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Coefficients of Determination in Logistic Regression Models—A New Proposal: The Coefficient of Discrimination
Abstract
Many analogues to the coefficient of determination R2 in ordinary regression models have been proposed in the context of logistic regression. Our starting point is a study of three definitions related to quadratic measures of variation. We discuss the properties of these statistics, and show that the family can be extended in a natural way by a fourth statistic with an even simpler interpretation, namely the difference between the averages of fitted values for successes and failures, respectively. We propose the name “the coefficient of discrimination” for this statistic, and recommend its use as a standard measure of explanatory power. In its intuitive interpretation, this quantity has no immediate relation to the classical versions of R2, but it turns out to be related to these by two exact relations, which imply that all these statistics are asymptotically equivalent.
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Summarizing the predictive power of a generalized linear model
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A general and simple method for obtaining R 2 from generalized linear mixed‐effects models
Nakagawa, S., & Schielzeth, H. (2013) · Methods in Ecology and Evolution · doi:10.1111/j.2041-210x.2012.00261.x · Cited by 10,356
R-squared for Bayesian Regression Models
Gelman, A., Goodrich, B., Gabry, J., & Vehtari, A. (2019) · The American Statistician · doi:10.1080/00031305.2018.1549100 · Cited by 912
Joint Species Distribution Modelling: With Applications in R
Ovaskainen, O., & Abrego, N. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108591720 · Cited by 394
Pencina, M. J., D'Agostino, R. B., & Demler, O. V. (2012) · Statistics in Medicine · doi:10.1002/sim.4348 · Cited by 349
GANalyze: Toward Visual Definitions of Cognitive Image Properties
Goetschalckx, L., Andonian, A., Oliva, A., & Isola, P. (2019) · 2019 IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2019.00584 · Cited by 283
Metadata
- Authors
- Tjur, T.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 2009-11
- Volume
- 63
- Issue
- 4
- Pages
- 366-372
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W2062863260
- Cited by
- 911
- References
- 10
- FWCI
- 1.91
- Type
- journal article
- Language
- en
- Open access
- closed
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