Measures of dissimilarity (distance) between character vectors in R - r

Question

I have a seemingly easy question which however is troubling me a bit.
I have couples of vectors made up of nominal attributes. They can be of different length and sometimes some of the attributes in one might not be included in the other. See a and b as two potential examples.
a
1 mathematician
2 engineer
3 mathematician
4 mathematician
5 mathematician
6 engineer
7 mathematician
8 mathematician
9 mathematician
10 mathematician
11 mathematician
12 engineer
13 mathematician
14 mathematician
15 engineer
b
1 physicist
2 surgeon
3 physicist
4 surgeon
5 physicist
6 physicist
7 surgeon
8 surgeon
9 physicist
10 physicist
11 mathematician
Do you have in mind a measure (an index) that could summarize the dissimilarity between them? The type of measure I am looking for is something like the Euclidean distance, but for qualitative vectors.
One option I thought of is to actually compute the Euclidean distance among the categorical vectors earlier transformed into frequency vectors. In this way, they would become quantitative and would be of the same length. But my question is, do you find this a sound approach?
More generally, is there a R package that tackles these type of distances? Can you suggest other distances suitable to the case of nominal variables?
Many thanks!

Answer 1

I've only come across the unalikeability coefficient.
http://www.amstat.org/publications/jse/v15n2/kader.html
Weird name, intuitive approach, and incredibly simple implementation. For example:
> table(a)
a
engineer mathematician
4 11
> unalike(table(a))
[1] 0.391
> table(b)
b
mathematician physicist surgeon
1 6 4
> unalike(table(b))
[1] 0.562
It is clear just by eye-balling that b would be more dissimilar, and this coefficient gives a more quantitative measure.
There are some examples in the paper which I will calculate for you here:
> unalike(3,7)
[1] 0.42
> unalike(5,5)
[1] 0.5
> unalike(1,9)
[1] 0.18
The formula in this function is based on the paper I linked you to above:
unalike <- function(...) {
props <- c(...)
zzz <- 1 - sum(((props) / sum(props)) ** 2)
zzz <- round(zzz, 3)
return(zzz)
}
Let me know how your thing goes since this is a small side project for me as well.

Answer 2

I am not sure this is a programming question, because you do not know what you want to do yet, so we can't offer a solution. I think the main question here is what are you going to use this measure for, because you can measure dissimilarities in a lot of different ways, some will be good for what you want and some will not.
But trying to answer anyway, there is the utils::adist function and there is also a package called stringdist (these are the ones I have used before). But it seems that they are not quite what you want, based on your question, because they will measure the distance for each character string, and not for the whole matrix. But you could use them to have some ideas about how to measure the distance between the two vectors. For example, one measure could be how many changes you would have to make in vector a so it turns to vector b.

Answer 3

Thank you for keeping this open.
One option, which appears to have become available after this discussion, is R's qualvar (Gombin) package. The package provides functions for each of Wilcox's (1967, 1973) Indices of Qualitative Variation. Included with the package is a useful vignette summarizing implementation and results. I have found in limited experience that index selection requires some brute-force testing with actual and simulated data.