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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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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(img)], SEM estimation procedures minimize the residuals that are differences between the sample variances/covariances and the variances/covariances estimated from the model.

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

(1.8) equation

where img 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 ...

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