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 |

`which` |
character, one out of |

### 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- |

`McFaddenAdj` |
McFadden adjusted pseudo- |

`CoxSnell` |
Cox and Snell pseudo- |

`Nagelkerke` |
Nagelkerke pseudo |

`AldrichNelson` |
AldrichNelson pseudo- |

`VeallZimmermann` |
VeallZimmermann pseudo- |

`McKelveyZavoina` |
McKelvey and Zavoina pseudo- |

`Efron` |
Efron pseudo- |

`Tjur` |
Tjur's pseudo- |

`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

### See Also

### Examples

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

*DescTools*version 0.99.55 Index]