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Local influence in multilevel regression for growth curves

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  • Shi, Lei
  • Ojeda, Mario Miguel

Abstract

Influence analysis is important in modelling and identification of special patterns in the data. It is well established in ordinary regression. However, analogous diagnostics are generally not available for the multilevel regression model, in which estimation involves a complex iterative algorithm. This paper studies the local influence of small perturbations on the parameter estimates in the multilevel regression model with application to growth curves. The estimation is based on the iterative generalized least-squares (IGLS) method suggested by Goldstein (Biometrika 73 (1986) 43). The generalized influence function and generalized Cook statistic (Biometrika 84(1) (1997) 175) of IGLS of unknown parameters under some specific simultaneous perturbations are derived to study the joint influence of subject units on parameter estimators. The perturbation scheme is introduced through a variance-covariance matrix of error variables. A one-step approximation formula is suggested for simplifying the computations. The method is examined on growth-curve data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:91:y:2004:i:2:p:282-304
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    References listed on IDEAS

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    1. J. S. Hodges, 1998. "Some algebra and geometry for hierarchical models, applied to diagnostics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 497-536.
    2. Shi, Lei & Wang, Xueren, 1999. "Local influence in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 341-353, September.
    3. Goldstein, Harvey & Rasbash, Jon, 1992. "Efficient computational procedures for the estimation of parameters in multilevel models based on iterative generalised least squares," Computational Statistics & Data Analysis, Elsevier, vol. 13(1), pages 63-71, January.
    4. Jacob (Yaacov) Weisberg & Noah M. Meltz, 1999. "Education and Unemployment in Israel, 1976-1994: Reducing the Anomaly," Working Papers nmeltz-99-01, University of Toronto, Department of Economics.
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    Cited by:

    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. Lei Shi & Md. Mostafizur Rahman & Wen Gan & Jianhua Zhao, 2015. "Stepwise local influence in generalized autoregressive conditional heteroskedasticity models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 428-444, February.
    3. 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.
    4. Shi, Lei & Huang, Mei, 2011. "Stepwise local influence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 973-982, February.
    5. Jun Lu & Wen Gan & Lei Shi, 2022. "Local influence analysis for GMM estimation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 1-23, March.

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