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Biometrika 1994 81(2):219-235; doi:10.1093/biomet/81.2.219
© 1994 by Biometrika Trust
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Random effects and variances as a synthesis of nonlinear regression analyses of mitochondrial electron transport

A. T. JAMES1, W. N. VENABLES1, I. B. DRY2 and J. T. WISKICH2

1Department of Statistics, University of Adelaide Adelaide, South Australia 5005, Australia
2Department of Botany, University of Adelaide Adelaide, South Australia 5005, Australia

This cross-disciplinary paper develops random effects and variances methods, especially for small samples within effects, and applies them to mitochondrial enzyme kinetics. A new force flux kinetic model is introduced for the alternative oxidase of plant mitochondria, the results of 42 experiments are published and the force flux function is fitted by nonlinear regression for each experiment. The results of the regression analyses are synthesized by a random effects model specifying random nonlinear regression coefficients and random variances within experiments distributed in an inverse gamma distribution.

Key Words: Alternative oxidase • Best linear unbiased predictor • Electron transport • Enzyme kinetics • Heteroscedasticity • Inverse gamma distribution • Lagrange multiplier • Michaelis-Menten • Mitochondria • Nonlinear regression • Random effects • Random variances • Redox • Residual maximum likelihood • Singular variance matrix • Small sample random effects • Weighted mean


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