6533b7d4fe1ef96bd1262779
RESEARCH PRODUCT
A Comment on the Coefficient of Determination for Binary Responses
David CoxNanny Wermuthsubject
Statistics and ProbabilityCoefficient of determinationGeneral MathematicsProbit modelLinear regressionStatisticsConditional probabilityMultiple correlationStatistics Probability and UncertaintyLinear discriminant analysisLogistic regressionRegressionMathematicsdescription
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 these probabilities for success and failure are not too extreme. It is shown how this restriction on the probabilities translates into a restriction on the range of the coefficient of determination R 2 so that, as a consequence, R 2 is not suitable to judge the effectiveness of linear regressions with binary responses even if an important relation is present.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-02-01 | The American Statistician |