Pseudo R2 Statistics

The goodness of fit of the logistic regression model can be expressed by some variants of pseudo R squared statistics, most of which being based on the deviance of the model.

PseudoR2(x, which = NULL)
the glm, polr or multinom model object to be evaluated.
character, one out of "McFadden","AldrichNelson", "McFaddenAdj", "Nagelkerke", "CoxSnell", "Effron", "McKelveyZavoina", "Tjur", "all". Partial matching is supported.

Cox and Snell's $R^2$ is based on the log likelihood for the model compared to the log likelihood for a baseline model. However, with categorical outcomes, it has a theoretical maximum value of less than 1, even for a "perfect" model.

Nagelkerke's $R^2$ is an adjusted version of the Cox and Snell's $R^2$ that adjusts the scale of the statistic to cover the full range from 0 to 1.

McFadden's $R^2$ is another version, based on the log-likelihood kernels for the intercept-only model and the full estimated model.


AIC, LogLik, LogLikNull and G2 will only be reported with option "all".


Aldrich, J. H. and Nelson, F. D. (1984): Linear Probability, Logit, and probit Models, Sage University Press, Beverly Hills.

Cox D R & Snell E J (1989) The Analysis of Binary Data 2nd ed. London: Chapman and Hall.

Efron, B. (1978). Regression and ANOVA with zero-one data: Measures of residual variation. Journal of the American Statistical Association, 73(361), 113--121.

Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). Hoboke, NJ: Wiley.

McFadden D (1979). Quantitative methods for analysing travel behavior of individuals: Some recent developments. In D. A. Hensher & P. R. Stopher (Eds.), Behavioural travel modelling (pp. 279-318). London: Croom Helm.

McKelvey, R. D., & Zavoina, W. (1975). A statistical model for the analysis of ordinal level dependent variables. The Journal of Mathematical Sociology, 4(1), 103--120

Nagelkerke, N. J. D. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78(3), 691--692.

Tjur, T. (2009) Coefficients of determination in logistic regression models - a new proposal: The coefficient of discrimination. The American Statistician, 63(4): 366-372

See Also

logLik, AIC, BIC

  • PseudoR2
r.glm <- glm(Survived ~ ., data=Untable(Titanic), family=binomial)

PseudoR2(r.glm, c("McFadden", "Nagel"))
Documentation reproduced from package DescTools, version 0.99.19, License: GPL (>= 2)

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