[R] OT: a weighted rank-based, non-paired test statistic ?

[Torsten Hothorn]

> Date: Fri, 5 Jun 2009 16:09:42 -0700 (PDT)
> From: Thomas Lumley <tlumley at u.washington.edu>
> To: dylan.beaudette at gmail.com
> Cc: "'r-help at stat.math.ethz.ch'" <r-help at stat.math.ethz.ch>
> Subject: Re: [R] OT: a weighted rank-based, non-paired test statistic ?
>
> On Fri, 5 Jun 2009, Dylan Beaudette wrote:
>> Is anyone aware of a rank-based, non-paired test such as the 
>> Krustal-Wallis,
>> that can accommodate weights?
>
> You don't say what sort of weights, but basically, no.
>
> Whether you have precision weights or sampling weights, the test will no 
> longer be distribution-free.
>
>> Alternatively, would it make sense to simulate a dataset by duplicating
>> observations in proportion to their weight, and then using the 
>> Krustal-Wallis
>> test?
>
> No.
>

well, if you have case weights, i.e., w[i] == 5 means: there are five 
observations which look exactly like observation i, then there are several 
ways to do it:

> library("coin")
>
> set.seed(29)
> x <- gl(3, 10)
> y <- rnorm(length(x), mean = c(0, 0, 1)[x])
> d <- data.frame(y = y, x = x)
> w <- rep(2, nrow(d)) ### double each obs
>
> ### all the same
> kruskal_test(y ~ x, data = rbind(d, d))

 	Asymptotic Kruskal-Wallis Test

data:  y by x (1, 2, 3)
chi-squared = 12.1176, df = 2, p-value = 0.002337

>
> kruskal_test(y ~ x, data = d[rep(1:nrow(d), w),])

 	Asymptotic Kruskal-Wallis Test

data:  y by x (1, 2, 3)
chi-squared = 12.1176, df = 2, p-value = 0.002337

>
> kruskal_test(y ~ x, data = d, weights = ~ w)

 	Asymptotic Kruskal-Wallis Test

data:  y by x (1, 2, 3)
chi-squared = 12.1176, df = 2, p-value = 0.002337

the first two work by duplicating data, the latter one is more memory 
efficient since it computes weighted statistics (and their distribution).

However, as Thomas pointed out, other forms of weights are more difficult 
to deal with.

Best wishes,

Torsten


> 	-thomas
>
> Thomas Lumley			Assoc. Professor, Biostatistics
> tlumley at u.washington.edu	University of Washington, Seattle
>
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