Ed231A
Multivariate Analysis
Linear Structural Models

It's Greek to me

Β - beta
η - eta
ξ - xi
ζ - zeta
Γ - gamma
Λ - lambda (upper case)
λ - lambda (lower case)
δ - delta
ε - epsilon

Structural Equation Model

Notation

  • Β - coefficients of effects among endogenous variables.
  • Γ - coefficients of effects of exogeneous variables on endogenous variables.
  • η - vector of latent endogenous variables.
  • ξ - vector of latent exogenous variables.
  • ζ - vector of residuals or errors.

    Measurement Model

    Notation

  • y - vector of measures of dependent variables.
  • Λy - matrix of coefficients or loadings of y on the latent endogenous variables.
  • η - vector of latent endogenous variables.
  • ε - vector of errors of measurement of y.
  • x - vector of measures of predictor variables.
  • Λx - matrix of coefficients or loadings of x on the latent exogenous variables.
  • ξ - vector of latent exogenous variables.
  • δ - vector of errors of measurement of x.

    Example with Full Notation

    In Mplus the above model would be written as follows: 

    
MODEL:
* measurement model/confirmatory factor analysis
  xi1  by   x1 x2 x3;
  xi2  by   x4 x5;
  eta1 by   y1 y2;
  eta2 by   y2 y3 y4;
  
* structural model
  xi1  with xi2;
  eta1 on   xi1;
  eta2 on   xi2 eta1;

    Ed231A Page
    UCLA Department of Education

    Phil Ender, 30nov05, 19Feb98