A GENERAL METHOD FOR ESTIMATING A LINEAR STRUCTURAL EQUATION SYSTEM*

TLDR

The paper introduces a general method for estimating unknown coefficients in linear structural equation systems and examines two special cases separately. The method handles errors in equations and variables, estimating residual variance–covariance and measurement error variances, and includes special cases with only equation errors or only variable errors. The approach is demonstrated on artificial, economic, and psychological data.

Abstract

ABSTRACT A general method for estimating the unknown coefficients in a set of linear structural equations is described. In its most general form the method allows for both errors in equations (residuals, disturbances) and errors in variables (errors of measurement, observational errors) and yields estimates of the residual variance‐covariance matrix and the measurement error variances as well as estimates of the unknown coefficients in the structural equations, provided all these parameters are identified. Two special cases of this general method are discussed separately. One is when there are errors in equations but no errors in variables. The other is when there are errors in variables but no errors in equations. The methods are applied and illustrated using artificial, economic and psychological data.