This fit statistic applies only to logistic regression.
Also known as Tjur’s D or Tjur’s coefficient of discrimination, the Tjur pseudo R2 value compares the average fitted probability ˉπ 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 n1 1s and n0 0s then,
Note that 0≤R2Tjur≤1. If the model has no discriminating power, then R2Tjur=0. If the model has perfect discriminating power, then R2Tjur=1.
References
Tue Tjur. Coefficients of determination in logistic regression models–a new proposal: the coefficient of discrimination. The American Statistician, 63(4):366–372, November 2009.