GENERAL METHOD FOR ESTIMATING A LINEAR STRUCTURAL EQUATION SYSTEM (FROM STRUCTURAL EQUATION MODELS IN THE SOCIAL SCIENCES, 1973, BY ARTHUR S GOLDBERGER AND OTIS D DUNCAN - SEE NCJ-52004)

• NCJ Number: 52009
• Author(s): K G JORESKOG
• Date Published: 1973
• Length: 28 pages
• Sponsoring Agency: Russell Sage Foundation
• Corporate Author: Seminar Press, Inc
• Publication Format: Document
• Publication Type: Report (Study/Research)
• Language: English
• Country: United States of America
• Note: REVISION OF A PAPER PRESENTED AT A CONFERENCE COSPONSORED BY THE SOCIAL SCIENCE RESEARCH COUNCIL AND THE SOCIAL SYSTEMS RESEARCH INSTITUTE OF THE UNIVERSITY OF WISCONSIN, MADISON, NOV 12-16, 1970

Annotation

A METHOD IS DESCRIBED FOR ESTIMATING UNKNOWN COEFFICIENTS IN A SET OF LINEAR STRUCTURAL EQUATIONS THAT ALLOWS FOR ERRORS IN EQUATIONS AND ERRORS IN VARIABLES.

Abstract

BY ALLOWING PARAMETERS OF THE GENERAL MODEL TO BE FIXED, FREE, OR CONSTRAINED, GREAT FLEXIBILITY IS OBTAINED IN THAT THE METHOD CONTAINS A WIDE RANGE OF SPECIFIC MODELS. WHEN A MODEL IS SPECIFIED IN SUCH A WAY THAT EACH PARAMETER IS IDENTIFIED, THAT MODEL MAY BE ESTIMATED BY THE MAXIMUM-LIKELIHOOD METHOD BASED ON THE ASSUMPTION THAT OBSERVED VARIABLES HAVE A MULTINORMAL DISTRIBUTION. THE LIKELIHOOD FUNCTION IS NUMERICALLY MAXIMIZED USING THE DAVIDON-FLETCHER-POWELL METHOD AND AN INFORMATION MATRIX. WHEN ESTIMATES HAVE BEEN OBTAINED, THE MATRIX MAY BE USED TO COMPUTE STANDARD ERRORS OF ESTIMATED PARAMETERS. A SPECIAL CASE OF THE GENERAL MODEL OCCURS WHEN THERE ARE NO MEASUREMENT ERRORS IN OBSERVED VARIABLES. IN THE SPECIAL CASE, THE LIKELIHOOD FUNCTION IS BEST MINIMZED BY THE NEWTON-RAPHSON PROCEDURE. THERE IS ONE OBSERVED VARIABLE FOR EACH TRUE VARIABLE IN THE GENERAL MODEL. SEPARATE COMPUTER PROGRAMS HAVE BEEN WRITTEN FOR THE GENERAL MODEL AND FOR THE CASE OF NO MEASUREMENT ERRORS. MATHEMATICAL DERIVATIONS OF THE METHOD FOR ESTIMATING UNKNOWN COEFFICIENTS ARE CONTAINED IN AN APPENDIX. (DEP)