The ultrastructural relation: A synthesis of the functional and structural relations

SUMMARY 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...

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Bibliographic Details
Published in:Biometrika 1976-01, Vol.63 (1), p.39-50
Main Author: Dolby, G. R.
Format: Article
Language:English
Subjects:
Allometry
Coefficients
Consistent estimators
Covariance matrices
Equation roots
Errors in both variables
Estimators
Functional relation
Geometric mean regression
Mathematical relations
Maximum likelihood
Maximum likelihood estimation
Maximum likelihood estimators
Sampling
Standard deviation
Statistical variance
Structural relation
Ultrastructural relation
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Summary:SUMMARY 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).
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/63.1.39