[R] Deviance Residuals

[John Fox]

Dear Iasonas,


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
> Behalf Of Iasonas Lamprianou
> Sent: August-20-10 5:55 AM
> To: r-help at r-project.org
> Subject: [R] Deviance Residuals
> 
> 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). 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 on the scale of the response, y - E(y); in a binary logistic regression, y is 0 or 1 and E(y) is the fitted probability of a 1. As it turns out, response residuals aren't terribly useful for a logit model.

> residuals(glm1, "pearson")

Components of the Pearson goodness-of-fit statistic.

> residuals(glm1, "deviance")

Components of the residual deviance for the model.

> residuals(glm1, "working") - especially this one confuses me a lot!

Residuals from the final weighted-least-squares regression of the IWLS procedure used to fit the model; useful, for example, for detecting nonlinearity.

> 
> What is the "working" option and how is this different?

See above.

I hope this helps,
 John

--------------------------------
John Fox
Senator William McMaster 
  Professor of Social Statistics
Department of Sociology
McMaster University
Hamilton, Ontario, Canada
web: socserv.mcmaster.ca/jfox

> 
> Thank you
> Jason
> 
> Dr. Iasonas Lamprianou
> 
> 
> Assistant Professor (Educational Research and Evaluation)
> Department of Education Sciences
> European University-Cyprus
> P.O. Box 22006
> 1516 Nicosia
> Cyprus
> Tel.: +357-22-713178
> Fax: +357-22-590539
> 
> 
> Honorary Research Fellow
> Department of Education
> The University of Manchester
> Oxford Road, Manchester M13 9PL, UK
> Tel. 0044  161 275 3485
> iasonas.lamprianou at manchester.ac.uk
> 
> 
> 
> 
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