classAgreement: Coefficients comparing classification agreement

Description

classAgreement() computes several coefficents of agreement between the columns and rows of a 2-way contingency table.

Usage

classAgreement(tab, match.names=FALSE)

Arguments

tab

A 2-dimensional contingency table.

match.names

Flag whether row and columns should be matched by name.

Value

A list with components
diagPercentage of data points in the main diagonal of tab.
kappadiag corrected for agreement by chance.
randRand index.
crandRand index corrected for agreement by chance.

Details

Suppose we want to compare two classifications summarized by the contingency table $T=[t_{ij}]$ where $i,j=1,\ldots,K$ and $t_{ij}$ denotes the number of data points which are in class $i$ in the first partition and in class $j$ in the second partition. If both classifications use the same labels, then obviously the two classification agree completely if only elements in the main diagonal of the table are non-zero. On the other hand, large off-diagonal elements correspond to smaller agreement between the two classifications. If match.names is TRUE, the class labels as given by the row and column names are matched, i.e. only columns and rows with the same dimnames are used for the computation.

If the two classification do not use the same set of labels, or if identical labels can have different meaning (e.g., two outcomes of cluster analysis on the same data set), then the situation is a little bit more complicated. Let $A$ denote the number of all pairs of data points which are either put into the same cluster by both partitions or put into different clusters by both partitions. Conversely, let $D$ denote the number of all pairs of data points that are put into one cluster in one partition, but into different clusters by the other partition. Hence, the partitions disagree for all pairs $D$ and agree for all pairs $A$. We can measure the agreement by the Rand index $A/(A+D)$ which is invariant with respect to permutations of the columns or rows of $T$.

Both indices have to be corrected for agreement by chance if the sizes of the classes are not uniform.

References

J.~Cohen. A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37--46, 1960.

Lawrence Hubert and Phipps Arabie. Comparing partitions. Journal of Classification, 2, 193--218, 1985.

Examples

Run this code

## no class correlations: both kappa and crand almost zero
g1 <- sample(1:5, size=1000, replace=TRUE)
g2 <- sample(1:5, size=1000, replace=TRUE)
tab <- table(g1, g2)
classAgreement(tab)

## let pairs (g1=1,g2=1) and (g1=3,g2=3) agree better
k <- sample(1:1000, size=200)
g1[k] <- 1
g2[k] <- 1

k <- sample(1:1000, size=200)
g1[k] <- 3
g2[k] <- 3

tab <- table(g1, g2)
## both kappa and crand should be significantly larger than before
classAgreement(tab)

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