Structural model estimation with correlated measurement errors

Abstract

Maximum likelihood estimators for model parameters in linear structural relationships having correlated measurement errors are presented. Comparisons between asymptotic mean squared errors of least squares and maximum likelihood estimators of the slope parameter indicate that the least squares estimator is only preferable when the slope parameter is sufficiently small relative to the ratio of error standard deviations; however, unlike structural relationships having independent measurement errors, the region of preference is not simply given by an upper bound on this scaled slope parameter.