Extending El-Hadri-Sahli-Hanafi procedure for path analysis with non standardized variables

Path analysis is a powerful statistical technique for studying both the direct and indirect causal relationships among observed variables. The estimation step is the core of the whole modeling process. It is conventionally performed using the well-known BFGS procedure, especially when the variables are standardized. Recently, a new alternative procedure has been introduced by El Hadri, Sahli and Hanafi. This new procedure possesses remarkable convergence properties, including monotone convergence and convergence of the error toward zero. Furthermore, it is faster in practice than the BFGS procedure. However, these properties have been proven only in the case of standardized variables. Given that the general case of non standardized variables is more prevalent and important, this limitation hinders its broader application. The present paper extends the new procedure to the case of non standardized variables. On the theoretical level, we show that the monotone convergence and the convergence of the error are maintained. On the practical level, several simulations show that the parameters obtained by the proposed procedure are close to those provided by the R lavaan package.