# PseudoR2

##### 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.

- Keywords
- 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.

##### 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.

##### Value

`AIC`

, `LogLik`

, `LogLikNull`

and `G2`

will only be reported with option `"all"`

.##### 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

##### Examples

```
r.glm <- glm(Survived ~ ., data=Untable(Titanic), family=binomial)
PseudoR2(r.glm)
PseudoR2(r.glm, c("McFadden", "Nagel"))
```

*Documentation reproduced from package DescTools, version 0.99.19, License: GPL (>= 2)*