The class of Least Orthogonal Distance Estimator of structural parameters for SEM

Abstract

The aim of this paper is to present the results obtained on the class of Least Orthogonal Distance Estimator - full and limited infomation - of structural parameters for SEM. The LODE method of estimation has been derived under the consideration that the over-identifying restriction are nothing else but linear relations between variables affected by error (Naccarato and Pieraccini, 2008; Naccarato, 2007). The original form of LODE was based on characteristic roots and vectors, the simulation experiments conducted show that full information and limited information LODE works better than the other classical limited and full information estimators but in terms of variability the results wasn’t so good. In this work are presented some solution adopted to reduce the estimation variability, the first solution was based on a computational procedure links to the minimization of the trace of structural errors’ matrix Variance-Covariance and this procedure together with the result of the simulation experiment are in the chapter 2. Then - always to improve the LODE performance in terms of mean square error - it was developed a new version of LODE based on Singular Value Decomposition (chapter 4 and 5) instead of Spectral Decomposition, this because an algorithm based on SVD is numerically more robust respect to algorithm based on SD, where robustness means the greatest algorithm’s probability to converge (Markovsky and Van Huffel, 2007). The results of the new simulation adopting the LODE based on SVD better perfomances than the classical estimators both in terms of bias and variability.