IBM® SPSS® Amos™ 28

Steiger and Lind (1980) introduced the use of the population discrepancy function as a measure of model adequacy. The population discrepancy function, , is the value of the discrepancy function obtained by fitting a model to the population moments rather than to sample moments. That is,

in contrast to

.

Steiger, Shapiro and Browne (1985) showed that under certain conditions has a noncentral chi-square distribution with d degrees of freedom and noncentrality parameter . The Steiger-Lind approach to model evaluation centers around the estimation of and related quantities.

The present discussion of measures related to the population discrepancy relies mainly on Steiger and Lind (1980) and Steiger, Shapiro and Browne (1985). The notation is based on Browne and Mels (1992).