The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
A Coefficient of Determination for Generalized Linear Models
Abstract
The coefficient of determination, a.k.a. R2, is well-defined in linear regression models, and measures the proportion of variation in the dependent variable explained by the predictors included in the model. To extend it for generalized linear models, we use the variance function to define the total variation of the dependent variable, as well as the remaining variation of the dependent variable after modeling the predictive effects of the independent variables. Unlike other definitions that demand complete specification of the likelihood function, our definition of R2 only needs to know the mean and variance functions, so applicable to more general quasi-models. It is consistent with the classical measure of uncertainty using variance, and reduces to the classical definition of the coefficient of determination when linear regression models are considered.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
A new look at the statistical model identification
Akaike, H. (1974) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1974.1100705 · Cited by 51,879
Estimating the Dimension of a Model
Schwarz, G. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344136 · Cited by 47,033
Limited-dependent and qualitative variables in econometrics
Maddala, G. S. (1983) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810176 · Cited by 13,240
Advances in Neural Information Processing Systems 25
Zhang, Y., Sutton, C. A., Storkey, A., & Zoubin Ghahramani, A. (2012) · Cited by 12,653
A note on a general definition of the coefficient of determination
NAGELKERKE, N. J. D. (1991) · Biometrika · doi:10.1093/biomet/78.3.691 · Cited by 5,927
(1947) · The American Statistician · doi:10.1080/00031305.1947.10501534 · Cited by 3,660
An Introduction to Categorical Data Analysis
Musiol, G. (1997) · Computational Statistics & Data Analysis · doi:10.1016/s0167-9473(97)84760-3 · Cited by 1,960
Sirinukunwattana, K., Raza, S. E. A., Tsang, Y.-W., Snead, D. R. J., Cree, I. A., & Rajpoot, N. M. (2016) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2016.2525803 · Cited by 1,224
An R-squared measure of goodness of fit for some common nonlinear regression models
Colin Cameron, A., & Windmeijer, F. A. G. (1997) · Journal of Econometrics · doi:10.1016/s0304-4076(96)01818-0 · Cited by 1,180
Cited by
Chicco, D., Warrens, M. J., & Jurman, G. (2021) · PeerJ Computer Science · doi:10.7717/peerj-cs.623 · Cited by 5,380
Integrating gene annotation with orthology inference at scale
Kirilenko, B. M., Munegowda, C., Osipova, E., Jebb, D., Sharma, V., Blumer, M., Morales, A. E., Ahmed, A.-W., Kontopoulos, D.-G., Hilgers, L., et al. (2023) · Science · doi:10.1126/science.abn3107 · Cited by 209
Guo, P., Meng, W., Xu, M., Li, V. C., & Bao, Y. (2021) · Materials · doi:10.3390/ma14123143 · Cited by 114
Metadata
- Authors
- Zhang, D.
- Venue
- The American Statistician
- Publisher
- Informa UK Limited
- Published
- 2017-10-02
- Volume
- 71
- Issue
- 4
- Pages
- 310-316
- ISSN
- 0003-1305 (ISSN-L)
- 1537-2731
- OpenAlex
- W2565739165
- Cited by
- 444
- References
- 14
- FWCI
- 10.71
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A Coefficient of Determination for Generalized Linear Models. https://app.cochat.ai/papers/10.1080/00031305.2016.1256839
- The paper
- Zhang, D. (2017). A Coefficient of Determination for Generalized Linear Models. The American Statistician. https://doi.org/10.1080/00031305.2016.1256839
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
