Cox & Snell's R2Source:
Calculates the pseudo-R2 value based on the proposal from Cox & Snell (1989).
This index was proposed by Cox and Snell (1989, pp. 208-9) and, apparently independently, by Magee (1990); but had been suggested earlier for binary response models by Maddala (1983). However, this index achieves a maximum of less than 1 for discrete models (i.e. models whose likelihood is a product of probabilities) which have a maximum of 1, instead of densities, which can become infinite (Nagelkerke, 1991).
Cox, D. R., Snell, E. J. (1989). Analysis of binary data (Vol. 32). Monographs on Statistics and Applied Probability.
Magee, L. (1990). R 2 measures based on Wald and likelihood ratio joint significance tests. The American Statistician, 44(3), 250-253.
Maddala, G. S. (1986). Limited-dependent and qualitative variables in econometrics (No. 3). Cambridge university press.
Nagelkerke, N. J. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78(3), 691-692.
model <- glm(vs ~ wt + mpg, data = mtcars, family = "binomial") r2_coxsnell(model) #> Cox & Snell's R2 #> 0.4401407