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IDENTIFICATION PROBLEM FOR STRUCTURAL EQUATION MODELS WITH UNMEASURED VARIABLES (FROM STRUCTURAL EQUATION MODELS IN THE SOCIAL SCIENCES, 1973, BY ARTHUR S GOLDBERGER AND OTIS D DUNCAN - SEE NCJ-52004)

NCJ Number
52008
Author(s)
D E WILEY
Date Published
1973
Length
15 pages
Annotation
A GENERAL FRAMEWORK FOR CONSIDERING MODELS WITH ERROR IN MEASURED VARIABLES THAT WERE NOT MEASURED DIRECTLY IS PRESENTED, AND A STRATEGY TO INCORPORATE MEASUREMENT AND STRUCTURAL PARAMETERS IS PROPOSED.
Abstract
A PRIMARY SPECIFICATION THAT SHOULD BE MADE IN BUILDING A CAUSAL MODEL IS THE DESIGNATION OF EACH TERM IN THE MODEL AS EITHER A RANDOM VARIABLE OR A FIXED CONSTANT. THE USUAL PRACTICE IN IMPLEMENTING A STRUCTURAL MODEL IS TO STANDARDIZE SCORES OF RANDOM VARIABLES SO THEY HAVE A MEAN OF ZERO AND UNIT VARIANCE IN THE SAMPLE. A GENERAL STRATEGY FOR THE DESIGN OF RESEARCH STUDIES IS SUGGESTED THAT ASSURES THE IDENTIFICATION OF RELEVANT STRUCTURAL PARAMETERS. IT CONSISTS OF GENERATING TWO NOMINALLY PARALLEL MEASUREMENTS FOR EACH LATENT EXOGENOUS VARIABLE. NOMINALLY PARALLEL MEASUREMENTS HAVE TWO PROPERTIES: THEIR LATENT VARIABLES ARE LINEARLY DEPENDENT AND THEIR MEASUREMENT ERRORS ARE INDEPENDENT. AN EXAMPLE OF A RECURSIVE MODEL TO EXPLORE THE EFFECTS OF VARIOUS ASSUMPTIONS ON IDENTIFICATION AND ESTIMATION, WITH AND WITHOUT THE PRESENCE OF MEASUREMENT ERROR, AND AN EXAMPLE OF A RECURSIVE MODEL WITH AN UNMEASURED VARIABLE ARE PRESENTED. A GENERAL MODEL FOR A SIMULTANEOUS EQUATION SYSTEM IN THE PRESENCE OF MEASUREMENT ERROR AND UNMEASURED VARIABLES IS THEN INTRODUCED. GENERAL REQUIREMENTS FOR IDENTIFICATION IN SIMULTANEOUS EQUATION MODELS ARE LACK OF COLLINEARITY IN EXOGENOUS VARIABLES AND RANK AND ORDER CONDITIONS. PROCEDURES FOR TENTATIVELY DETERMINING THE IDENTIFIABILITY OF A COMPLETE MODEL ARE OUTLINED: CALCULATE A DERIVATIVE MATRIX ALGEBRAICALLY, SUBSTITUTE SOME REASONABLE NUMERICAL VALUES FOR PARAMETERS, AND EVALUATE THE RANK OF THE RESULTING MATRIX. SUPPORTING EQUATIONS ARE GIVEN. (DEP)