On the Estimation Accuracy of the Total Effect Using Intermediate Characteristics

Abstract

When observed data is generated according to a linear structural equation model, this paper considers of estimating a total effect of a treatment on a quality characteristic using intermediate characteristics. Under the assumption that the treatment has an effect on the quality characteristic through a univariate intermediate characteristic, Cox (1960) showed that the estimation accuracy of the total effect based on the recursive regression model is superior to that based on the single regression model in the viewpoint of the asymptotic variance. In this paper, we extend the results of Cox (1960) to the case where there are several intermediate characteristics. In addition, we propose one of selection criteria for intermediate characteristics in the viewpoint of the estimation accuracy of the total effects and apply our results to a case study of the IC production process data.