[R] Deviance Residuals

[David Winsemius]

On Aug 20, 2010, at 5:54 AM, Iasonas Lamprianou wrote:

> Dear all,
>
> I am running a logistic regression and this is the output:
>
> glm(formula = educationUniv ~ brncntr, family = binomial)
>
> Deviance Residuals:
>    Min       1Q   Median       3Q      Max  # αυτά είναι  
> τα υπόλοιπα
> -0.8825  -0.7684  -0.7684   1.5044   1.6516
>
> Coefficients:
>            Estimate Std. Error z value Pr(>|z|)
> (Intercept) -1.06869    0.01155 -92.487   <2e-16 ***
> brncntrNo    0.32654    0.03742   8.726   <2e-16 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> (Dispersion parameter for binomial family taken to be 1)
>
> Null deviance: 49363  on 42969  degrees of freedom
> Residual deviance: 49289  on 42968  degrees of freedom
> AIC: 49293
>
>
> I thought that the residuals should all be restricted in the range 0  
> to 1 (since I am predicting a binary outcome).

The internal regression calculations are done on the log-odds scale so  
the working residuals are on that scale. Those are stored in the  
glm.obj as the "residuals" item. I believe that if you tried  
mean(glm.obj$residuals) you should get 0.  Presumably the deviance  
residuals are offered in preference to the working residuals because  
the deviance residual's use as an influence measure is made readily  
interpretable by reference to chi-square statistics. Page 205 of the  
Hastie and Pregibon citation has all the definitions.

-- 
David.



> I read many posts on this list and I realized that there are  
> four(!?) different types of residuals. I need a simple account of  
> these four types of residuals, if anyone can help it will be great.
>
> residuals(glm1, "response")
> residuals(glm1, "pearson")
> residuals(glm1, "deviance")
> residuals(glm1, "working") - especially this one confuses me a lot!
>
> What is the "working" option and how is this different?
>
> Thank you
> Jason
>
> Dr. Iasonas Lamprianou
>
-- 

David Winsemius, MD
West Hartford, CT