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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
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)

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