Comparative Calibration, Linear Structural Relationships and Congeneric Measurements

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Abstract
The problem of estimating calibration equations (assumed to be linear) and precisions of a number of measuring instruments on the basis of observations on a common group of specimens is examined in its structural and functional relationship forms. Barnett''s (1969) structural relationship version of the problem is equivalent to a model used for mental test scores, itself a particular case of the standard factor analysis model. Maximum likelihood estimation is considered for this and certain constrained models. Williams''s (1969) attempt at deriving maximum likelihood estimators for the functional relationship version is shown to be unworkable, but a consistent method of estimation is suggested. Barnett''s data on comparison of two instruments for measuring human lung capacity are re-analyzed.

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