proc logistic prediction residual

[superbug]

I am using logistic regression for a project, I want to examine whether prediction residuals differ between groups. From SAS output, it provides both Pearson residual and Deviance residual. If I want to examine whether prediction residual differ between groups, which one should I use, Pearson residual or Deviance residual? As SAS code below,reschi=pr is Pearson residual, resdev=dr is Deviance residual.

I spent some time searching, but I haven't got clear idea yet, so I come here to ask the experts. thanks! 

proc logistic data=Have;
where first=1;
class aaa ppp;
model pass (event="1")=aaa ppp timeaftergrad schoolpass1;
output out=out_first p=prob xbeta=logit resdev=dr h=pii reschi=pr difchisq=difchi; 
run;

[StatDave]

Well, for the purpose of assessing whether residuals are unusually large, Collett (2003) recommends standardized deviance residuals (STDRESDEV=) or likelihood residuals (RESLIK=), stating that these two residuals perform similarly and are well-approximated by the standard normal distribution. As such, most values would lie between -2 and 2. McCullagh and Nelder (1989) also recommend standardized deviance residuals. Hosmer and Lemeshow (2000) discuss residuals, diagnostics, useful plots, and their interpretation.

[superbug]

@StatDave 

Thanks much for your reply!

Another question, in regular regression residual is calculated as yhat minus y observed, could the residual in logistic regression be calculated similarly, say prob estimated minus prob caculated by plugging in the estimated coefficients?

[StatDave]

Those are the same thing - the estimated probability *is* calculated from the estimated model parameters and the input data. You could certainly compute a raw residual as the observed response (either 1 or 0) minus the estimated probability.

[superbug]

@StatDave 

Thanks much!

I very much appreciate the information you provided!