Tuesday, August 9, 2011

Estimates in LISREL output

Parameter estimates

"In LISREL 7 there are two kinds of standardized solutions: SS (Standardized Solution) and SC (Completely Standardized Solution). In the SS solution the latent variables are scaled to have standard derivations equal to unity; the observed variables are left in their original metric. In the SC solution, the observed as well as the latent variables are standardized."*

For tau (intercepts), a standardized solution is not provided. However, tau does depends on the scale of the observed variable (and on other model parameters). So some kind of standardized solution would be informative.

Obviously, for lambda (factor loadings), standardized and completely standardized solutions are printed, as it depends on the scale of observed and latent variables. For theta-epsilon, only completely standardized estimates are printed, as it only depends on the scale of the observed variables (unstandardized theta epsilon is the (co)variances of the observed variables, unexplained by the factor).

Indicators for model modifications

"When a model does not fit well, the modification indices will often be the most useful way of deciding how to change the model to improve the fit. They give an estimate of how much the chi-square will decrease if a fixed parameter is freed."*

A fitted residual is the observed mean or (co)variance (provided in LISREL input), minus the model implied mean and (co)variance.

"A standardized residual is a fitted residual divided-by the large-sample standard error of the residual."*

Expected change is the predicted estimated change in the parameter when set free, for fixed parameters. I'm not sure by what values expected change is divided to obtain the (completely) standardized estimated change.

* Taken from: Jöreskog, K., & Sörbom, D. (1996). LISREL 8: User's reference guide. Chicago, IL: Scientifi c Software International, Inc.

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