[R] Bootstrap CIs for weighted means of paired differences

[i.petzev]

Hi David,

thanks a lot for the response. I see that this works. I am not sure, however, what the appropriate way to do this is. It also works if you do not define weights in the boot() function (weighted bootstrap) but rather in the vw_m_diff function (ordinary bootstrap), i.e., 


vw_m_diff <- function(dataset,d) {
  differences <- dataset[d,1]-dataset[d,2]
  weights <- dataset[d, "weights"]
  return(weighted.mean(x=differences, w=weights))
}

with 

boot(dataset, statistic=vw_m_diff, R = 1000)

I guess this is rather a statistical question and hence I will have to look further into it. 

In any case, thanks a lot for your help.

Best



On 15 Nov 2014, at 17:27, David Winsemius <dwinsemius at comcast.net> wrote:

> 
> On Nov 14, 2014, at 3:18 PM, David Winsemius wrote:
> 
>> 
>> On Nov 14, 2014, at 12:15 PM, ivan wrote:
>> 
>>> Hi,
>>> 
>>> I am trying to compute bootstrap confidence intervals for weighted means of
>>> paired differences with the boot package. Unfortunately, the weighted mean
>>> estimate lies out of the confidence bounds and hence I am obviously doing
>>> something wrong.
>>> 
>>> Appreciate any help. Thanks. Here is a reproducible example:
>>> 
>>> 
>>> library(boot)
>>> set.seed(1111)
>>> x <- rnorm(50)
>>> y <- rnorm(50)
>>> weights <- runif(50)
>>> weights <- weights / sum(weights)
>>> dataset <- cbind(x,y,weights)
>>> vw_m_diff <- function(dataset,w, d) {
>> 
>> My understanding of the principle underlying the design of the bootstrapped function was that the data was the first argument and the index vector was the second. (I admit to not knowing what it would do with a third argument. So I would have guessed that you wanted:
>> 
>> vw_m_diff <- function(dataset,w) {
>>    differences <- dataset[d,1]-dataset[d,2]
>>   weights <- dataset[w, "weights"]
>>   return(weighted.mean(x=differences, w=weights))
>> } 
> 
> I'm sorry. That was the code I first editted. This is the code that produced that output:
> 
> vw_m_diff <- function(dataset,w) {
>      differences <- dataset[w,1]-dataset[w,2]
>     weights <- dataset[w, "weights"]
>     return(weighted.mean(x=differences, w=weights))
>   }
> 
>> 
>> I get what appears to me as a sensible set of estimates (since they seem centered on zero) although I further admit I do not know what the theoretic CI _should_ be for this problem:
>> 
>>> res_boot <- boot(dataset, statistic=vw_m_diff, R = 1000, w=dataset[,3])
>>> boot.ci(res_boot)
>> BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
>> Based on 1000 bootstrap replicates
>> 
>> CALL : 
>> boot.ci(boot.out = res_boot)
>> 
>> Intervals : 
>> Level      Normal              Basic         
>> 95%   (-0.5657,  0.4962 )   (-0.5713,  0.5062 )  
>> 
>> Level     Percentile            BCa          
>> 95%   (-0.6527,  0.4249 )   (-0.5579,  0.5023 )  
>> Calculations and Intervals on Original Scale
>> 
>> 
>>>  differences <- dataset[d,1]-dataset[d,2]
>>>  weights <- w[d]
>>>  return(weighted.mean(x=differences, w=weights))
>>> }
>>> res_boot <- boot(dataset, statistic=vw_m_diff, R = 1000, w=dataset[,3])
>>> boot.ci(res_boot)
>>> 
>>> *BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS*
>>> *Based on 1000 bootstrap replicates*
>>> 
>>> *CALL : *
>>> *boot.ci <http://boot.ci>(boot.out = res_boot)*
>>> 
>>> *Intervals : *
>>> *Level      Normal              Basic         *
>>> *95%   (-0.8365, -0.3463 )   (-0.8311, -0.3441 )  *
>>> 
>>> *Level     Percentile            BCa          *
>>> *95%   (-0.3276,  0.1594 )   (-0.4781, -0.3477 )  *
>>> 
>>> weighted.mean(x=dataset[,1]-dataset[,2], w=dataset[,3])
>>> 
>>> *[1] -0.07321734*
>>> 
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>>> 
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>> 
>> David Winsemius
>> Alameda, CA, USA
>> 
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
> 
> David Winsemius
> Alameda, CA, USA


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