R help - Nov 2008 - binomial glm???

Hi everyone,

newbee query!

I've installed R 2.8.0 and tried to run this simple glm -
      x is no of cars in a given year, y is the number voted in an election
that year while n is the population 18+:


       votes <- data.frame(x = c(0.62,0.77,0.71,0.74,0.77,0.86,1.13,1.44),
      +                           y=c(502,542,711,653,771,806,934,1123), n     
c(1617,1734,1680,1793,1678,1751,1807,1879))
      > votes$YM <- cbind(votes$y, votes$n - votes$y)
      > fml <- glm(YM ~ x, family = binomial, data = votes)
      > summary(fml)

and got the following which seem really wrong!


      Coefficients:
                  Estimate Std. Error z value Pr(>|z|)
      (Intercept) -1.43498    0.06233  -23.02   <2e-16 ***
      x            1.30739    0.06705   19.50   <2e-16 ***


      > dfr = votes
      > prd.mdl <- predict(fml,newdata=dfr)
      > prd.mdl
                1           2           3           4           5
      6           7           8
      -0.62439978 -0.42829203 -0.50673513 -0.46751358 -0.42829203
      -0.31062738  0.04236657  0.44765592


      > predict(fml, type="response")
              1         2         3         4         5         6         7
      8
      0.3487815 0.3945343 0.3759592 0.3852049 0.3945343 0.4229616 0.5105901
      0.6100818

the original proportions are
      |------+------+------+------+------+------+-------+------|
      |  0.76|  0.76|  0.70|  0.73|  0.69|  0.68|   0.66|  0.63|
      |------+------+------+------+------+------+-------+------|



and I would expect intercept to be about -0.14 and beta = 0.83?

Am I missing something obvious? Any help or suggestions appreciated!

Thanks
Gerard



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Gerard M. Keogh <GMKeogh <at> justice.ie> writes:
> 
> 
> Hi everyone,
> 
> newbee query!
> 
> I've installed R 2.8.0 and tried to run this simple glm -
>       x is no of cars in a given year, y is the number voted in an election
> that year while n is the population 18+:

  I strongly suspect that you're confused between
the definition of a generalIZED linear model (glm in
R, PROC GENMOD in Some other stAtisticS program) and
a generAL linear model (lm in R, PROC GLM in S*S).
As shown below, the actual predictions are nearly
identical in this case between the linear model
(assuming normal errors and linearity)
and the generalized linear model (assuming binomial
errors and a logistic curve), because the logistic
curve is very close to linear in the middle of
its range.

votes <- data.frame(x = c(0.62,0.77,0.71,0.74,0.77,0.86,1.13,1.44),
                    y=c(502,542,711,653,771,806,934,1123),
                    n= c(1617,1734,1680,1793,1678,1751,1807,1879))
votes$YM <- cbind(votes$y, votes$n - votes$y)
fml <- glm(YM ~ x, family = binomial, data = votes)
summary(fml)

with(votes,plot(y/n~x,ylim=c(0,1)))
xvec <- seq(0.5,1.6,length=100)
lines(xvec,predict(fml,newdata=data.frame(x=xvec,n=1),type="response"))

## or:

lm1 <- lm(y/n~x,data=votes)
abline(lm1,col=2)

  Ben Bolker