R help - Dec 2001 - Pearson residuals in quasi family

Hi all,
This is a very silly question or something escapes me:
Let obj a simple gam poisson model. Let
>obj<-gam(....,family=poisson)
>obj1<-update(obj, family=quasi(link="log", var="mu"))
>From summary.glm(obj1) the dispersion parameter is estimated 1.165; In fact
it is:
> (predict(obj1, se.fit=T)$se.fit[1:5]/predict(obj, se.fit=T)$se.fit[1:5])^2
        4        5        6        7        8
 1.165767 1.165767 1.165767 1.165767 1.165767

The standard errors of the fitted values are greater in the quasi-Lik
approach, of course.
Because of this, it's expected that the pearson residuals are smaller in the
quasi-Lik, approach; but
> residuals(obj, type="pearson")[1:5]-residuals(obj1,
type="pearson")[1:5]
 4 5 6 7 8
 0 0 0 0 0

That is
resid(obj1, type="pearson")!=resid(obj1,
"response")/(predict(obj1,
se.fit=T)$se.fit

Am I wrong or is there any problem?

Thanks for your attention,
best,
vito

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at
stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._

On Wed, 19 Dec 2001, MUGGEO VITO wrote:
> Hi all,
> This is a very silly question or something escapes me:
> Let obj a simple gam poisson model. Let
>
> >obj<-gam(....,family=poisson)
> >obj1<-update(obj, family=quasi(link="log",
var="mu"))
>
<snip>
> That is
> resid(obj1, type="pearson")!=resid(obj1,
"response")/(predict(obj1,
> se.fit=T)$se.fit
>
> Am I wrong or is there any problem?
I don't know about gam() (is this the one in mgcv?) but certainly for
glm() the pearson residuals are the same for quasilikelihood fits.

The Pearson residuals are typically defined as (Y-mu)/sqrt(V(mu))
and the variance function V(mu) doesn't include a scale factor for
quasilikelihood fits since the scale factor doesn't affect the fitting.

If Pearson residuals were rescaled by the estimated dispersion parameter
then for a Gaussian linear model they wouldn't agree with the other
flavours of residual.

	-thomas

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at
stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._