Local influence in multilevel regression for growth curves

• Published in: Journal of multivariate analysis Vol. 91; no. 2; pp. 282 - 304
• Main Authors: Shi, Lei, Ojeda, Mario Miguel
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.11.2004; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: Exact sciences and technology; Generalized cook statistic; Hierarchical linear models; Linear inference, regression; Longitudinal data; Longitudinal data Multilevel linear models Hierarchical linear models Random coefficients models Perturbation scheme Generalized cook statistic; Mathematical models; Mathematics; Multilevel linear models; Multivariate analysis; Nonparametric inference; Pattern recognition; Perturbation scheme; Probability and statistics; Random coefficients models; Regression analysis; Sciences and techniques of general use; Statistical analysis; Statistics; Theory; Generalized cook statistic; 62J05; Multilevel linear models; Hierarchical linear models; Random coefficients models; Perturbation scheme; Longitudinal data; 62J20; 62J99; Influence function; Error estimation; Regression model; Least squares method; Generalized least square; Iterative method; Small perturbation; Covariance matrix; Multivariate analysis; Joint distribution; Local influence; Growth curve
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2003.08.007

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.