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Biometrika 1976 63(1):39-50; doi:10.1093/biomet/63.1.39
© 1976 by Biometrika Trust
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The ultrastructural relation: A synthesis of the functional and structural relations

G. R. DOLBY

Division of Mathematics and Statistics, C.S.I.R.O., St Lucia, and University of Queensland Australia

A maximum likelihood solution is presented for a model which is a synthesis of the linear functional and structural relations. In the replicated case, the slope estimate is a root of a quadratic equation, the coefficients of which are symmetrical with respect to the within and between-groups sample covariances. In the unreplicated case it is shown that two variance ratios must be known, whereupon the slope estimator is a root of a quintic equation. When one of these variance ratios is zero, we obtain an estimator which was proposed on heuristic grounds by Teissier (1948).

Key Words: Allometry • Errors in both variables • Functional relation • Geometric mean regression • Maximum likelihood • Sampling • Structural relation • Ultrastructural relation


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