A numerical value that expresses how badly a structural model reproduces the observed data. The larger the value of the discrepancy function, the worse (in some sense) the fit of model to data. In general, the parameter estimates for a given model are selected to make a discrepancy function as small as possible.

The discrepancy functions employed in Structural Equation Modeling all satisfy the following basic requirements:

They are non-negative, i.e., always greater than or equal to zero.

They are zero only if fit is perfect, i.e., if the model and parameter estimates perfectly reproduce the observed data.

The discrepancy function is a continuous function of the elements of S, the sample covariance matrix, and S(q), the "reproduced" estimate of S obtained by using the parameter estimates and structural model.