Tjur R-Squared

This fit statistic applies only to logistic regression.

Also known as Tjur’s \(D\) or Tjur’s coefficient of discrimination, the Tjur pseudo \(R^2\) value compares the average fitted probability \(\bar{\pi}\) of the two response outcomes. In particular it is the difference between the average fitted probability for the binary outcome coded to 1 (success level) and the average fitted probability for the binary outcome coded to 0 (the failure level).

If the coded response \(y\) has \(n_1\) 1s and \(n_0\) 0s then,

Note that \(0 \leq R_{Tjur}^2 \leq 1\). If the model has no discriminating power, then \(R_{Tjur}^2 = 0\). If the model has perfect discriminating power, then \(R_{Tjur}^2 = 1\).

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