Discrepancy function

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.[1] 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.

See also

References

  1. ^ "Discrepancy Functions Used in SEM". Archived from the original on 2008-08-21. Retrieved 2008-08-18.
Stub icon

This statistics-related article is a stub. You can help Wikipedia by adding missing information.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.