[R] statistical test for comparison of two classifications (nominal)

[Mattia Prosperi]

Another useful measure to compare partitions is the adjusted Rand
index which is implemented in the library(e1071) within the
classAgreement function.
If you have your data partitions to be compared in a matricial form
(where each column is a different partition), the syntax is
ARI<-classAgreement(table(data[,i],data[,j]))$crand

Other useful measures of goodness-of-fit for clustering are the
silhouette index or the c-index or the Goodman-Kruskal index. although
they evaluate in general inter/intra-cluster distance distributions.
For instance, you can maximise/minimise these indices to find the best
partition among a set of candidate ones.

Mattia Prosperi.


2010/11/17 Marc Schwartz <marc_schwartz at me.com>:
> On Nov 17, 2010, at 7:33 AM, Martin Tomko wrote:
>
>> Dear all,
>> I am having a hard time to figure out a suitable test for the match between two nominal classifications of the same set of data.
>> I have used hierarchical clustering with multiple methods (ward, k-means,...) to classify my dat into a set number of classesa, and I would like to compare the resulting automated classification with the actual - objective benchmark one.
>> So in principle I have a data frame with n columns of nominal classifications, and I want to do a mutual comparison and test for significance in difference in classification between pairs of columns.
>>
>> I just need to identify a suitable test, but I fail. I am currently exploring the possibility of using Cohen's Kappa, but I am open to other suggestions. Especially the fact that kappa seems to be moslty used on failible, human annotators seems to bring in limitations taht do not apply to my automatic classification.
>> Any help will be appreciated, especially if also followed by a pointer to an R package that implements it.
>>
>> Thanks
>> Martin
>
>
> In addition to Matt's comments, you might want to consider marginal homogeneity tests. There are extensions of the pairwise McNemar test to greater than two categories. Some online information is here:
>
>  http://www.john-uebersax.com/stat/mcnemar.htm
>
> and there is the ?mh_test implemented in the 'coin' package on CRAN.
>
> HTH,
>
> Marc Schwartz
>
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