Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series B, Pt. 3, 301--321

A Likelihood Approximation And Shrinkage For Unbalanced Repeated Measures

By

IAN ABRAMSON, University of California, San Diego, USA, University of the Witwatersrand, Johannesburg, South Africa,

TANYA WOLFSON, and THE HNRC GROUP

University of California, San Diego, USA

SUMMARY. A simplifying likelihood approximation based on a sufficient data reduction by least squares is given for the mixed repeated measures (RM) model. Efficient parameter estimation is based on the approximation and on a transparent and numerically simple EM--algorithm. BLUPs of the random effects are obtained by an empirical Bayes shrinkage applicable even under relaxed distributional assumptions, and an application to an HIV case study is illustrated with graphics.

AMS (1991) subject classification}. 62J99, 62F12, 62C12.

Key words and phrases. AIDS markers, antiretroviral drugs, BLUP,(dated) seroconverters, discrimination, dispersion-preserving transformation,EM--algorithm, empirical Bayes, fanplot, fixed and random effects,growth curves, likelihood approximation, location and variance parameters,nonnormality, one-step efficient updates, progression to AIDS,regression to the mean, repeated measures, shrinkage,sufficient data reduction.

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