[R] individual scales in random subset of pairwise distance survey

[Gabor Grothendieck]

Perhaps you could try clustering the objects.

# generate test data
set.seed(1)
n <- 25 # number of items
mat <- matrix(0, n, n)
# use different labelling scheme if > 26 items
rownames(mat) <- colnames(mat) <- letters[1:n]
mat[lower.tri(mat)] <- sample(5, n * (n-1)/2, TRUE)
mat <- mat + t(mat) + diag(1, n)

# cluster and plot
plot(hclust(as.dist(mat)))


On 6/15/06, context grey <mobygeek at yahoo.com> wrote:
>
> Hello,
>
> I'm curious if anyone has encounted a version of this
> problem
> (and it's solution) involving finding a consistent set
> of scales
> for subsets of survey data.
>
> The goal is to obtain peoples' rankings of pairwise
> similarity of a large
> number of items, on a 1..5 scale for example, and
> average these
> across people to use as input to MDS:
>  How similar is object A to B    on a 1..5 scale ___
>  How similar is object A to C    on a 1..5 scale ___
> etc.
>
> Because there are many items, there are N(N-1)/2
> pairs, so it is not
> practical to show every pair to everyone.   Showing
> people the
> pairs corresponding to random subsets of the objects
> seems desirable.
>
> THe problem is that, a particular random subset might
> by chance
> contain objects that would all be rated "5" if one
> were to see
> the entire dataset.  When ranking pairs from this
> subset, the scale
> of 1..5 is different.
>
> If we ensure that each pair of people must see some
> data in common,
> then one can think about obtaining a set of scales,
> one for each
> person, that causes the data that is commonly ranked
> to have
> as similar scores as possible, summed across all pairs
> of people.
>
>
> Please let me know if you know of a standard procedure
> for
> this or any similar problems.
>
> Thank you.
>
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