[R] Calculating/understanding variance-covariance matrix of logistic regression (lrm $var)

[Karl Knoblick]

Hallo!

I want to understand / recalculate what is done to get
the CI of the logistic regression evaluated with lrm.
As far as I came back, my problem is the
variance-covariance matrix fit$var of the fit
(fit<-lrm(...), fit$var). Here what I found and where
I stucked:

-----------------
library(Design)
# data
D<-c(rep("a", 20), rep("b", 20))
V<-0.25*(1:40)
V[1]<-25
V[40]<-15
data<-data.frame(D, V)
d<-datadist(data)
options(datadist="d")

# Fit
fit<-lrm(D ~ V, data=data, x=TRUE, se.fit=TRUE)
plot(fit, conf.int=0.95) # same as plot(fit)

# calculation of upper and lower CI (pred$lower,
pred$upper)
pred<-predict(fit, data.frame(V=V), conf.int=0.95,
se.fit=TRUE)
points(V, pred$upper, col=2, pch=3) # to check

# looking in function predict, the CI are calculated
with the se
# using fit$var:
X<-cbind(rep(1, length(fit$x)), fit$x) # fit$x are the
V
cov<-fit$var # <- THIS I DO NOT UNDERSTAND (***) s.
below
se <- drop(sqrt(((X %*% cov) * X) %*% rep(1,
ncol(X))))

# check if it is the same
min(se - pred$se.fit) # result: 0
max(se - pred$se.fit) # result: 0

# looking at the problem:
cov
-----------------
Result:
           Intercept           V
Intercept  0.7759040 -0.12038969
V         -0.1203897  0.02274177


(***)
fit$var is the estimated variance-covariance matrix.
How is it calculated? (Meaning of intercept and x?)

Does anybody know how calculationg this "by hand" or
can give me a reference (preferable in the internet)?

Thanks!
Karl.