unalike: Coefficient of unalikeability
In raredd/ragree: Rater agreement

Description Usage Arguments Details Value Author(s) References See Also Examples

Function to calculate the unalikeability coefficient to quantify the amount of variability in categorical data.

unalike(x, ...)

## Default S3 method:
unalike(x, ..., method = 1L)

## S3 method for class 'matrix'
unalike(x, ...)

## S3 method for class 'data.frame'
unalike(x, id = "id", rater = "rater",
  score = "score", summary = TRUE, plot = FALSE, ...)

`x`	a vector of categorical data alternatively, an `n x r` matrix of `n` subjects by `r` raters or an `n x m` data frame of `n` subjects; when `x` is a data frame, the user must specify which columns correspond to `id`, `rater`, and `score`
`...`	additional arguments passed to or from other methods
`method`	the method for calculating the unalikeability coefficient; see details
`id, rater, score`	column names corresponding to IDs, raters, and scores
`summary`	logical; if `TRUE`, prints summary statistics for the unalikeability coefficients
`plot`	logical; if `TRUE`, prints a heat map of unalikeability coefficients

The coefficient of unalikeability describes a concept of variability for categorical variables and provides a quantitative method for its measurement. A smaller coefficient is better corresponding to less variation in the scores.

For the case of a finite number of observations (n), a finite number of categories (m) and a finite number of objects, k_i, within category i, will allow expression of the coefficient of unalikeablity as:

u = 1 - ∑ p_i ^ 2

where p_i = k_i / n.

The interpretation of u is that it represents the proportion of possible comparisons (pairings) which are unalike. Note that u includes comparisons of each response with itself.

Currently, two methods for calculating the coefficient are implemented. If method = 1, then the formula described above is used. If method = 2, then the formula described in Perry (2005).

A list containing the following:

	`$method`	agreement method
	`$ragree.name`	method type
	`$subjects`	number of subjects
	`$raters`	number of raters
	`$categories`	number of categories
	`$value`	median of all unalikeability coefficients
	`$summary`	a data frame with the summary information printed when `summary = TRUE`
	`$data`	a long data frame with all coefficients

Robert Redd rredd@jimmy.harvard.edu

Kader, GD. Variability for Categorical Variables. Journal of Statistics Education, Vol. 15, No. 2 (2007).

Perry, M. and Kader, G. Variation as Unalikeability. Teaching Statistics, Vol. 27, No. 2 (2005), pp. 58-60.

RcmdrPlugin.ISCSS::unalike

unalike(1, 2)
unalike(rep(1, 10))


## examples in Kader (2007):
l <- list(
  group1 = rep(c('A', 'B'), c(7, 3)),
  group2 = rep(c('A', 'B'), c(5, 5)),
  group3 = rep(c('A', 'B'), c(1, 9)),
  group4 = rep(c('A', 'B', 'C'), c(2, 3, 5))
)

sapply(l, unalike)


## matrix/data frames are assumed to be subjects x raters
mat <- do.call('cbind', l[1:3])
unalike(mat) ## see Kader


library('irr')
data(diagnoses)

kappam.fleiss(diagnoses)
unalike(as.matrix(diagnoses))

library('ggplot2')
unalike(as.matrix(diagnoses), plot = TRUE)


dat <- data.frame(
  id    = rep(seq.int(nrow(diagnoses)), ncol(diagnoses)),
  rater = rep(names(diagnoses), each = nrow(diagnoses)),
  score = unlist(diagnoses)
)
unalike(dat)