Biostatistics | Center for Clinical and Translational Science
  1. Biostatistics Core
  2. /
  3. Biostatistics Resources
  4. /
  5. By Project Phase
  6. /
  7. Analysis and Reporting
  8. /
  9. Goodness of Fit

Goodness of Fit

This page includes publications and tools that our consultants have found useful. The resource list can be downloaded in PDF and BibTeX format at the bottom of this page. For more information on this topic, including advice about how to apply it in your research, consider scheduling a consultation with a biostatistician.

While we hope this resource list serves as a helpful starting point for other researchers, we provide no guarantee of its comprehensiveness or of the accuracy or reliability of the works cited. If you have concerns or suggestions to improve this page, please contact us.

Resources

Cameron, A. Colin and Frank A.G. Windmeijer (1997). “An R-squared measure of goodness of fit for some common nonlinear regression models”. In: Journal of Econometrics 77.2, pp. 329-342. DOI: 10.1016/s0304-4076(96)01818-0. https://doi.org/10.1016/s0304-4076(96)01818-0.

Cox, David R. and E. J. Snell (1989). The analysis of binary data. 2nd. London: Chapman & Hall.

Delgado, Miguel A., Javier Hidalgo, and Carlos Velasco (2005). “Distribution free goodness-of-fit tests for linear processes”. In: The Annals of Statistics 33.6. DOI: 10.1214/009053605000000606. https://doi.org/10.1214/009053605000000606.

Edwards, Lloyd J., Keith E. Muller, Russell D. Wolfinger, et al. (2008). “An R^2 statistic for fixed effects in the linear mixed model”. In: Statistics in Medicine 27.29, pp. 6137-6157. DOI: 10.1002/sim.3429. https://doi.org/10.1002/sim.3429.

Efron, Bradley (1978). “Regression and ANOVA with Zero-One Data: Measures of Residual Variation”. In: Journal of the American Statistical Association 73.361, pp. 113-121. DOI: 10.1080/01621459.1978.10480013. https://doi.org/10.1080/01621459.1978.10480013.

Fagerland, Morten W. and David W. Hosmer (2017). “How to Test for Goodness of Fit in Ordinal Logistic Regression Models”. In: The Stata Journal: Promoting communications on statistics and Stata 17.3, pp. 668-686. DOI: 10.1177/1536867x1701700308. https://doi.org/10.1177/1536867x1701700308.

Gelman, Andrew, Ben Goodrich, Jonah Gabry, et al. (2019). “R-squared for Bayesian Regression Models”. In: The American Statistician 73.3, pp. 307-309. DOI: 10.1080/00031305.2018.1549100. https://doi.org/10.1080/00031305.2018.1549100.

Jaeger, Byron C., Lloyd J. Edwards, Kalyan Das, et al. (2016). “An R^2 statistic for fixed effects in the generalized linear mixed model”. In: Journal of Applied Statistics 44.6, pp. 1086-1105. DOI: 10.1080/02664763.2016.1193725. https://doi.org/10.1080/02664763.2016.1193725.

Jaeger, Byron C., Lloyd J. Edwards, and Matthew J. Gurka (2018). “An R^2 statistic for covariance model selection in the linear mixed model”. In: Journal of Applied Statistics 46.1, pp. 164-184. DOI: 10.1080/02664763.2018.1466869. https://doi.org/10.1080/02664763.2018.1466869.

Jiménez-Gamero, M. Dolores, Sangyeol Lee, and Simos G. Meintanis (2019). “Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models”. In: TEST 29.3. GARCH and autoregressive conditional duration models., pp. 682-703. DOI: 10.1007/s11749-019-00676-0. https://doi.org/10.1007/s11749-019-00676-0.

Johnson, Paul C.D. (2014). “Extension of Nakagawa & Schielzeth’s R^2-GLMM to random slopes models”. In: Methods in Ecology and Evolution 5.9. Ed. by Robert B. O’Hara, pp. 944-946. DOI: 10.1111/2041-210x.12225. https://doi.org/10.1111/2041-210x.12225.

Maddala, G. S. (1983). Limited-dependent and qualitative variables in econometrics. Cambridge: Cambridge University Press.

Magee, Lonnie (1990). “R^2 Measures Based on Wald and Likelihood Ratio Joint Significance Tests”. In: The American Statistician 44.3, p. 250. DOI: 10.2307/2685352. https://doi.org/10.2307/2685352.

Nagelkerke, N. J. D. (1991). “A note on a general definition of the coefficient of determination”. In: Biometrika 78.3, pp. 691-692. DOI: 10.1093/biomet/78.3.691. https://doi.org/10.1093/biomet/78.3.691.

Nakagawa, Shinichi and Holger Schielzeth (2012). “A general and simple method for obtaining R^2 from generalized linear mixed-effects models”. In: Methods in Ecology and Evolution 4.2. Ed. by Robert B. O’Hara, pp. 133-142. DOI: 10.1111/j.2041-210x.2012.00261.x. https://doi.org/10.1111/j.2041-210x.2012.00261.x.

Pan, Zhiying and D. Y. Lin (2005). “Goodness-of-Fit Methods for Generalized Linear Mixed Models”. In: Biometrics 61.4, pp. 1000-1009. DOI: 10.1111/j.1541-0420.2005.00365.x. https://doi.org/10.1111/j.1541-0420.2005.00365.x.

Peng, Heng and Ying Lu (2012). “Model selection in linear mixed effect models”. In: Journal of Multivariate Analysis 109, pp. 109-129. DOI: 10.1016/j.jmva.2012.02.005. https://doi.org/10.1016/j.jmva.2012.02.005.

Piepho, Hans-Peter (2018). A Coefficient of Determination (R^2) for Linear Mixed Models. DOI: 10.48550/ARXIV.1805.01124. https://arxiv.org/abs/1805.01124.

Piepho, Hans-Peter (2019). “A coefficient of determination (R^2) for generalized linear mixed models”. In: Biometrical Journal. DOI: 10.1002/bimj.201800270. https://doi.org/10.1002/bimj.201800270.

Rights, Jason D. and David A. Cole (2018). “Effect Size Measures for Multilevel Models in Clinical Child and Adolescent Research: New R-Squared Methods and Recommendations”. In: Journal of Clinical Child & Adolescent Psychology 47.6, pp. 863-873. DOI: 10.1080/15374416.2018.1528550. https://doi.org/10.1080/15374416.2018.1528550.

Rights, Jason D. and Sonya K. Sterba (2019). “New Recommendations on the Use of R-Squared Differences in Multilevel Model Comparisons”. In: Multivariate Behavioral Research 55.4, pp. 568-599. DOI: 10.1080/00273171.2019.1660605. https://doi.org/10.1080/00273171.2019.1660605.

Tang, Min, Eric V. Slud, and Ruth M. Pfeiffer (2014). “Goodness of fit tests for linear mixed models”. In: Journal of Multivariate Analysis 130, pp. 176-193. DOI: 10.1016/j.jmva.2014.03.012. https://doi.org/10.1016/j.jmva.2014.03.012.

Zhang, Dabao (2017). “A Coefficient of Determination for Generalized Linear Models”. In: The American Statistician 71.4, pp. 310-316. DOI: 10.1080/00031305.2016.1256839. https://doi.org/10.1080/00031305.2016.1256839.

Zhang, Dabao (2020). Coefficients of determination for generalized linear mixed models. Technical Report 20-01. Department of Statistics: Purdue University. https://www.stat.purdue.edu/research/technical-reports/docs/tr20-01.pdf.

Zheng, Beiyao (2000). “Summarizing the goodness of fit of generalized linear models for longitudinal data”. In: Statistics in Medicine 19.10, pp. 1265-1275. DOI: 10.1002/(sici)1097-0258(20000530)19:10<1265::aid-sim486>3.0.co;2-u. https://doi.org/10.1002/(sici)1097-0258(20000530)19:10%3C1265::aid-sim486%3E3.0.co;2-u.

Zheng, Yao, Wai Keung Li, and Guodong Li (2017). “A robust goodness-of-fit test for generalized autoregressive conditional heteroscedastic models”. In: Biometrika 105.1, pp. 73-89. DOI: 10.1093/biomet/asx063. https://doi.org/10.1093/biomet/asx063.

Attachments