A Note on the Maximum Likelihood Estimation of a Linear Structural Relationship

Abstract

It is shown that the maximum likelihood estimate of a structural relationship line with uncorrelated errors is usually the same when both error variances are known as when only the ratio is known though exceptionally the slope of the line may be indeterminate. It is also shown how the equations given by Madansky [2] for the maximum likelihood estimates in the case when one error variance is known needs to be modified when, under certain circumstances, they are inconsistent.