Structural Equation Modeling: Applications Using Mplus

7.2 Satorra and Saris's Method for Sample Size Estimation

Satorra and Saris (1985) proposed an approach to estimate statistical power for SEM models. The idea behind the method is when a model is misspecified (but not severely so) the model fit test statistic does not follow a central χ² distribution, but a noncentral χ² distribution. The model χ² statistic of the misspecified model can be considered as an approximation of the noncentrality parameter () of the noncentral χ² distribution (note, the here is not the that denotes factor loadings in our CFA models). Once the parameter has been estimated, statistical power can be obtained either from a table for noncentral χ² distribution for specific degrees of freedom and level (Saris and Stonkhorst, 1984) or calculated using statistical packages, such as SAS or SPSS (Brown, 2006; http://www.statmodel.com/power.shtml).

Several steps are followed in application of Satorra and Saris's method to estimate statistical power and thus sample size ...