Discrepancy function
Open-knowledge reference entry
In structural equation modeling, a discrepancy function is a mathematical function which describes how closely a structural model conforms to observed data; it is a measure of goodness of fit. 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. Analogous concepts in statistics are known as goodness of fit or statistical distance, and include deviance and divergence.
Examples
There are several basic types of discrepancy functions, including maximum likelihood (ML), generalized least squares (GLS), and ordinary least squares (OLS), which are considered the "classical" discrepancy functions. 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.
In order for "maximum likelihood" to meet the first criterion, it is used in a revised form as the deviance.
This brief starts where responsible research should: with the source description of “Discrepancy function” as open-knowledge reference entry. Everything that follows is an evidence route, not borrowed authority.
Why this record matters
The subject matters to the general reference register because the source frames it as open-knowledge reference entry. Its deeper value depends on whether names, dates, institutions and citations support that framing.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Feb 3, 2024. The linked authority identifier is Q5282031. None of the 0 selected statements returned an explicit reference.
A concise general-reference account can conceal disagreements about scope, terminology or the weight assigned to individual sources. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “Discrepancy function”, its source revision and the description used here.
- Expand the search: follow Discrepancy function primary sources, Discrepancy function archive and Discrepancy research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “Discrepancy function”?
- Which cited source is closest to the event, object or claim?
- What terminology or title could unlock a more precise catalogue search?
Search terms from this dossier
This entry incorporates text from “Discrepancy function” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.