[R] proportions confidence intervals

[Spencer Graves]

      Please see: 

      Brown, Cai and DasGupta (2001) Statistical Science, 16:  101-133 
and (2002) Annals of Statistics, 30:  160-2001 

      They show that the actual coverage probability of the standard 
approximate confidence intervals for a binomial proportion are quite 
poor, while the standard asymptotic theory applied to logits produces 
rather better answers. 

      I would expect "confint.glm" in library(MASS) to give decent 
results, possibly the best available without a very careful study of 
this particular question.  Consider the following: 

  library(MASS)# needed for confint.glm
  library(boot)# needed for inv.logit
  DF10 <- data.frame(y=.1, size=10)
  DF100 <- data.frame(y=.1, size=100)
  fit10 <- glm(y~1, family=binomial, data=DF10, weights=size)
  fit100 <- glm(y~1, family=binomial, data=DF100, weights=size)
  inv.logit(coef(fit10))
 
  (CI10 <- confint(fit10))
  (CI100 <- confint(fit100))
 
  inv.logit(CI10)
  inv.logit(CI100)

      In R 1.9.1, Windows 2000, I got the following: 

>   inv.logit(coef(fit10))
(Intercept)
        0.1
>  
>   (CI10 <- confint(fit10))
Waiting for profiling to be done...
     2.5 %     97.5 %
-5.1122123 -0.5258854
>   (CI100 <- confint(fit100))
Waiting for profiling to be done...
    2.5 %    97.5 %
-2.915193 -1.594401
>  
>   inv.logit(CI10)
      2.5 %      97.5 %
0.005986688 0.371477058
>   inv.logit(CI100)
    2.5 %    97.5 %
0.0514076 0.1687655
>
>   (naiveCI10 <- .1+c(-2, 2)*sqrt(.1*.9/10))
[1] -0.08973666  0.28973666
>   (naiveCI100 <- .1+c(-2, 2)*sqrt(.1*.9/100))
[1] 0.04 0.16

      hope this helps.  spencer graves

Darren Shaw wrote:

> Dear R users
>
> this may be a simple question - but i would appreciate any thoughts
>
> does anyone know how you would get one lower and one upper confidence 
> interval for a set of data that consists of proportions.  i.e. taking 
> a usual confidence interval for normal data would result in the lower 
> confidence interval being negative - which is not possible given the 
> data (which is constrained between 0 and 1)
>
> i can see how you calculate a upper and lower confidence interval for 
> a single proportion, but not for a set of proportions
>
> many thanks
>
>
> Darren Shaw
>
>
>
> -----------------------------------------------------------------
> Dr Darren J Shaw
> Centre for Tropical Veterinary Medicine (CTVM)
> The University of Edinburgh
> Scotland, EH25 9RG, UK
>
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