lecture3_s10 preliminaries

# Lecture3_s10 - Notation and preliminaries Psychology 588 Covariance structure and factor models Notation for path diagrams x1 1 1 2 observed

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Notation and preliminaries Psychology 588: Covariance structure and factor models Jan 27, 2010

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Notation for path diagrams 2 observed variables x 1 ξ 1 latent variables causal path or factor loading/weight covariance or unconstrained (nonzero) relationship between exogenous variables δ 1 error terms (unenclosed)
Multiple regression 3 11 2 2 33 yb x b x b x e e =+ + + bx x1 x2 x3 y e b 1 b2 3 1 • How could the intercept term enter into the diagram?

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Principal component model (rank-reduced) () cov =+ xA fe A Θ • 2 orthogonal components fitted to 4 manifest variables • Rotationally indeterminant if no component loadings are constrained (e.g., to zero) f1 x1 e1 a 1 1 x2 e2 2 1 f2 x3 e3 x4 e4 3 1 4 1
LISREL notation 5 • Like the standard matrix notation, the LISREL notation uses Lower italic: a scalar (as a variable or a parameter; cf . X ) Lower bold: vector Upper bold: matrix • Uses Roman letters only for observed (or manifest, indicator) variables (e.g., x , y ) and Greek letters for all others (i.e., latent variables and model parameters; ξ , Γ ) • Distinguishes between exogenous (independent) vs. endogenous (dependent) variables parts ¾ We will consider later an alternative notation and model representation --- the reticular action model (RAM, chap. 9)

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Notation for latent variables 6 Symbol size Definition Variables ξ n ×1 latent exogenous variables η m latent endogenous variables ζ m specification error terms Coefficients Γ m × n coefficient matrix for ξ Β m × m coefficient matrix for η Covariance matrix Φ n × n covariance matrix of ξ , E ( ξξ ' ) Ψ m × m covariance matrix of ζ , E ( ζζ ' )
Notation for measurement models 7 Symbol size Definition variables x q ×1 observed indicators of ξ y p

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## This note was uploaded on 06/11/2010 for the course PSYC 588 taught by Professor Sunjinghong during the Spring '10 term at University of Illinois at Urbana–Champaign.

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Lecture3_s10 - Notation and preliminaries Psychology 588 Covariance structure and factor models Notation for path diagrams x1 1 1 2 observed

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