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Local influence in multilevel regression for growth curves. (English) Zbl 1056.62082

Summary: 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 H. Goldstein [Biometrika 73, 43–56 (1986; Zbl 0587.62143)]. The generalized influence function and generalized Cook statistic [see the first author, ibid. 84, 175–186 (1997; Zbl 0883.62060)] of the 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.

MSC:

62J20 Diagnostics, and linear inference and regression
62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models

Software:

ML3; ARC; MLwiN
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Full Text: DOI

References:

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