Structural Equation Modeling: Applications Using Mplus

1.3 Model Estimation

Estimation of SEM models is different from that of multiple regressions. Instead of minimizing the discrepancies between the fitted and observed values of the response variable [i.e., Σ()], SEM estimation procedures minimize the residuals that are differences between the sample variances/covariances and the variances/covariances estimated from the model.

Let use to denote the population covariance matrix of observed variables y and x; can be expressed as a function of free parameters in a hypothesized model (Appendix 1.A). The basic hypothesis in SEM is:

(1.8)

where is the model implied variance/covariance matrix; that is, the variance/covariance matrix implied by the population parameters for the hypothesized model. The purpose of model estimation or model fit is to find a set of model parameters to produce so that [ − ] can be minimized. The discrepancy between ...