David Winsemius wrote:
On Dec 12, 2009, at 8:19 PM, casperyc wrote:
for an example,
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9); treatment <- gl(3,3)
glm.D93 <- glm(counts ~ outcome + treatment, family=poisson())
confint(glm.D93)
confint.default(glm.D93) # based on asymptotic normality
to verify the confidence interval (confint.default(glm.D93)) for
outcome2
-4.542553e-01 + c(-1,1) * 0.2021708 * qt(0.975,df=4)
-1.0155714 0.1070608
does not give me
outcome2 -0.8505027 -0.05800787
as in confint.default(glm.D93)
But this does (up to rounding anyway):
> coef(summary(glm.D93))[2,1] + c(-1,1) *
coef(summary(glm.D93))[2,2]*qnorm(0.975)
[1] -0.85050267 -0.05800787
I can understand thinking that the CI's might be t-distributed but the
usual formulation is that they are normally distributed.
Right, and 4 DF is just plain wrong. There is no "estimated variance"
for the Poisson distribution like there is in the Gaussian models. E.g.,
it makes sense to calculate a CI for the true log-mean based on a single
Poisson outcome:
> x <- 50
> confint(glm(x~1, family=poisson))
Waiting for profiling to be done...
2.5 % 97.5 %
3.621423 4.176967
--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907
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