PseudoR2 {DescTools} R Documentation

## Pseudo R2 Statistics

### Description

Although there's no commonly accepted agreement on how to assess the fit of a logistic regression, there are some approaches. 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", "McFaddenAdj", "CoxSnell", "Nagelkerke", "AldrichNelson", "VeallZimmermann", "Efron", "McKelveyZavoina", "Tjur", "all". Partial matching is supported.

### 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 (also sometimes called Cragg-Uhler) 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.

Veall and Zimmermann concluded that from a set of six widely used measures the measure suggested by McKelvey and Zavoina had the closest correspondance to ordinary least square R2. The Aldrich-Nelson pseudo-R2 with the Veall-Zimmermann correction is the best approximation of the McKelvey-Zavoina pseudo-R2. Efron, Aldrich-Nelson, McFadden and Nagelkerke approaches severely underestimate the "true R2".

### Value

the value of the specific statistic. AIC, LogLik, LogLikNull and G2 will only be reported with option "all".

 McFadden McFadden pseudo-R^2 McFaddenAdj McFadden adjusted pseudo-R^2 CoxSnell Cox and Snell pseudo-R^2 (also known as ML pseudo-R^2) Nagelkerke Nagelkerke pseudoR^2 (also known as CraggUhler R^2) AldrichNelson AldrichNelson pseudo-R^2 VeallZimmermann VeallZimmermann pseudo-R^2 McKelveyZavoina McKelvey and Zavoina pseudo-R^2 Efron Efron pseudo-R^2 Tjur Tjur's pseudo-R^2 AIC Akaike's information criterion LogLik log-Likelihood for the fitted model (by maximum likelihood) LogLikNull log-Likelihood for the null model. The null model will include the offset, and an intercept if there is one in the model. G2 differenz of the null deviance - model deviance

### Author(s)

Andri Signorell <andri@signorell.net> with contributions of Ben Mainwaring <benjamin.mainwaring@yougov.com> and Daniel Wollschlaeger

### 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

Veall, M.R., & Zimmermann, K.F. (1992) Evalutating Pseudo-R2's fpr binary probit models. Quality&Quantity, 28, pp. 151-164

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