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Multilevel cumulative logistic regression model with random effects: Application to British social attitudes panel survey data

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  • Chan, Moon-tong
  • Yu, Dalei
  • Yau, Kelvin K.W.

Abstract

A multilevel model for ordinal data in generalized linear mixed models (GLMM) framework is developed to account for the inherent dependencies among observations within clusters. Motivated by a data set from the British Social Attitudes Panel Survey (BSAPS), the random district effects and respondent effects are incorporated into the linear predictor to accommodate the nested clusterings. The fixed (random) effects are estimated (predicted) by maximizing the penalized quasi likelihood (PQL) function, whereas the variance component parameters are obtained via the restricted maximum likelihood (REML) estimation method. The model is employed to analyze the BSAPS data. Simulation studies are conducted to assess the performance of estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:88:y:2015:i:c:p:173-186
    DOI: 10.1016/j.csda.2015.02.018
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    References listed on IDEAS

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    1. 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.
    2. M. C. Donohue & R. Overholser & R. Xu & F. Vaida, 2011. "Conditional Akaike information under generalized linear and proportional hazards mixed models," Biometrika, Biometrika Trust, vol. 98(3), pages 685-700.
    3. Wan, Alan T.K. & Zhang, Xinyu & Wang, Shouyang, 2014. "Frequentist model averaging for multinomial and ordered logit models," International Journal of Forecasting, Elsevier, vol. 30(1), pages 118-128.
    4. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    5. Antony Fielding & Min Yang, 2005. "Generalized linear mixed models for ordered responses in complex multilevel structures: effects beneath the school or college in education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 159-183, January.
    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. 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. Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
    9. Franses,Philip Hans & Paap,Richard, 2010. "Quantitative Models in Marketing Research," Cambridge Books, Cambridge University Press, number 9780521143653, January.
    10. Li C. Liu & Donald Hedeker, 2006. "A Mixed-Effects Regression Model for Longitudinal Multivariate Ordinal Data," Biometrics, The International Biometric Society, vol. 62(1), pages 261-268, March.
    11. Jeroen K. Vermunt, 2004. "An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 220-233, May.
    12. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    13. Lin, Kuo-Chin, 2010. "Goodness-of-fit tests for modeling longitudinal ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1872-1880, July.
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