confint for coefficients from lm model (PR#10496)

Christian.Lajaunie at ensmp.fr wrote:

Full_Name: Christian Lajaunie
Version: 2.5.1
OS: Fedora  fc6
Submission from: (NULL) (193.251.63.39)


confint() does not use the appropriate variance term when the design
matrix contains a zero column (which of course should not happen).
Example:

A 10x2 matrix with trivial column 1:

junk <- data.frame(x=rep(0,10), u=factor(sample(c("Y", "N"), 10, replace=T)))

The response:

ans <- as.integer(junk$u) + rnorm(10)

and the model:

junk.model <- lm(ans ~ junk$x + junk$u)

3 coefficients:

coefficients(junk.model)

(Intercept)      junk$x     junk$uY
  0.6808802          NA   1.5912192

and a 2x2 variance (X^tX)^-1:

vcov(junk.model)

            (Intercept)     junk$uY
(Intercept)  0.09905378 -0.09905378
junk$uY     -0.09905378  0.19810756

result in no confidence interval for the third term:

confint(junk.model)

                  2.5 %   97.5 %
(Intercept) -0.04488412 1.406644
junk$x               NA       NA
junk$uY              NA       NA

confint() seems to be looking for diag(vcov(junk.model))[3]
instead of diag(vcov(junk.model))[2]

(You should upgrade, but this is the same in 2.6.1)

Yes. And confint.glm and confint.default are bad too.  The glm method
must be a different issue, but the other two share the vcov issue.

I'm a bit unsure what is the right fix, though.  Is vcov really
returning the wrong thing? Should we rather have

vcov(junk.model)

          [,1] [,2]       [,3]
[1,]  0.5525259   NA -0.5525259
[2,]         NA   NA         NA
[3,] -0.5525259   NA  0.6906574

which is not massively hard to achieve.

Alternatively we could just skip the aliased coefficients. For GLMs we
definitely do not want to profile them...