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Influence diagnostics and outlier tests for semiparametric mixed models

Author

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  • Wing‐Kam Fung
  • Zhong‐Yi Zhu
  • Bo‐Cheng Wei
  • Xuming He

Abstract

Summary. Semiparametric mixed models are useful in biometric and econometric applications, especially for longitudinal data. Maximum penalized likelihood estimators (MPLEs) have been shown to work well by Zhang and co‐workers for both linear coefficients and nonparametric functions. This paper considers the role of influence diagnostics in the MPLE by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component. We focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the MPLE algorithm. We also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers. The influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example.

Suggested Citation

  • Wing‐Kam Fung & Zhong‐Yi Zhu & Bo‐Cheng Wei & Xuming He, 2002. "Influence diagnostics and outlier tests for semiparametric mixed models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 565-579, August.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:3:p:565-579
    DOI: 10.1111/1467-9868.00351
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    Cited by:

    1. Ping Chen & Jing Yang & Linyuan Li, 2015. "Synthetic detection of change point and outliers in bilinear time series models," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(2), pages 284-293, January.
    2. Xueying Zheng & Wing Fung & Zhongyi Zhu, 2013. "Robust estimation in joint mean–covariance regression model for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 617-638, August.
    3. Germán Ibacache-Pulgar & Gilberto Paula & Francisco Cysneiros, 2013. "Semiparametric additive models under symmetric distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 103-121, March.
    4. Hadi Emami, 2018. "Local influence for Liu estimators in semiparametric linear models," Statistical Papers, Springer, vol. 59(2), pages 529-544, June.
    5. Kim, Choongrak & Park, Byeong U. & Kim, Woochul, 2002. "Influence diagnostics in semiparametric regression models," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 49-58, November.
    6. Vanegas, Luis Hernando & Rondón, Luz Marina & Cysneiros, Francisco José A., 2012. "Diagnostic procedures in Birnbaum–Saunders nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1662-1680.
    7. Li, Zaixing & Xu, Wangli & Zhu, Lixing, 2009. "Influence diagnostics and outlier tests for varying coefficient mixed models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2002-2017, October.
    8. Juvêncio S. Nobre & Julio M. Singer, 2011. "Leverage analysis for linear mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 1063-1072, February.
    9. Xu, Liang & Lee, Sik-Yum & Poon, Wai-Yin, 2006. "Deletion measures for generalized linear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1131-1146, November.
    10. Vanegas, Luis Hernando & Cysneiros, Francisco José A., 2010. "Assessment of diagnostic procedures in symmetrical nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1002-1016, April.
    11. Zeller, Camila B. & Labra, Filidor V. & Lachos, Victor H. & Balakrishnan, N., 2010. "Influence analyses of skew-normal/independent linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1266-1280, May.
    12. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    13. Emami, Hadi, 2015. "Influence diagnostic in ridge semiparametric models," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 106-113.
    14. Michael Martin & Steven Roberts, 2010. "Jackknife-after-bootstrap regression influence diagnostics," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 257-269.
    15. Qin, Guo You & Zhu, Zhong Yi & Fung, Wing K., 2008. "Robust estimating equations and bias correction of correlation parameters for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4745-4753, June.
    16. Wei, Wen Hsiang, 2004. "Derivatives diagnostics and robustness for smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 335-356, June.
    17. Xie, Feng-Chang & Wei, Bo-Cheng, 2007. "Diagnostics analysis for log-Birnbaum-Saunders regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4692-4706, May.
    18. Whasoo Bae & Soonyoung Hwang & Choongrak Kim, 2008. "Influence diagnostics in the varying coefficient model with longitudinal data," Computational Statistics, Springer, vol. 23(2), pages 185-196, April.
    19. Liya Fu & Zhuoran Yang & Fengjing Cai & You-Gan Wang, 2021. "Efficient and doubly-robust methods for variable selection and parameter estimation in longitudinal data analysis," Computational Statistics, Springer, vol. 36(2), pages 781-804, June.
    20. Xibin Zhang & Maxwell L. King, 2002. "Influence Diagnostics in GARCH Processes," Monash Econometrics and Business Statistics Working Papers 19/02, Monash University, Department of Econometrics and Business Statistics.
    21. M. P. Wand, 2003. "Smoothing and mixed models," Computational Statistics, Springer, vol. 18(2), pages 223-249, July.
    22. Fan, Yali & Qin, Guoyou & Zhu, Zhongyi, 2012. "Variable selection in robust regression models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 156-167.
    23. Germán Ibacache-Pulgar & Cristian Villegas & Javier Linkolk López-Gonzales & Magaly Moraga, 2023. "Influence measures in nonparametric regression model with symmetric random errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 1-25, March.
    24. Clécio S. Ferreira & Gilberto A. Paula, 2017. "Estimation and diagnostic for skew-normal partially linear models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 3033-3053, December.

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