[R] R-squared in Logistic Regression

[Frank E Harrell Jr]

Johan Stenberg wrote:
> 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

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

> 
> 
>>y<-cbind(para,unpara)
>>model<-glm(y~log(larvae),binomial)
>>summary(model)
> 
> 
> 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
> 
> 
>>anova(model,test="F")
> 
> 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 **
> 
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-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University