By J. (John) Scott Long
Whereas many readers can be unusual with the complete complexity of the covariance constitution version, many could have mastered at the least one in all its elements - every one of that's a strong and famous statistical method in its personal correct. the 1st is the confirmatory issue version often utilized in psychometrics; the second one, the structural equation version, is commonplace to econometricians. The dialogue during this quantity could be rather precious for estimating versions with equality constraints and correlated mistakes throughout a few yet now not all equations. the ultimate bankruptcy incorporates a consultant to suitable software program programs.
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Additional info for Covariance Structure Models: An Introduction to LISREL (Quantitative Applications in the Social Sciences)
The first component is the confirmatory factor model considered in psychometrics; the second component is the structural equation model considered in econometrics. This monograph is designed to take advantage of a reader's familiarity with one or both of these components. The reader is assumed to be familiar with the confirmatory factor model and the mathematical tools presented in a companion volume in the Sage Series on Quantitative Applications in the Social Sciences: Confirmatory Factor Analysis: A Preface to LISREL.
The observed x's and y's can be correlated. Their covariances are contained in the (q × p) matrix Sxy, whose (i,j)th element is the covariance between xi and yj. Similarly, the exogenous x-factors and endogenous h-factors can be correlated. Their covariances are contained in the (s × r) matrix COV(x,h), or the (r × s) matrix COV(h,x). Just as the unique factors are assumed to be uncorrelated with the common factors in their own factor equation, they are assumed to be uncorrelated with the common factors in the other equation.
3 would be written as h1 = g11x1 + g12x2 + z1 More realistic models are constructed using multiple equation systems, both with and without reciprocal causation. 2. This model states that the observed variable h1 is causally determined by the observed variables h2, x1, and x2. That these three variables do not perfectly explain h1 is reflected by the error in equation z1. Similarly, h2 is causally determined by h1, x2 and x3, with an error in equation z2. These structural relations would be written as In its general form the structural equations are written as Page 16 where h is a vector of observed dependent variables measured without error; x is a vector of observed independent variables measured without error; z is a vector of errors in equations; B is a matrix of coefficients relating the dependent variables to one another; and G is a matrix of coefficients relating the independent variables to the dependent variables.