Open AccessGAUSS‐SEIDEL COMPUTING PROCEDURES FOR A FAMILY OF FACTOR ANALYTIC SOLUTIONS *
Author(s) -
Browne Michael
Publication year - 1968
Publication title -
ets research bulletin series
Language(s) - English
Resource type - Journals
eISSN - 2333-8504
pISSN - 0424-6144
DOI - 10.1002/j.2333-8504.1968.tb01003.x
Subject(s) - gauss–seidel method , mathematics , residual , gauss , factor (programming language) , least squares function approximation , maximum likelihood , value (mathematics) , mathematical optimization , calculus (dental) , iterative method , algorithm , computer science , statistics , physics , medicine , quantum mechanics , estimator , programming language , dentistry
Gauss‐Seidel computing procedures have previously been used to obtain Maximum Likelihood and Minres factor analytic solutions. This paper is concerned with the use of Gauss‐Seidel computing procedures to obtain five solutions: Maximum Likelihood, Minres, Alpha and two recently derived weighted least squares solutions. The treatment of negative residual variances is considered, modifications of approaches suggested by Harman and Fukuda [1966] and by Jöreskog [1967a] being used. Three “generalized characteristic value” problems occur and procedures for solving them are provided. Finally, examples of the application of the Gauss‐Seidel procedures are given and are used to illustrate properties of the five factor analytic solutions.