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The report reviews random coefficient models in linear regression and proposes a bias correction to the maximum likelihood (ML) estimator. Asymptotic expansions of the ML equations are given when the between individual variance is much larger or smaller than the variance from within individual fluctuations. Random coefficient models are considered where some of the covariates do not vary in any single individual. The number of individuals necessary to estimate the regression coefficients (beta) and the covariance matrix increases significantly in the presence of more than one between covariate. When the number of individuals is sufficient to estimate beta but not the entire matrix, additional assumptions must be imposed on the structure. A simple model fails because it is not invariant under linear coordinate transformations and can significantly overestimate the variance of new observations. A covariance structure without these difficulties is proposed by first projecting the within covariates on to the space perpendicular to the between covariates.

Additional information

Authors: RIEDEL K S, New York University, Courant Institute of Mathematical Sciences (US)
Bibliographic Reference: Report: IPP 5/36 EN (1990) 27 pp.
Availability: Available from Max-Planck-Institut für Plasmaphysik, 8046 Garching bei München (DE)
Record Number: 199011417 / Last updated on: 1994-12-02
Original language: en
Available languages: en