An iterative method for the computation of the correlation matrix implied by a recursive path model

Abstract

In Path Analysis, especially in social sciences studies, many researchers usually assume that errors in the model are uncorrelated with all exogenous variables as well as with each other. These assumptions, in most cases, are not valid in reality and were introduced to facilitate the model estimation. This article establishes a new algorithm for the computation of the correlation matrix implied by a recursive path model that overcomes these drawbacks. We compare our algorithm to two other methods used in the literature. The comparison was made mathematically through an illustrated example and numerically with a simulation study. The findings show that, unlike the classical methods, the proposed method gives more accurate results.