[Rd] confint for coefficients from lm model (PR#10496)

[Peter Dalgaard]

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...
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-- 
   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.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907