AMOS, like other SEM packages offers standardized and unstandardized estimates of the parameters. What is the difference? Are unstandardized estimates based on the covariance matrix and standarized on the correlation matrix? Or is it something else?
Solved – the difference between standardized and unstandardized estimates in SEM (thinking of AMOS in particular)
structural-equation-modeling
Best Answer
I don't think the currently accepted answer is correct. What it describes is identification, not standardization. The unstandardized coefficients is what comes directly out of the estimation procedure. The standardized coefficients recast regression coefficients and covariance in metrics of correlations, and unique variances, in terms of $R^2$. So if you have a confirmatory factor analysis model $$ y_j = \alpha_j + \lambda_j \xi + \delta_j $$ with ${\rm E}\delta_j=0$, ${\rm E}\delta_j^2 = \psi_j$, ${\rm E}\xi=0$, ${\rm E}\xi^2=\phi$ in the standard SEM notation, then we have ${\rm Var}[y_j] = \lambda_j^2 \phi + \psi_j$, and the standardized coefficients are: $\tilde\alpha_j-$irrelevant; $$ \tilde\lambda_j = {\rm Corr}(y_j,\xi) = \lambda_j {\rm Var}^{1/2}[\xi] {\rm Var}^{-1/2}[y_j]=\frac{\lambda_j \phi^{1/2}}{\sqrt{\lambda_j^2 \phi + \psi_j}} $$ $$ \tilde \psi_j = \frac{\psi_j}{\lambda_j^2 \phi + \psi_j} $$ Unlike the ``raw'' estimates, standardized estimates and standard errors do not depend on particular parameterization and the choice of the identifying scale parameter (i.e., whether the model is identified by setting $\phi=1$ or one of $\lambda_j=1$ -- and is then independent of the choice of the particular scaling variable, provided $\lambda_j\neq0$ in population).