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Stepwise local influence analysis


  • Shi, Lei
  • Huang, Mei


A new method called stepwise local influence analysis is proposed to detect influential observations and to identify masking effects in a dataset. Influential observations are detected step-by-step such that any highly influential observations identified in a previous step are removed from the perturbation in the next step. The process iterates until no further influential observations can be found. It is shown that this new method is very effective to identify the influential observations and has the power to uncover the masking effects. Additionally, the issues of constraints on perturbation vectors and bench-mark determination are discussed. Several examples with regression models and linear mixed models are illustrated for the proposed methodology.

Suggested Citation

  • Shi, Lei & Huang, Mei, 2011. "Stepwise local influence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 973-982, February.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:973-982

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    References listed on IDEAS

    1. Shi, Lei & Chen, Gemai, 2008. "Case deletion diagnostics in multilevel models," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1860-1877, October.
    2. Frank Critchley & Richard A. Atkinson & Guobing Lu & Elenice Biazi, 2001. "Influence analysis based on the case sensitivity function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 307-323.
    3. W.-Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    4. Shi, Lei & Ojeda, Mario Miguel, 2004. "Local influence in multilevel regression for growth curves," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 282-304, November.
    5. Frank Critchley, 2004. "Data-informed influence analysis," Biometrika, Biometrika Trust, vol. 91(1), pages 125-140, March.
    6. Hong-Tu Zhu & Sik-Yum Lee, 2001. "Local influence for incomplete data models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 111-126.
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    Cited by:

    1. Schützenmeister, André & Piepho, Hans-Peter, 2012. "Residual analysis of linear mixed models using a simulation approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1405-1416.
    2. Fukang Zhu & Shuangzhe Liu & Lei Shi, 2016. "Local influence analysis for Poisson autoregression with an application to stock transaction data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(1), pages 4-25, February.
    3. Fukang Zhu & Lei Shi & Shuangzhe Liu, 2015. "Influence diagnostics in log-linear integer-valued GARCH models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 311-335, July.
    4. repec:bla:stanee:v:71:y:2017:i:2:p:86-114 is not listed on IDEAS
    5. Shuangzhe Liu & Víctor Leiva & Tiefeng Ma & Alan Welsh, 2016. "Influence diagnostic analysis in the possibly heteroskedastic linear model with exact restrictions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(2), pages 227-249, June.
    6. Shi, Lei & Lu, Jun & Zhao, Jianhua & Chen, Gemai, 2016. "Case deletion diagnostics for GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 176-191.
    7. Xiaowen Dai & Libin Jin & Lei Shi & Cuiping Yang & Shuangzhe Liu, 2016. "Local influence analysis in general spatial models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 313-331, July.


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