The use of R2, the coefficient of determination, also called the multiple correlation coefficient, is well established in classical regression analysis (Rao,1973)

R2 is the square of the Pearson correlation between x and the coefficient score of the model p(), that is the derivative with respect to Beta of log{p(y¦Beta.x+lambda)} at Beta=0

For discrete models does not go all the way to 1.

Max(R2)=1-exp{2n-1l(0)}=1-L(0)2/n

Nagelkerke rescales R2 so that it’s maximum is 1 such that R2 = R2 /max(R2)