for glmms is also explored. Simulation results show that the estimator performs well. The proposed criterion demonstrates a high proportion of correct model identification for glmms. Two sets of real data (epilepsy seizure count data and polio incidence data) are used to illustrate the proposed model identification method.

Suggested Citation

  • Yu, Dalei & Yau, Kelvin K.W., 2012. "Conditional Akaike information criterion for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 629-644.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:629-644
    DOI: 10.1016/j.csda.2011.09.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003318
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.09.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Noh, Maengseok & Lee, Youngjo, 2008. "Hierarchical-likelihood approach for nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3517-3527, March.
    2. Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
    3. Zhen Chen & David B. Dunson, 2003. "Random Effects Selection in Linear Mixed Models," Biometrics, The International Biometric Society, vol. 59(4), pages 762-769, December.
    4. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    5. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    6. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185, April.
    7. Bo Cai & David B. Dunson, 2006. "Bayesian Covariance Selection in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 62(2), pages 446-457, June.
    8. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    9. Azari, Rahman & Li, Lexin & Tsai, Chih-Ling, 2006. "Longitudinal data model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3053-3066, July.
    10. Hua Liang & Hulin Wu & Guohua Zou, 2008. "A note on conditional aic for linear mixed-effects models," Biometrika, Biometrika Trust, vol. 95(3), pages 773-778.
    11. Kelvin K. W. Yau & Anthony Y. C. Kuk, 2002. "Robust estimation in generalized linear mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 101-117, January.
    12. Sonja Greven & Thomas Kneib, 2010. "On the behaviour of marginal and conditional AIC in linear mixed models," Biometrika, Biometrika Trust, vol. 97(4), pages 773-789.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chan, Moon-tong & Yu, Dalei & Yau, Kelvin K.W., 2015. "Multilevel cumulative logistic regression model with random effects: Application to British social attitudes panel survey data," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 173-186.
    2. María José Lombardía & Esther López‐Vizcaíno & Cristina Rueda, 2017. "Mixed generalized Akaike information criterion for small area models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1229-1252, October.
    3. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    4. Simon N. Wood & Natalya Pya & Benjamin Säfken, 2016. "Smoothing Parameter and Model Selection for General Smooth Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1548-1563, October.
    5. Lai, Xin & Yau, Kelvin K.W. & Liu, Liu, 2017. "Competing risk model with bivariate random effects for clustered survival data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 215-223.
    6. Yuki Kawakubo & Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "Conditional AIC under Covariate Shift with Application to Small Area Prediction," CIRJE F-Series CIRJE-F-944, CIRJE, Faculty of Economics, University of Tokyo.
    7. Yu, Dalei & Zhang, Xinyu & Yau, Kelvin K.W., 2013. "Information based model selection criteria for generalized linear mixed models with unknown variance component parameters," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 245-262.
    8. Braun, Julia & Sabanés Bové, Daniel & Held, Leonhard, 2014. "Choice of generalized linear mixed models using predictive crossvalidation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 190-202.
    9. Dalei Yu, 2016. "Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1214-1235, December.
    10. Xinyu Zhang & Hua Liang & Anna Liu & David Ruppert & Guohua Zou, 2016. "Selection Strategy for Covariance Structure of Random Effects in Linear Mixed-effects Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 275-291, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    2. Sun-Joo Cho & Paul Boeck & Susan Embretson & Sophia Rabe-Hesketh, 2014. "Additive Multilevel Item Structure Models with Random Residuals: Item Modeling for Explanation and Item Generation," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 84-104, January.
    3. Braun, Julia & Sabanés Bové, Daniel & Held, Leonhard, 2014. "Choice of generalized linear mixed models using predictive crossvalidation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 190-202.
    4. Overholser, Rosanna & Xu, Ronghui, 2014. "Effective degrees of freedom and its application to conditional AIC for linear mixed-effects models with correlated error structures," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 160-170.
    5. Noh, Maengseok & Wu, Lang & Lee, Youngjo, 2012. "Hierarchical likelihood methods for nonlinear and generalized linear mixed models with missing data and measurement errors in covariates," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 42-51.
    6. Yu, Dalei & Zhang, Xinyu & Yau, Kelvin K.W., 2013. "Information based model selection criteria for generalized linear mixed models with unknown variance component parameters," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 245-262.
    7. Benjamin R. Saville & Amy H. Herring, 2009. "Testing Random Effects in the Linear Mixed Model Using Approximate Bayes Factors," Biometrics, The International Biometric Society, vol. 65(2), pages 369-376, June.
    8. Mojtaba Ganjali & Taban Baghfalaki, 2018. "Application of Penalized Mixed Model in Identification of Genes in Yeast Cell-Cycle Gene Expression Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(2), pages 38-41, April.
    9. Philipp F. M. Baumann & Enzo Rossi & Alexander Volkmann, 2020. "What Drives Inflation and How: Evidence from Additive Mixed Models Selected by cAIC," Papers 2006.06274, arXiv.org, revised Aug 2022.
    10. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    11. Jonathan Bradley & Noel Cressie & Tao Shi, 2015. "Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 1-28, March.
    12. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    13. Chan, Moon-tong & Yu, Dalei & Yau, Kelvin K.W., 2015. "Multilevel cumulative logistic regression model with random effects: Application to British social attitudes panel survey data," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 173-186.
    14. Xinyu Zhang & Hua Liang & Anna Liu & David Ruppert & Guohua Zou, 2016. "Selection Strategy for Covariance Structure of Random Effects in Linear Mixed-effects Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 275-291, March.
    15. Kruse, René-Marcel & Silbersdorff, Alexander & Säfken, Benjamin, 2022. "Model averaging for linear mixed models via augmented Lagrangian," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    16. Abhik Ghosh & Magne Thoresen, 2018. "Non-concave penalization in linear mixed-effect models and regularized selection of fixed effects," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 179-210, April.
    17. Kubokawa, Tatsuya, 2011. "Conditional and unconditional methods for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 641-660, March.
    18. Dimova, Rositsa B. & Markatou, Marianthi & Talal, Andrew H., 2011. "Information methods for model selection in linear mixed effects models with application to HCV data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2677-2697, September.
    19. Cho, S.-J. & Rabe-Hesketh, S., 2011. "Alternating imputation posterior estimation of models with crossed random effects," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 12-25, January.
    20. Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:3:p:629-644. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.