[S] Overdispersion vs. Lack of fit..

Tsung-Hsin Lin (tlin@leland.stanford.edu)
Fri, 20 Feb 1998 13:55:54 -0800 (PST)

Dear S users:

Here I'd like to check if V(Y)=E(Y)(1-E(Y)).Y=status.

May I do the following and said that V(Y)=E(Y)(1-E(Y))

in the logistic regression model

Data set:
Y X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
0 1 .12911 .05359 0 .07650 .09662 .00000 .00000 128 105
0 1 .08815 .02957 0 .03307 .13316 .01061 .04186 136 35
0 1 .37154 .07035 0 .18940 .10179 .20643 .00000 129 98
0 0 -.02375 .17381 0 -.11621 -.00090 .02716 .00000 184 94
1 0 .35253 .00092 1 .53456 .00395 .23932 .00000 139 111
. . . . . . . . . .
. . . . . . . . . .

> tmp<-glm(Y~.,data=AAA,family=binomial)

Null Deviance: 925.7443 on 884 degrees of freedom

Residual Deviance: 621.8521 on 871 degrees of freedom

> var(status)
[1] 0.1700744
> ey<-mean(tmp\$fit)
> ey*(1-ey)
[1] 0.1698823

So can I conclude that V(Y)=E(Y)(1-E(Y)) and no overdipersion?

Actually,in theory binomials with m=1 can't have overdispersion

but have "lack of fit" instead.Thus,may I conclude that there

is no "lack of fit" here?