[R] residuals in logistic regression model

[John Fox]

Dear Urania,

> -----Original Message-----
> From: Urania Sun [mailto:suncertain at gmail.com] 
> Sent: Thursday, November 24, 2005 8:52 PM
> To: John Fox
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] residuals in logistic regression model
> 
> Thanks, Professor. 
>  
> But is it ok to write residuals in the right hand side of the 
> logistic regression formula? Some people said I cannot since 
> the generalized linear model is to use a function to link the 
> expectation to a linear model. So there should not be 
> residuals in the right hand side. 
>  
> My question is that If residuals do exist (as in the glm 
> model output), why not put them in the formula (for example, 
> if I write the left-hand side as the estimated odds-ratio)?
> 

There are several kinds of residuals for generalized linear models, as I
mentioned (see ?residuals.glm). The residuals in the glm output are deviance
residuals, which are the casewise (signed) components of the residual
deviance; differences between y and fitted-y are called response residuals
(and aren't generally as useful). The left-hand side of a logit model
transformed with the logit-link is the log-odds, not the odds or odds-ratio.
The form of the model to which the response residuals applies has the
proportion, not the logit, on the left-hand side.

These matters are discussed in the references given in ?residuals.glm, and
in many other places, such as Sec. 6.6 of my R and S-PLUS Companion to
Applied Regression.

> Many thanks!
>  
> Happy Thanksgiving!

Unfortunately we celebrate Thanksgiving in Canada in October, probably
because the weather here in late November leaves little to be thankful for.

Regards,
 John

>  
> On 11/24/05, John Fox <jfox at mcmaster.ca> wrote: 
> 
> 	Dear Urania,
> 	
> 	The residuals method for glm objects can compute 
> several kinds of residuals;
> 	the default is deviance residuals. See ?residuals.glm 
> for details and 
> 	references.
> 	
> 	I hope this helps.
> 	John
> 	
> 	--------------------------------
> 	John Fox
> 	Department of Sociology
> 	McMaster University
> 	Hamilton, Ontario
> 	Canada L8S 4M4
> 	905-525-9140x23604
> 	http://socserv.mcmaster.ca/jfox 
> <http://socserv.mcmaster.ca/jfox> 
> 	--------------------------------
> 	
> 	> -----Original Message-----
> 	> From: r-help-bounces at stat.math.ethz.ch
> 	> [mailto: r-help-bounces at stat.math.ethz.ch] On Behalf 
> Of Urania Sun
> 	> Sent: Thursday, November 24, 2005 1:36 PM
> 	> To: r-help at stat.math.ethz.ch 
> 	> Subject: [R] residuals in logistic regression model
> 	>
> 	> In the logistic regression model, there is no residual
> 	>
> 	> log (pi/(1-pi)) = beta_0 + beta_1*X_1 + .....
> 	>
> 	> But glm model will return 
> 	>
> 	> residuals
> 	>
> 	> What is that?
> 	>
> 	> How to understand this? Can we put some residual in the
> 	> logistic regression model by replacing pi with pi' 
> (the estimated pi)?
> 	>
> 	>  log (pi'/(1-pi')) = beta_0 + beta_1*X_1 + .....+ ei 
> 	>
> 	> Thanks!
> 	>
> 	>       [[alternative HTML version deleted]]
> 	>
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