Comparative Calibration, Linear Structural Relationships and Congeneric Measurements

Abstract

The problem oj'estimating the calibration equations (assumled to be linear) and precisions of a number oj measuring instruments oil the basis oj'observations onl a common group q/specimnens is examined in both its structural and its functional relationship Jbrns. It is shown',i that Barrzett's (1969) structural relationship version of the problem is equivalent to a model usedjo/b mental test scores, itself a particular case of the standard Jactor anal 'sis model. Maximum likelihood estimation is consideredJbr this and certain constrained models. Williams's (1969) attempt at deriving maximnumn likelihood estimators Jbr the juinctional relationship version is shown to be unworkable, but a consistent method of estimation is suggested. Barnlett's data onl the comparison of twvo instruments Jbr measuring human lung capacity are re-analJvsed.