Discrepancy function

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A discrepancy function is a mathematical function which describes how closely a structural model conforms to observed data. Larger values of the discrepancy function indicate a poor fit of the model to data. In general, the parameter estimates for a given model are chosen so as to make the discrepancy function for that model as small as possible.^[1]

There are several basic types of discrepancy functions, including Maximum Likelihood (ML), Generalized Least Squares (GLS), and Uweighted Least Squares (ULS), which are considered the "classical" discrepancy functions.^[2] Discrepancy functions all meet the following basic criteria:

• They are non-negative, i.e., always greater than or equal to zero.
• They are zero only if the 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 Σ(θ), the "reproduced" estimate of S obtained by using the parameter estimates and the structural model.^[1]

[edit] References

1. ^ ^{a b} Department of Chemistry and Biochemistry at Florida State University. Retrieved on September 10, 2006.
2. ^ Discrepancy Functions Used in SEM. Retrieved on September 10, 2006.

[edit] See also

• Low-discrepancy sequence
• Constructions of low-discrepancy sequences