Generalizing the properties of Finite Iterative Method for the Computation of the Covariance Matrix Implied by a Recursive Path Model

Abstract

In this paper, we generalize the properties of the correlation matrix implied bya recursive path model using the Finite Iterative Method into the covariance case wherevariables are no more supposed to be standardized. We demonstrate that the implied co-variance matrix computed using the Finite Iterative Method is affine with respect to themodel parameters. Moreover, many other properties derive from this affinity and will be usedto simplify the computation of the first as well as the second derivatives of the UnweightedLeast Square Function used as an objective function in the estimation of the model param-eters. Illustrated and numerical examples are given to show the advantage of the proposedproperties as an alternative to the classical approximation used to compute the aforemen-tioned derivatives.