= Cox–Snell likelihood pseudo-R-squared
{c}
{title2=$R^2_{\mathrm{CS}}$}
A likelihood-based analogue of the <coefficient of determination> compares the fitted and intercept-only <log-likelihoods> $\ell_1$ and $\ell_0$:
$$
R^2_{\mathrm{CS}}=1-\exp\left\{-\frac{2(\ell_1-\ell_0)}n\right\}.
$$
For a <Cox proportional-hazards model>, these are maximized <partial likelihood> logarithms with and without the <covariates>. The expression measures improvement in fit, rather than the fraction of variation in event times explained. Its attainable maximum can be below one. It does not test the <proportional hazards> assumption or establish predictive calibration.
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