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R-squared in Logistic Regression

3 messages · Johan Stenberg, Henric Nilsson, Frank E Harrell Jr

#
Dear all,

How do I make R show the R-squared (deviance explained by the model) in
a logistic regression?

Below is how I write my syntax. Basically I want to investigate
density-dependence in parasitism of larvae. Note that in the end I
perform a F-test because the dispersion factor (residual deviance /
residual df) is significantly higher than 1. But how do I make R show
the "R-squared"?

Best wishes
Johan
Call:
glm(formula = y ~ log(larvae), family = binomial)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-2.0633  -1.6218  -0.1871   0.7907   2.7670

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   1.0025     0.7049   1.422  0.15499
log(larvae)  -1.0640     0.3870  -2.749  0.00597 **

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 35.981  on 12  degrees of freedom
Residual deviance: 27.298  on 11  degrees of freedom
AIC: 40.949

Number of Fisher Scoring iterations: 4
Analysis of Deviance Table

Model: binomial, link: logit

Response: y

Terms added sequentially (first to last)


            Df Deviance Resid. Df Resid. Dev      F   Pr(>F)
NULL                           12     35.981
log(larvae)  1    8.683        11     27.298 8.6828 0.003212 **
#
On Ti, 2005-03-29, 10:56, Johan Stenberg skrev:
Several definitions of R^2 exists in the GLM case. See e.g.

Menard, S. (2000) Coefficients of determination for multiple logistic
regression analysis. American Statistician, 54, 17-24.

Mittlbock, M. and Schemper, M. (2002) Explained variation for logistic
regression - small sample adjustments, confidence intervals and predictive
precision. Biometrical Journal, 44, 263-272.

Liao, J.G. and McGee, D. (2003) Adjusted coefficients of determination for
logistic regression. American Statistician, 57, 161-165.

IIRC, the last paper contains R code.

HTH,
Henric
#
Johan Stenberg wrote:
The proportion of deviance explained has been shown to not be such a 
good measure.  You can use the lrm function in the Design package to get 
various measures including ROC area (C index), Somers' Dxy and Kendall 
tau rank correlation, Nagelkerke generalization of R-squared for maximum 
likelihood-based models (related to Maddala and others).

Frank Harrell