DescTools (version 0.99.19)

PseudoR2: Pseudo R2 Statistics

Description

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.

Usage

PseudoR2(x, which = NULL)

Arguments

x

the glm, polr or multinom model object to be evaluated.

which

character, one out of "McFadden","AldrichNelson", "McFaddenAdj", "Nagelkerke", "CoxSnell", "Effron", "McKelveyZavoina", "Tjur", "all". Partial matching is supported.

Value

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

Details

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.

References

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

Examples

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

PseudoR2(r.glm, c("McFadden", "Nagel"))