Coefficients of Determination in Logistic Regression Models—A New Proposal: The Coefficient of Discrimination

@article{Tjur2009CoefficientsOD,
  title={Coefficients of Determination in Logistic Regression Models—A New Proposal: The Coefficient of Discrimination},
  author={Tue Tjur},
  journal={The American Statistician},
  year={2009},
  volume={63},
  pages={366 - 372}
}
  • T. Tjur
  • Published 2009
  • Mathematics
  • The American Statistician
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… Expand
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References

SHOWING 1-10 OF 12 REFERENCES
Coefficients of Determination for Multiple Logistic Regression Analysis
Abstract Coefficients of determination for continuous predicted values (R 2 analogs) in logistic regression are examined for their conceptual and mathematical similarity to the familiar R 2 statisticExpand
An R-squared measure of goodness of fit for some common nonlinear regression models
Abstract For regression models other than the linear model, R -squared type goodness-of-fit summary statistics have been constructed for particular models using a variety of methods. We propose an RExpand
Summarizing the predictive power of a generalized linear model.
This paper studies summary measures of the predictive power of a generalized linear model, paying special attention to a generalization of the multiple correlation coefficient from ordinary linearExpand
A Comment on the Coefficient of Determination for Binary Responses
Abstract Linear logistic or probit regression can be closely approximated by an unweighted least squares analysis of the regression linear in the conditional probabilities provided that theseExpand
A comparison of goodness-of-fit tests for the logistic regression model.
TLDR
An examination of the performance of the tests when the correct model has a quadratic term but a model containing only the linear term has been fit shows that the Pearson chi-square, the unweighted sum-of-squares, the Hosmer-Lemeshow decile of risk, the smoothed residual sum- of-Squares and Stukel's score test, have power exceeding 50 per cent to detect moderate departures from linearity. Expand
Applied Logistic Regression
TLDR
Applied Logistic Regression, Third Edition provides an easily accessible introduction to the logistic regression model and highlights the power of this model by examining the relationship between a dichotomous outcome and a set of covariables. Expand
On Measures of Monotone Association
Abstract A family of coefficients for measuring monotone association is presented. These include measures of association of ordinal or interval variables such as gamma of Goodman and Kruskal,Expand
A note on a general definition of the coefficient of determination
SUMMARY A generalization of the coefficient of determination R2 to general regression models is discussed. A modification of an earlier definition to allow for discrete models is proposed.
The analysis of binary data
  • D. Cox
  • Computer Science, Mathematics
  • 1970
Binary response variables special logistical analyses some complications some related approaches more complex responses. Appendices: Theoretical background Choice of explanatory variables in multipleExpand
Applied Logistic Regression (2nd ed.)
  • Wiley Series in Probability and Statistics,
  • 2000
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